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1. 2 4 6 5 10 soll 2s f dsolve dift diff iqit os feathnb saath J Arame gij 0 Dig Oy 0 7 r iqttiide plot 4 3 cos t 4 3 e we Al Figure 4 5 ODE Analyzer Assistant Solve Symbolically Dialog When solving numerically or symbolically you can view a plot of the solution by clicking the Plot button e To plot the solution to a symbolic problem all conditions and parameters must be set e To customize the plot click the Plot Options button to open the Plot Options window To view the corresponding Maple commands as you solve the problem or plot the solution select the Show Maple commands check box You can control the return value of the ODE Analyzer using the On Quit Return drop down list You can select to return nothing the displayed plot the computed numeric pro cedure for numeric solutions the solution for symbolic solutions or the Maple commands needed to produce the solution values and the displayed plot 124 4 Basic Computations For more information refer to the ODEAnalyzer help page The dsolve Command The ODE Analyzer provides a point and click interface to the Maple dsolve command For ODEs or systems of ODEs the dsolve command can find e Closed form solutions e Numerical solutions e Series solutions In addition the dsolve command can find e Formal power series solutions to linear ODEs with polynomial coefficient Formal solutions to line
2. Edit Matrix Solve System The Solve the system of equations in Row Echelon Form dialog ap pears Click the buttons on the right to calculate the solution firs fin the Equations then solve for each vari able Click the Solution button to display the solution in the tutor W Solve the system of equations in Row Echelon Form Linear System of Equations id 10 145 435 43 43 7 Click the Close button to return the solution to your document For more information on linear systems and matrices see Linear Algebra page 155 76 2 Document Mode 3 Worksheet Mode The Worksheet mode of the Standard Worksheet interface 1s designed for e Interactive use through Maple commands which offers advanced functionality and cus tomized control not available using context menus or other syntax free methods e Programming using the powerful Maple language Using Worksheet mode you have access to all of the Maple features described in Chapter 1 and most of those described in Chapter 2 including e Math and Text modes e Palettes e Context menus e Assistants and tutors For information on these features see Chapter 1 Getting Started page 1 and Chapter 2 Document Mode page 61 Note Using a document block you can use all Document mode features in Worksheet mode For information on document blocks see Document Blocks page 50 Note This chapter and the following chapters except
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4. integral in terms of u Press Enter re ee Right click the output and select Solve u ig esin 2 x Solve for Variable u ee l The solution is arcsin 5x Example 6 Initial Value Problem Solve and plot the solution of the initial value problem y t 4y t 13 y t cos 2 t y 0 2 y 0 1 5 8 Clickable Math 233 Solution by ODE Analyzer Assistant The ODE Analyzer Assistant lets you solve ODEs numerically or symbolically and displays a plot of the solution 1 Enter the ODE ina blank document y 7 4 y r 13 y t cos 2 t block region l l 2 Right click the equation and select Solve DE Interactively The ODE Analyzer Assistant displays with the ODE automatically inserted To insert the initial conditions 3 In the Conditions region click Edit The Edit Conditions dialog opens In the Add Condition region with y selected in the drop down menu enter 0 in the firs text fiel to the right and 2 in the second text field Click Add Your entry should match the one shown to the right Gi ODE Analyzer Assistant IM Edit Conditions Differential Equations SS o y t 4y l 13 p t cos 2 t Conditions Parameters Solve Numerically Solve Symbolically Classify ES Add Condition Wily lat Edit Conditions Add Condition Ww at Edit Conditions y O 2 234 e 5 Mathematical Problem Solving 5 To enter the initial condition f
5. Replace the current equation with the one Solve Analytically in a Specified Interval from this example Ent ion i ple nter an expression wi aba ia ee ee 6 cos x cos x 2 0 and then 6 cos x cos x 2 0 execute the commands Notice that Find the rootsina gt Sndent Calculus Roots 15 0 2 7 specified interval 7 2 4 3 equation labels are used to reference the EN a arccos A 16 A 3 results Express the roots in gt evalf 16 floating point form 0 8410686706 2 094395103 4 188790204 17 5 442116637 Analytic Solution 1 Ctrl drag the equation vee x cos x 2 0 6 cos x cos x 2 0 to a blank docu ment block region 2 Right click the expression and select Left hand Side left hand side 6 cos x cos x 2 0 I 6 cos x cos x 2 224 e 5 Mathematical Problem Solving 3 Right click the output and select Factor FAR x PE 2 factor 2 cos x 1 3 cos x 2 Ctrl drag the firs factor to a blank document block region 2 cos x 1 lt 2 r 3 Right click and select Solve Solve Ctrl drag the second factor to a blank docu solve ment block region 3 cos x 2 gt lx arccos Right click and select Solve Solve Notice that you have not found all of the solutions as with the above methods These are all of the solutions in the interval 0 1 Example 4
6. 11 2 Writing to Files Maple supports fil formats in addition to the standard mw fil format After using Maple to perform a computation you can save the results to a fil for later processing with Maple or another program Saving Data to a File If the result of a Maple calculation is a long list or a large array of numbers you can convert it to Matrix form and write the numbers to a fil using the ExportMatrix command This command writes columns of numerical data to a file allowing you to import the numbers into another program To convert a list or a list of lists to a Matrix use the Matrix construct or For more information refer to the Matrix help page 407 408 11 Input Output and Interacting with Other Products 81 98 76 4 29 38 77 72 27 44 gt L 18 37 2 8 92 Sf ff 32 09 3 33 93 74 99 67 gt ExportMatrix matrixdata txt L If the data is a Vector or any object that can be converted to type Vector use the Ex portVector command To convert lists to Vectors use the Vector constructor For more information refer to the Vector help page gt R 3 3 1415 65 0 R 3 3 1415 65 0 11 1 gt V Fector R 3 3 1415 V 11 2 65 0 gt ExportVector vectordata txt V You can extend these routines to write more complicated data such as complex numbers or symbolic expressions For more information refer to the ExportMatrix and ExportVector h
7. 1 In the Type drop down list select Dictionary Topic 2 Inthe Target field enter a topic name Dictionary topics begin with the prefi Definition for example Definition dimensio 3 Click OK Linking to a Maplet Application To link to a Maplet application 1 In the Type drop down list select Maplet 2 In the Target field enter the local path to a fil with the maplet extension Optionally click Browse to locate the file If the Maplet application exists clicking the link launches the Maplet application If the Maplet application contains syntax errors then error messages are displayed in a pop up window When linking to a custom Maplet application the path is absolute When sharing documents that contain links to Maplet applications ensure that target Maplet applications are in the same directory 3 Click OK Note To link to a Maplet application available on a MapleNet Web page use the URL hyperlink type to link to the Web page For information on MapleNet see Embedded Components and Maplets page 385 Example For this example link the text horizontal range to the dictionary page for domain As in dicated in the section for Linking to a Dictionary Topic select Dictionary Topic in the Type drop down list and then enter Definition domai_ in the Target field 324 e 7 Creating Mathematical Documents Links to dictionary topics appear underlined and in red Result plot create a two dimensional pl
8. When you use the assume command to place another assumption on x all previous assump tions are removed gt assume x lt Q y xX X Displaying Assumptions To view the assumptions on an expression use the about com mand gt about x Originally x renamed x is assumed to be RealRange infinity Open 0 Imposing Multiple Assumptions To simultaneously impose multiple conditions on an expression specify multiple arguments in the assume calling sequence gt assume 0 lt x x lt 2 To specify additional assumptions without replacing previous assumptions use the addi tionally command The syntax of the additionally calling sequence is the same as that of the assume command gt additionally x integer about x Originally x renamed x is assumed to ber 1 The only integer in the open interval 0 2 is 1 Testing Properties To test whether an expression always satisfie a condition use the is command 144 4 Basic Computations gt assume 15 lt x 7 lt y is 100 lt xy true The following test returns false because there are values of x and y x 0 y 10 that sat isfy the assumptions but do not satisfy the relation in the is calling sequence gt assume x nonnegint 10 lt y is 10 lt x y false To test whether an expression can satisfy a condition use the coulditbe command gt coulditbe 10 lt x y true Removing Assumptions To remove all assumptions on a
9. 1 73205085075688 77293527446 Note When appropriate Maple performs floating poin computations directly using your computer s underlying hardware Sources of Error By its nature floating poin computation normally involves some error Controlling the effect of this error is the subject of active research in Numerical Analysis Some sources of error are i l e An exact quantity may not be exactly representable in decimal form 3 and 7 are ex amples e Small errors can accumulate after many arithmetic operations e Subtraction of nearly equal quantities can result in essentially no useful information For example consider the computation x sin x for x 0 gt x sin x 0000 0 No correct digits remain If however you use Maple to analyze this expression and replace this form with a representation that is more accurate for small values of x a fully accurate 10 digit result can be obtained gt taylor x sin x x gt t x 0 00001 1 666666667 10 106 4 Basic Computations For information on evaluating an expression at a point see Substituting a Value for a Subexpression page 353 For information on creating a series approximation see Series page 178 For more information on floating poin numbers refer to the floa and type floa help pages 4 3 Integer Operations In addition to the basic arithmetic operators Maple has many specialized commands for performing more
10. 64 2 Document Mode 3 Enter e Note To enter the exponential e use the expression palette or command completion To evaluate the integral and display the result inline press Ctrl Command s for Macintosh or Enter For more information see Computing with Palettes page 67 You can enter any expression using symbol names and the symbol completion list 1 Begin typing the name of the symbol diff and press the symbol completion key see Shortcut Keys by Platform page xviii diff_table Function and derivatives PDEtoois aff table expr diff_table representation of Function and derivatives DETools df table expr difFalg diffalg diffop2de differential operator DEToois dffop2de oper p lt gt Select the partial differentiation item 8 diff inline partial ae Replace the placeholder with t Use the right arrow to move out of the denomin ator Enter e as in the previous ex ample Example 2 Define a Mathematical Function Defin the function twice which doubles its input In the Expression palette click the single variable function definitio item pS Replace the placeholder f with the function name twice Press Tab to move to the next placeholder Replace the parameter placeholder a with the inde pendent variable x Press Tab 2 4 Evaluating Expressions 65 4 Replace the output placeholder y with the desired pice x g
11. Bessel Note In 1 D and 2 D Math input when accessing a help page using you do not need to include a trailing semicolon or colon Top Commands Here are a few of the most frequently used Maple commands A complete list of top level commands is available at Help Manuals Resources and more List of Commands Table 3 1 Top Commands iat eompute an indent or dt nega For symbolic summation It is used to compute a closed form for an indefinit or definit sum assume is Set variable properties and relationships between variables Similar function ality is provided by the assuming command assuming Compute the value of an expression under assumptions simplify Apply simplificatio rules to an expression Factor a polynomial 3 3 Commands 83 Type checking command In many contexts it is not necessary to know the exact value of an expression it suffice to know that an expression belongs to a broad class or group of expressions that share some common properties These classes or groups are known as types series Generalized series expansion map ssid Apply a procedure to each operand of an expression Package Commands To use a package command the calling sequence must include the package name and the command name enclosed in square brackets package commana arguments If you are frequently using the commands in a package load the package To load a package e Use the with command
12. Maximize cx subject to Ax lt b where x is the vector of problem variables 1 Defin the column vector c of the linear objective function gt with LinearAlgebra gt c Random Vector column 20 outputoptions datatype float 2 Defin the matrix A the coefficien matrix for the linear inequality constraints gt A RandomMatrix 19 20 outputoptions datatype float 3 Defin the column vector b the linear inequality constraints gt b RandomVector column 19 outputoptions datatype float 4 The QPSolve command solves quadratic programs gt Optimization LPSolve c A b maximize assume nonnegative 7 rom I 20 Vector column Data Type float 43 2673034492019 Storage rectangular Order Fortran_order This example uses a random data set to demonstrate the problem You could also read data from an external fil as Matrices and use that data For details and an example see Reading from Files page 409 Note For information on creating matrices and vectors including how to use the Matrix palette to easily create matrices see Linear Algebra page 155 For additional information on performing efficien computations refer to the Optimiza tion Computation help page MPS X File Support To import linear programs from a standard MPS X data file use the ImportMPS command 5 6 Statistics 189 Optimization Package Commands Each Optimization pac
13. al lt archyperbolic gt W Figure 5 11 Calculus 1 Differentiation Methods Tutor Tutors provide point and click interfaces to the Student package functionality To launch a tutor 1 From the Tools menu select Tutors 2 Select a subject for example Calculus Multivariate 3 Select a tutor for example Gradients Maple inserts the Student MultivariateCalculus GradientTutor calling sequence in Worksheet mode and launches the Multivariate Calculus Gradient Tutor 5 7 Teaching and Learning with Maple 199 By rotating the three dimensional plot you can show that the gradient points in the direction of greatest increase of the surface see Figure 5 12 and show the direction of the gradient vector in the x y plane by rotating the plot see Figure 5 13 Gradient File Help Multivariate Calculus Plot Window Options F e x 1 Y J 2 1 Values Atx y 2 1 srad f Display Gradient Field Plot Plot Options 1 output plot axes boxed Maple Command Gradient e 3 ix ef y 2 1 x 2 scaling unconstrained Figure 5 12 Multivariate Calculus Gradient Tutor 200 e e 5 Mathematical Problem Solving w Multivariate Calculus Gradient Ed File Help Plot Window Options F xSiiesZtye2 1 Px ey eto Values 10 Aix y 2 1 f grad 9 9 Display Gradient Field Plot Plot Options M
14. sinewave 280 6 Plots and Animations 6 9 Exporting You can export a generated plot or animation to an image in various fil formats including DXF and X3D for 3 D plots EPS GIF JPEG JPG POV Windows BMP and WMF Exporting an animation to GIF produces an animated image file The exported images can be included in presentations web pages Microsoft Word or other software To export an image 1 Right click the plot region Control click for Macintosh 2 Select Export and the fil format Alternatively 1 Click the plot 2 From the Plot menu select Export and then the fil format Maple has various plot drivers By setting the plotdevice a fil can be automatically created without returning the image to the document For more information refer to the plot device help page 6 10 Code for Color Plates Generating impressive graphics in Maple can require only a few lines of code as shown by the examples in this chapter However other graphics require many lines of code Code for the color plates is available at the Maple Application Center From the Help menu select On the Web User Resources and then Application Center To access the color plate code 1 Go to the Maple Application Center 2 In the Keyword or phrase region enter Color Plate 7 Creating Mathematical Documents Maple allows you to create powerful documents as business and education tools technical reports presentations assignments
15. 1 0 gt Fi l Calculate the volume of revolution i Siuderi Calculus FoleneOfRevolutiion 1 J 4 zap 2 Er 2 Display the floating point value using the evalf command ly eval 2 B 6952445131 3 Figure 5 16 Inserted Task Template 6 When a Task Template is inserted parameters are marked as placeholders denoted by purple font To navigate between placeholders press the Tab key After updating any parameters execute the command by pressing Enter Check for Instructions Help Page and Example Worksheet The help system provides command syntax information To access a help page l 2 From the Help menu select Maple Help In the search field enter volume of revolution and click Search The search results in clude the command help page the dictionary definition and the associated tutor help page Review the calling sequence parameters and description in the Student Calcu lus1 VolumeOfRevolution help page Copy the examples into your worksheet from the help system Edit menu select Copy Examples Close the Help Navigator 208 e e 5 Mathematical Problem Solving 6 In your document from the Edit menu select Paste The examples are pasted into your document 7 Execute the examples and examine the results To access an example worksheet 1 In the worksheet enter index examples The Example Worksheet Index opens 2 Expand the Calculus topic 3 Click the examples Ca
16. 1 Getting Started ee Dex 1 x 1 Copy Special Paste Ctrl Evaluate and Display Inline Ctrl Explore Apply a Command Assign to a Name Coefficients Collect Combine Differentiate Evaluate at a Point Factor Integrate Limit Plots Series Simplify Solve Complete Square Complex Maps Constructions Conversions Integer Functions Integral Transforms Language Conversions Optimization Sequence Sorts Units 2 D Math b n vU v v v v v v v v YV Y Y Y Y Y Y wY Y v Isolate Expression for gt Numerically Solve Numerically Solve w complex Numerically Solve From point Obtain Solutions For b Solve N Solve explicit Solve general solution Solve for Yariable b Figure 1 8 Right click the expression to see a menu of applicable operations Task Templates Cut Ctrl x Copy Ctrl C Copy full precision Paste Ctrl Style gt Line Symbol gt Point X Line gt Surface with Line Color gt Surface Transparency b Surface with Contour Glossiness gt Contour Orientation gt Hidden Lighting b AXes d Title b Scaling Constrained Manipulator b Export b Figure 1 9 Right click the plot to see a menu of plot options Task templates help you perform specifi tasks in Maple such as e performing a mathematical computation such as solving an equation symbolically or numerically or determining the Taylor approximation of a function of one variable e constructin
17. 2 From the Insert menu select Canvas A canvas with grid lines appears in the document at the insertion point The Drawing icon is available and associated context bar icons are displayed The tools include the following selection tool pencil free style drawing eraser text insert straight line rectangle rounded rectangle oval diamond alignment drawing outline drawing fill drawing linestyle and drawing canvas properties Drawing To draw with the pencil tool in the canvas 1 From the Drawing icons select the pencil icon 2 Click and drag your mouse in the canvas to draw lines Release the mouse to complete the drawing To adjust the color of drawing tools 1 From the Drawing icons select the Drawing Outline icon See Figure 7 16 2 Select one of the color swatches available or select the color wheel RGB ranges or eye dropper icon at the bottom of the dialog and customize the color to your preference 3 After selecting a new color draw on the canvas using the pencil icon and notice the new color Figure 7 16 Drawing Outline Color Icon In your document there are three plots two of which are 2 D plots that can be drawn on All of the information in the table you made in the previous section could be drawn onto the plot putting the information in a more concise layout 318 7 Creating Mathematical Documents Consider one of the plots from the table Se SS Click on the plot and notice tha
18. Canva o VIE a A ERED ES eee DE TC REET Pee wee RSET Art 318 AS C111 Tma n CS oat ati ot lait aterm adnate ionamin vol eave Labo aremeaee nue nuales 319 PONY GENS aerian rte sri hee NGA ea SHEA om a eA NG tes na Aen EG ons 320 Inserting a Hyperlink in a Document cece cc cece e cence cece eee eeeeeeeesenenes 321 Bookmark 34s c0hs ten ddntad Makes peta an a a beiadhs 324 Th EMbedded COMP OM CIS oct hd iaa ea Moiese thalnec e 326 Adding Graphical Interface Component cccccccecec ea eeeeeeneeeeeeneeenes 326 Task Template with Embedded Component cc ccc eeceeeceeeeeesen sees 327 LS DPE NM sere NO mirne mE renee ME RGM inet ee een ne a nT er ner 328 How to Use the spellcheck UUH cist ticie airtel ati oie nieh A ER 329 DELECUIMG a SUC LESON enei cuzin e RAE TEE e Ronan ERE 330 User DIC HOUNAL poesia feet Goleta e e a ict Ses 330 179 Creating Graded A Ssiommicits lt jAsme ness i atesonctens ss Lachiestumiccesiuateswunteeatn laces 331 Creatine a Questi i aatteen eree e niches bac luet send e 331 Viewing Questions mm Maple i cncscarutarsiecauwenvaviasesere tween E EE 331 Savine TSEC ONEA osha each cre Ge li pce eee ae cates leet al ie ually ween cel 331 TAO Worksheet Compatibilty ask tacts tata teemas met a e nh heutadaucs 332 Viale EE Xpression kairaa e eaaa a 333 D oe E E E E rs E O E E E E EE 333 8 2 Creating and Using Data Structures 14 ciiie tec Cotesia aint nth oaelds ee Gteeaatal 333 Expression
19. Find the Inverse Function If f x x 1 x gt 0 fin and graph the rule for f x its functional inverse We solve this problem using the following methods e Implement the Definitio Graphically page 225 Solution by Tutor page 228 5 8 Clickable Math 225 Implement the Definition Graphically The graph of the inverse function is the set of ordered pairs formed by interchanging the ordinates and abscissas 1 Ina blank document block enter Ez 1 x and press Enter 2 Right click the output and select Plots aaee W Interactive Plot Builder Select Plot Type Select Plot Type and Functions eet v Select Plot 2 D parametric plot 2 D plot 2 D polar plot 3 D conformal plot of a complex valued Function 2 D conformal plot of a complex valued Function 2 D complex plot 3 D complex plot Select Variable Purposes Ranges and Plot Options On Plot return plot command d 226 e 5 Mathematical Problem Solving In the Plot Builder Select Plot Type dia log ensure that 2 D parametric plot is se lected in the Select Plot region Adjust the domain for x to the interval 0 1 Click Plot to return the plot to the docu ment 5 8 Clickable Math 227 6 Ctrl drag the expression x 1 onto this graph Notice that the axis ranges alter 7 Ctrl drag the expression x onto this graph The resulting graph shows f x f x and the line y x 228 e 5 Mathematical
20. Integral EE Integration E O Approximate Integration Methods of Integration Applications ie T Arc Length of a Univariate Fu 0 Solids of Revolution T Surface Area fT Molume ee gt Series el S Calculus Multivariate ie 465 Calculus Vector T Convert Expression to Function A 4 5 Curve Fitting 4 4 9 Differential Equations H Document Templates H Evaluating Geometry H Integers 4 4 9 Linear Algebra Lists H Maple T A E Plots H Polynomials 4 4 Statistics 4 4 9 Transformations H 0 Units Constants and Errors ask VolumeorReyvUnivariateFcn Figure 3 4 Task Browser Sex Copy Task to Clipboard Insert Default Content Insert Minimal Content C Insert into New Worksheet Display task markers Volume of Revolution Description Calculate the volume of revolution for a solid of revolution when a function is rotated about the honzontal or vertical axis Enter the function as an expression and specify the range gt sin x cos x 1 0 ate s x 1 04 x Calculate the volume of revolution gt Student CalculusI VolumeOfRevolution 1 9 3 m 76 T Display the floating point value using the evalf command gt evalf 2 693245131 Display a plot using the output p ot option gt Student Calculus VolumeOfRevolution 1 output plot scaling constrained title For details on inserting and using task templates see Ta
21. i 3 Instructions Example Worksheets _ Applications Checkfor lt Other Ready gt Maple to Use Resources Application Center Figure 5 14 Flowchart of solving a problem Check for Existing Tools Tutor Begin by examining the Tools menu for a Tutor to a Volume of Revolution problem To access a Tutor for the Volume of Revolution 1 From the Tools menu select Tutors and then Calculus Single Variable Notice that a Volume of Revolution tutor exists 2 Click the Volume of Revolution menu item The following Maple command is entered in your document 5 7 Teaching and Learning with Maple 205 gt Student Calculus 1 VolumeOfRevolutionTutor The Volume of Revolution Tutor is displayed See Figure 5 15 Use this tutor to enter a function and an interval view and manipulate the corresponding plot and view the full Maple command associated with your entries and selections 206 5 Mathematical Problem Solving 3 Calculus 1 Volume of Revolution File Help Plot Window Enter 1 or 2 Functions and an interval Fix 14 10 cos 10 x g x a 0 b 6 Riemann sum Method Number of partitions 6 volume of the Solid 6 x 1 10 cos 10 x dx 0 1892510790 Display voume Disks Region None Line of Revolution Horizontal Vertical Distance of rotation line From coordinate axis 0 VolumeOfRevolution 1 10 cos i0 x O 6 axis h
22. ssign to a Mame Integer Factors Next Prime Test Primality More b Number Theory Functions bo Divisors be Number of Positive Divisors Number of Primes Sum of Divisors Totienkt Function Figure 3 2 Integer Context Menu In Worksheet mode you can use context menus to perform operations on 2 D Math and output 3 5 Context Menus 89 To use a context menu 1 Right click Control click for Macintosh the expression The context menu is displayed 2 From the context menu select an operation Maple inserts a new execution group containing e The calling sequence that performs the operation e The result of the operation Example Using Context Menus Determine the rational expression fraction that approximates the floating poin number 0 3463678 1 7643 1 Enter and execute the expression gt 0 3463678 1 7643 2 1106678 2 Right click Control click for Macintosh the 2 1106678 output floating poin number Copy Special Numeric Formatting Explore Apply a Command Assign to a Name Next Float Previous Float Conversions Continued Fraction Integer Functions Exact Rational Units Rational N 3 From the context menu select Conversions gt pon vert 3 3 rationa Rational The inserted calling sequence in cludes an equation label reference to the num 32270 ber you are converting 15289 Notice that an equation label reference has been used For information on equati
23. y 13 xf 13 x 13 y x yy A true Important You must insert a space character or a multiplication operator between adjacent variables names Otherwise they are interpreted as a single variable For example x does not divide the single variable xy gt divide xy x false But x divides the product of x and vy gt divide x y x divide x y x true true For information on polynomial arithmetic over finit rings and fields refer to the mod help page Sorting Terms To sort the terms of a polynomial use the sort command gt pl x x42 pli x x x4x gt sort pl x x x yx Note The sort command returns the sorted polynomial and updates the order of the terms in the polynomial The terms of p1 are sorted gt pl x x x To specify the unknowns of the polynomial and their ordering include a list of names 5 2 Algebra 151 gt sort ax x xa at b a 3 2 2 x ad t txatat x hb gt sortld X 2 xa a b x b a x ax b a By default the sort command sorts a polynomial by decreasing total degree of the terms gt pix x gt sort p2 x y x P44 gt The firs term has total degree 4 The other two terms have total degree 3 The order of the fina two terms is determined by the order of their names in the list To sort the terms by pure lexicographic order that is firs by decreasing order of the firs unknown in the list option and then by
24. 10 5 Click Plot to open the Interactive Parameter window Note To apply plot options before interactively adjusting the plot click Options to open the Plot Options window After setting the plot options click Plot to display the Interactive Parameter window 6 To adjust the numeric values use the slider 7 Click Done to place the plot in the Maple document To see the Maple syntax used to generate this plot see Maple commands from Creating Plots Interactive Plot Builder page 249 For information on customizing plots using the Interactive Plot Builder refer to Custom izing Plots Interactive Plot Builder Options page 263 Context Menu A context menu in Maple displays a list of commands to manipulate display or calculate using a Maple expression The commands in the menu depend on the type of the expression To display the context menu for a Maple expression right click Control click for Macin tosh the expression For expressions the context menu lists e 2 D or 3 D plot e 2 D or 3 D implicit plot e Interactive Plot Builder based on the expression selected When you invoke the Interactive Plot Builder through the context menu the expression automatically passes to the builder and Maple does not display the Specify Expression window 246 e 6 Plots and Animations One advantage of using the context menu is the simplicity of creating an expression using menus By using this method you do not need any k
25. 13 17 For more information on integers see Integer Operations page 106 Expanding To expand an expression e Use the expand command The expand command distributes products over sums and expands expressions within functions 350 e 8 Maple Expressions gt expand y 3 x 1 x y vytxy 3x8 yty 6x Sxy ty 3x 3y gt expand sin x y sin x cos y cos x sin y Combining To combine subexpressions in an expression e Use the combine command The combine command applies transformations that combine terms in sums products and powers into a single term gt combine sin x cos y cos x sin y sin x y Recall that a was previously assigned to represent a two dimensional array see Creating and Using Arrays page 336 1 2 gt combine x x The combine command applies only transformations that are valid for all possible values of names in the expression gt combine 4 ln x In y 4 ln x Iny To perform the operation under assumptions on the names use the assuming command For more information about assumptions see Assumptions on Variables page 142 8 3 Working with Maple Expressions 351 gt combine 4 ln x In yv assuming x gt 0 y gt 0 n x Converting To convert an expression e Use the convert command The convert command converts expressions to a new form type see Expression Types page 343 or in terms of a function For a com
26. 7 Creating Mathematical Documents plot create a two dimensional plot Calling Sequence plot f x plott x x0 x1 plotivl 2 Parameters f expression in independent variable x F independent variable x0 zl left and night endpoints of horizontal range il 72 x coordinates and y coordinates 3 Optional If necessary you can remove this style From the Edit menu select Undo Creating and Modifying Paragraph Styles You can create custom paragraph styles to apply to text or change existing paragraph styles New styles are automatically added to the styles drop down list in the context bar of your document 1 From the Format menu select Styles The Style Management dialog opens See Figure 7 4 To create a paragraph style e Click Create Paragraph Style The Paragraph Style dialog opens See Figure 7 6 e Inthe firs row of the dialog enter a style name in the blank text field To modify a paragraph style e Select a paragraph style to modify Recall that all paragraph styles are preceded by the letter P e Click Modify The Paragraph Style dialog opens with the current attributes displayed For either action continue 4 In the Units drop down menu select the units used to determine spacing and indentation Select from inches in centimeters em or points pt 5 Select the properties to use for this paragraph style such as Spacing Indent Alignment Bullets and Numbering
27. Differential ing Tools Tasks Browse GS Limits He Derivatives In the table of contents of the Task Browser 2 BeivarvesbyDetniton dialog select Calculus Differential Deriv Difference enion Guckient atives Graph f x and its Derivatives Ps Differentiation Formal Rules obo Expression Functional Operator Graph Fixi and Its Derivatives Click Insert Minimal Content at the top of the dialog to insert the task template into the Enter the function f x to be evaluated and the interval on which to plot it current document f x Interval Clear All Launch Differentiation Tutor 4 Enter the new expression x c os x in the f x Enter the function 7 x to be evaluated and the interval on which to plot it region f x a 5 Enter the interval 1 1 To insert the symbol for pi you can use command completion or Interval Zn 7 select T from the Common Symbols palette 216 5 Mathematical Problem Solving Click Launch Differentiation Tutor to launch the same tutor as in the previous solution When complete click Close A plot of the ex pression and its derivatives displays in the plot region of the inserted task template Example 2 Solve for x in a Quadratic Equation Solve for x in the equation x 7 x 1 4 x 1 x 4 We solve this problem using the following methods Solution through Equation Man
28. Display a plot of a single variable expression gt plot oy a 2 2 z Example 2 Display a plot of multiple expressions in 1 variable To display multiple expressions in a plot include the expressions in a list To enter d y i l A PR sin x and sin a dv use the Expression palette For more information see dy Palettes page 21 6 2 Creating Plots 251 sin x 1 sin x sin x arl x 7 z gt plot Fi 252 6 Plots and Animations Example 3 Display a plot of a multi variable expression gt plot3a l teinxy 20 2m y 20 28 view 0 0 5 x ry lightmodel light1 shading zgrayscale style patchnogrid grid 40 40 Example 4 Display a conformal plot A collection of specialized plotting routines is available in the plots package For access to a single command in a package use the long form of the command 6 2 Creating Plots 253 gt plots conformal 2 z 0 2 2 axes normal grid 20 20 PA CHa rT te LT Ng LE TAR ORD LE TT ALR OO CSS TAOS 3 QA Ooni SOOT Fetes wi Da Sees mere y dori 254 6 Plots and Animations Example 5 Display a plot in polar coordinates gt plots polarplot 1 4cos 4 0 0 8 1 color magenta la wA A AA X PS 6 2 Creating Plots 255 Example 6 Interactive Plotting gt plots animate plot x 3 sin xt x 0 5 t 0 10 f For more in
29. Maple contains over 200 types including CF e boolean e constant e integer e Matrix e trig 344 8 Maple Expressions e truefalse For more information and a complete list of Maple types refer to the type help page The type commands return true if the expression satisfie the type check Otherwise they return false Testing the Type of an Expression To test whether an expression is of a specifie type e Use the type command gt type sin x trig true gt type sin x cos x trig false For information on enclosing keywords in right single quotes see Delaying Evaluation page 361 Maple types are not mutually exclusive An expression can be of more than one type gt type 3 constant irue gt type 3 integer irue For information on converting an expression to a different type see Converting page 351 Testing the Type of Subexpressions To test whether an expression has a subexpression of a specifie type e Use the hastype command gt hastype sin x cos x trig true 8 3 Working with Maple Expressions 345 Testing for a Subexpression To test whether an expression contains an instance of a specifie subexpression e Use the has command gt has sin x y x true gt has sin x y x y true gt has sin x y sin x false The has command searches the structure of the expression for an exactly matching subex pression For example the f
30. Maple executes the statement se quence in the else clause gt x 12 gt if not type x integer then printf a is not an integer x elif x gt 10 then printf a is an integer with more than one digit x elif x gt 0 then printf a is an integer with one digit x else printf ta is a negative integer x end if 12 is a negative integer For more information on the if statement refer to the if help page 9 2 Flow Control 369 Repetition for Statement Using repetition statements you can repeatedly execute a statement sequence You can repeat the statements in three ways e Until a counter variable value exceeds a limit for from loop e For each operand of an expression for in loop e Until a boolean condition does not hold while loop for from Loop The for from loop statement repeats a statement sequence until a counter variable value exceeds a limit Syntax The for from loop has the following syntax for counter from initial by increment to final do statement sequence end do The behavior of the for from loop is 1 Assign the initial value to the name counter 2 Compare the value of counter to the value of fina If the counter value exceeds the fina value exit the loop This is the Joop bound test 3 Execute the statement sequence 4 Increment the counter value by the value of increment 5 Repeat steps 2 to 4 until Maple exits the loop The
31. Plot GIF Postscript Not ex Not ex Not ex Notex Static im Static im fil ported ported ported ported age age Animation Animated Not expor Not ex Not ex Notex Notex Notex Static im GIF ted ported ported ported ported ported j age Hidden Not expor Not expor Not ex Not ex Not ex Notex Notex Notexpor content ted ted ported ported ported ported ported ted d ed ed Manually Not suppor Not suppor Not sup Not sup Not sup Not sup RTF Main inserted te t ported ported ported ported page tained page break break ob ject Hyperlink Links to Plain text Plain Plain Plain Plain Plain text Plain text help pages text text text text become plain text Links to documents are renamed and conver ted to HTML links Embedded GIF Not expor Not ex Not ex Not ex Notex Static im Static im image or t ported ported ported ported age age sketch out put Spread HTML table LaTeX Not ex Not ex Not ex Notex RTF Static im sheet tables ported ported ported ported table age 11 4 Exporting to Other Formats 415 Content HTML LaTeX Maple Maplet Maple Plain PDF Input Applica Text Text Format tion Document Approxim LaTeX en Not ex Not ex Notex Not ex Main style ated by vironments ported ported ported ported tained HTML style and sec attributes tions LaTeX 2e macro calls MapleNet Overview of Map
32. The package supports a wide range of common statistical tasks including quantitative and graphical data analysis simulation and curve fitting In addition to standard data analysis tools the Statistics package provides a wide range of symbolic and numeric tools for computing with random variables The package supports over 35 major probability distributions and can be extended to include new distributions 190 5 Mathematical Problem Solving Probability Distributions and Random Variables The Statistics package supports Continuous distributions which are define along the real line by probability density functions Maple supports many continuous distributions including the normal Student t Laplace and logistic distributions Discrete distributions which have nonzero probability only at discrete points A discrete distribution is define by a probability function Maple supports many discrete distribu tions including the Bernoulli geometric and Poisson distributions For a complete list of distributions refer to the Statistics Distributions help page You can defin random variables by specifying a distribution in a call to the RandomVari able command gt with Statistics gt X RandomVariable Poisson A Find the probability distribution function for X For information on statistics computations see Statistical Computations page 191 gt PDF X t yee Di t k Adding Custom Distributi
33. To see the Maple syntax used to generate this plot see Maple Syntax for Creating Animations Interactive Plot Builder Example page 272 The plots animate Command You can also use the animate command in the plots package to generate animations 272 6 Plots and Animations Table 6 5 The animate Command animate plotcommand plotarguments t a b animate plotcommand plotarguments t L plotcommand Maple procedure that generates a 2 D or 3 D plot e plotarguments arguments to the plot command e t a b name and range of the animation parameter e t L name and list of real or complex constants To access the command use the short form name after invoking the with plots command gt with plots Maple Syntax for Creating Animations Interactive Plot Builder Example The following example shows the plotting command returned by the example in Interactive Plot Builder page 271 6 6 Creating Animations 273 anf HA I 6 6 y 6 6 style patchnogrid lightmodel light3 shading zgrayscale scaling constrained i 1 30 gt animate plot3d 274 6 Plots and Animations Animate a 2 D plot T 4 21 frames so gt animate polarplot 5 cos 2 6 0 0 t f 0 783540 For more information on the animate command refer to the plots animate help page The plot3d viewpoint Command You can use the viewpoint command to create an animation in wh
34. Unts SI Palete sinire E A E a ae eats 130 Figure 5 1 Sorting a Polynomial Using a Context Menu ccecececec seen ee eeees 152 Powe 2 Mite PE Menn a R 157 Figure 5 32 Matrix Palette Choosing the Size oyrini aan an a EEEE 158 Figure 5 4 Insert Matix Or Insert Vector sereine a ai E E N sesame 159 Feurco oS Matr BOWS T irean a AEN TOR 161 Xi xii List of Figures Figure 5 6 Computing the Infinit Norm of a Matrix ccccccececeneeeeeeeeeeeeeeaes 169 Figure 5 7 Directional Derivative Tutor zs seesieia wssaawae operate menkauda cout uuiawaeeiwie asked 177 Figure 5 8 Optimization A Ssistait rasni e a a EE 185 Figure 5 9 Optimization Assistant Plotter Window cccccceeeeeeeeeeeeeeeenenenees 187 Figure 5 10 Calculus 1 Derivatives Tutor wisi viadscntaredinticeahnot bhonthelt boehicub eondeebicind 197 Figure 5 11 Calculus 1 Differentiation Methods Tutor cccecececececeeeeeeeees 198 Figure 5 12 Multivariate Calculus Gradient Tutor ccccecececec eee eeneeenenen es 199 Figure 5 13 Multivariate Calculus Gradient Tutor Showing x y Plane 200 Figure 5 14 Flowchart of solving a problem c cece cscs e ce ec ec eee eeeeeeeeeeenenenes 204 Figure 5 15 Volume of Revolution Tutor cccc ccc ccc cece eee eeeeec ee eeeeeeeeneeeen ones 206 Figure 5 1 6 gt lnserted Task Template eiei a a dale 207 Figure Sk Example Worksheoleisniinn a a sawed nh E 2
35. gt solve x y 2x y 0l r Z y ii r E ly l For more information see Solving Equations and Inequations page 111 For more information on sets and lists refer to the set help page Arrays Conceptually the Array data structure is a generalized list Each element has an index that you can use to access it The two important differences are e The indices can be any integers e The dimension can be greater than one Creating and Using Arrays To defin an Array use the Array constructor Standard Array constructor arguments are e Expression sequences of ranges Specify the indices for each dimension e Nested lists Specify the contents For example gt a Array 1 3 1 3 1 2 3 4 5 6 7 8 9 123 a 456 789 gt b Array 1 2 2 5 1 2 4 9 6 3 7 1 9 2 5 5 2 4 1 7 b Array 1 2 2 5 1 2 1 2 1 3 4 9 1 4 6 3 1 5 7 1 2 2 9 2 2 3 5 5 2 4 2 4 2 5 1 7 datatype anything storage rectangular order Fortran_order To access entries in an Array use either square bracket or round bracket notation 8 2 Creating and Using Data Structures 337 Square bracket notation respects the actual index of an Array even when the index does not start at 1 gt al 1 1 gt al 2 3 6 gt bf 2 3 5 3 gt b 1 1 Error Array index out of range Round bracket indexing normalizes the dimensions to begin at 1 Since this method i
36. page 118 Multiple Equations To solve multiple equations specify them as a set For more inform ation see Creating and Using Data Structures page 333 The fsolve command solves for all unknowns gt fsolve In x l xy e x 3 396618823 y 0 4719962637 Univariate Polynomial Equations In general the fsolve command find one real solution However for a univariate polynomial equation the fsolve command returns all real roots l 2 gt equation3 y 3y 2y l 4 4 Solving Equations 117 gt fsolve equation3 y 0 3365322739 1 940392664 Controlling the Number of Solutions To limit the number of roots returned specify the maxsols option gt fsolve equation3 y maxsols 1 0 3365322739 To fin additional solutions to a general equation use the avoid option to ignore known solutions gt fsolve equation 2 z avoid z 4 8 2 498755 763 Complex Solutions To search for a complex solution or fin all complex and real roots for a univariate polynomial specify the complex option for the fsolve command gt fsolve equations y complex 1 13846246879373 0 485062494059435 I 1 13846246879373 0 485062494059435 I 0 336532273926790 1 94039266366067 If the fsolve command does not fin any solutions it is recommended that you specify a range in which to search for solutions or specify an initial value Range To search for a solution in a range specify the range in the cal
37. proc x sqrt a 2 x end proc gt f 1 assuming a gt 0 y ES gt assume a gt 0 f1 a 1 For more information on the assuming command refer to the assuming help page 146 4 Basic Computations 5 Mathematical Problem Solving This chapter focuses on solving problems in specifi mathematical disciplines The areas described below are not all that Maple provides but represent the most commonly used packages Examples are provided to teach you how to use the different methods of calculation available in Maple including tutors assistants commands task templates plotting and context menus The examples in this chapter assume knowledge of entering commands and mathematical symbols For information see Entering Expressions page 18 For information on basic computations including integer operations and solving equations see Basic Computations page 101 5 1 In This Chapter Algebra page 148 Performing algebra computa Polynomial Algebra tions Linear Algebra page 155 Performing linear al Creating Matrices and Vectors gebra computations e Accessing Entries in Matrices and Vectors Linear Algebra Computations Student LinearAlgebra Package Calculus page 172 Performing calculus compu Limits tations Differentiation Series Integration Differential Equations Calculus Packages Optimization page 184 Performing optimization Point and Click Interface computations using the Optimization packag
38. task template 40 task templates 91 106 127 155 172 taylor command 178 Taylor series 178 tcoeff command 154 Teacher Resource Center 59 teachers portal for 195 teaching with Maple 207 Technical Support access 60 temperature conversion 129 Text Area component 387 text fiel embedding 326 Text mode 19 text regions 92 tilde 115 143 358 to clause 369 excluding 369 Toggle Button component 387 Tolerances package 138 toolboxes Global Optimization 184 Tools menu assistants 32 Assistants and Tutors 90 Tasks 90 topic search 55 Torsion command 183 436 Index total degree 151 transparency of 3 D plots 267 transpose matrices and vectors 168 true 366 tutorials help system 55 Tutorials 57 Tutors 195 196 Derivatives 196 Differentiation Methods 197 Directional Derivative 176 Gradient 198 Linear System Solving 74 using 37 tutors accessing 37 type command 344 types 142 343 converting 351 series 179 testing 344 subexpressions 344 typesetting rule assistant 298 U unapply command 119 unassign command 94 unassigning names 94 362 uncertainty 138 quantities with 138 underline format 283 unevaluation quotes 94 361 union of sets 335 Unit Converter Assistant 351 units 72 127 351 adding to expressions 72 applying to expression 130 computing with 131 context 128 converting between 128 environment 131 evaluating with 73 in 1 D Math 131 ins
39. the mod operator uses positive representation modp command Symmetric representation is available using the mods command gt modp 27 4 gt mods 27 4 For information on setting symmetric representation as the default refer to the mod help page The modular arithmetic operators are listed in Table 4 2 Table 4 2 Modular Arithmetic Operators _ ae ss Multiplication displays in 2 D Math as Multiplicative inverse displays in 2 D Math as a su perscript 110 4 Basic Computations Operation SSS Operator Example O 4 Division displays in 2 D Math as A Exponentiation To enter a caret in 2 D Math enter a backslash character followed by a caret that is For information on solving an equation modulo an integer see Integer Equations in a Finite Field page 125 The mod operator also supports polynomial and matrix arithmetic over finit rings and fields For more information refer to the mod help page Gaussian Integers Gaussian integers are complex numbers in which the real and imaginary parts are integers The GaussInt package contains commands that perform Gaussian integer operations The GlIfactor command returns the Gaussian integer factorization gt GaussInt Glfactor 173 16 I 1 21 41 661 In Maple complex numbers are represented as a b I where the uppercase I represents the imaginary unit J 1 You can also enter the imaginary unit using the following two
40. univariate function using a Riemann sum or a Newton Cotes method Enter the function as an expression x42 1 Specify the range of integration and the method of approximation and then approximate the integral gt Student Calculus 1 Approximatelnt 1 x 0 2 z method trapezoid 100 4 6722 2 gt E j gt Alternatively you can use the Approximate Integrals tutor a point and click interface There are two ways to launch this tutor From the Tools menu select Tutors Calculus Single Variable and then Approximate Integrals e From the Tools menu select Tasks and then Browse The Browse Tasks dialog opens and displays the list of tasks The tasks are sorted by subject to help you quickly fin the desired task In the Browse Tasks dialog you can view tasks without inserting them into your document 42 1 Getting Started Inserting a Task into the Document To insert a task into your document 1 Select the Insert into New Worksheet check box to insert the task into a new document 2 Click one of the insert buttons e Click the Insert Default Content button Maple inserts the default content The default content level is set using the Options dialog For instructions see the usingtasks help page e Click the Insert Minimal Content button Maple inserts only the commands and embed ded components for example a button to launch the related assistant or tutor e Click the Copy Task
41. which displays in 2 D Math as The noncommutative matrix and vector multiplication operator is the period e There is no division operator for matrix algebra You can construct the inverse of a matrix using the exponent 1 Table 5 5 lists the basic matrix operators 93 43 19 37 48 20 19 37 gt B C 23 6 Table 5 5 Matrix and Vector Arithmetic Operators 5 3 Linear Algebra 167 Subtraction Multiplication 1116 516 228 444 Exponentiation A 986548 613868 271244 187092 37 __5 1396 349 19 12 1396 349 You can specify scalar multiplication explicitly by entering which displays in 2 D Math as In 2 D Math you can also implicitly multiply a scalar and a matrix or vector by placing a space character between them In some cases the space character is optional For example Maple interprets a number followed by a name as an implicit multiplication Scalar Multiplication In 2 D Math exponents display as superscripts A few additional matrix and vector operators are listed in Table 5 6 Defin two column vectors 168 5 Mathematical Problem Solving gt d lt 1 2 3 gt e lt 4 5 6 gt Table 5 6 Select Matrix and Vector Operators Hermitian Transpose Cross Product gt with LinearAlgebra 3 D vect l 3 D vectors only gt d amp xe Exponential operators display in 2 D Math as superscripts After loading the LinearAlgebra pac
42. 1 15 19374 871 For more information on writing procedures including options and local and global variables refer to the procedure help page Procedure Return Values When you run a procedure Maple returns only the last statement result value computed Maple does not return the output for each statement in the procedure It is irrelevant whether you use semicolons or colons as statement separators gt p proc a b a b a b end proc o Oil 2 380 9 Basic Programming Displaying Procedure Definitions Unlike simple Maple objects you cannot display the value of a procedure by entering its name gt geometric mean geometric_mean You must evaluate the name of the procedure using the print or eval command gt print geometric mean proc x y sqrt x y end proc Displaying Maple Library Procedure Definitions Maple procedure definition are a valuable learning tool To learn how to program in Maple it is recommended that you examine the procedures available in the Maple library By default the print command returns only the proc and end proc statements and if present the description field of a Maple procedure gt print lcm proc a b end proc To display a Maple library procedure definition firs set the value of the interface verb oseproc option to 2 Then re execute the print calling sequence gt interface verboseproc 2 9 4 Procedures 381 gt print lcm proc
43. 144 For more information on the VectorCalculus package including a complete list of com mands refer to the VectorCalculus help page To fin other calculus packages such as VariationalCalculus refer to the index package help page Student Calculus Packages The Student package contains subpackages that help instructors teach concepts and allow students to visualize and explore ideas These subpackages also contain computational 184 5 Mathematical Problem Solving commands The Student calculus subpackages include Calculus1 MultivariateCalculus and VectorCalculus The Student VectorCalculus package provides a simple interface to a limited subset of the functionality available in the VectorCalculus package For information on using Maple as a teaching and learning tool and some computational examples see Teaching and Learning with Maple page 194 5 5 Optimization Using the Optimization package you can numerically solve optimization problems The package uses fast Numerical Algorithms Group NAG algorithms to minimize or maximize an objective function The Optimization package solves constrained and unconstrained problems e Linear programs e Quadratic programs e Nonlinear programs e Linear and nonlinear least squares problems The Optimization package contains local solvers In addition for univariate finitely bounde nonlinear programs with no other constraints you can compute global solutions using the NLPSol
44. 4 4 y 4 4 filled true numpoints 750 Multiple Plots in the Same Plot Region List of Expressions To display multiple expressions in the same plot region enter the expressions in a list data structure To distinguish the surfaces apply different shading options styles or colors to each surface 262 6 Plots and Animations gt plot3d cos 5 x co0s 5y 2 3 y 4 x 2 2 y 1 1 shading zgrayscale none color default grey style patchnogrid patch lightmodeFlight3 transparenc 0 1 The display Command To display different types of plots in the same plot region use the display command in the plots package This example plots a curve over a hill with the shadow of the curve projected onto the hill gt z 10 7 y A eb 9 gt hill plot3d z x 2 2 y 2 5 2 5 shading zhue style patchnogrid lightmodel light3 orientation 125 60 gt xt cos f gt yt 2sin f Maple can draw curves in three dimensional space 6 3 Customizing Plots 263 gt curve spacecurve xt yt 10 t 0 10 color red thickness 2 gt zt subs x xt y yt z gt shadow spacecurve xt yt zt t z 2 color black thickness 2 gt display hill curve shadow 6 3 Customizing Plots Maple provides many plot options to display the most aesthetically pleasing illustrative results Plot options include line s
45. 7 Creating Mathematical Documents e Row insertion can be above or below the marker or selection In your table add a third column on the right to display the plots of these expressions Add the heading and insert a blank plot region in each cell below it by selecting Insert Plot 2 D or 3 D for the second expression Then Ctrl drag Control drag for Macintosh each expression in the row into its plot region to display it For details on this procedure see Plots and Animations page 237 Resize the plots and table as desired 5x cos wx we o s5 sin wx ei 8 sin x cos x Deleting Rows and Columns With deleting operations using the Delete key the Delete Table Contents dialog opens allowing you to specify the desired behavior For example you can delete the selected rows or delete the contents of the selected cells See Figure 7 11 7 4 Tables 307 Delete Table Contents Delete Cell Contents Figure 7 11 Delete Table Contents Verificatio Dialog Pasting Pasting a table subselection into a table may result in the creation of additional rows or columns overwriting existing cell content or the insertion of a subtable within the active table cell When there is a choice the Table Paste Mode dialog opens allowing you to choose See Figure 7 12 Table Paste Mode EQ LS eae Replace cell contents Figure 7 12 Table Paste Mode Selection Dialog Merging Cells To merge adjac
46. 97 Equation Manipulator 36 216 equations solving 111 for real solutions 141 numerically 116 symbolically 113 Index 425 transcendental 115 errors quantities with 138 Euclidean algorithm 155 eval command 354 380 evalb command 357 evalc command 357 evalf command 104 115 136 139 356 with Int command 181 with Limit command 173 evaln command 361 evaluation boolean expressions 357 complex expressions 357 delaying 361 levels of 360 Maple expressions 353 of expression at a point 353 output below 65 output inline 65 68 updated computations 66 exact computation 103 numbers 102 quantities converting to floating point 104 example worksheets copy 56 execution group 79 execution groups 18 expand command 349 document block 301 execution group 301 series 178 Exploration Assistant 43 exponents entering 6 export 381 to HTML 412 to LaTeX 412 to Maple input 413 to Maple T A 416 426 Index to Maple text 413 to Maplet application 413 to other formats 415 to PDF 413 to plain text 413 to Rich Text Format 413 worksheets 412 exporting embedded components 388 expression sequences 113 334 creating 375 expressions 63 333 adding 375 evaluating 353 manipulating 348 multiplying 375 right click 40 versus functional operators 340 F factor integers 106 polynomials 154 QR factorization 170 factor command 154 349 factored
47. A You can use Maple to create graded questions for use in Maple T A For information on creating and testing questions see Creating Graded Assignments page 331 Using the Maple T A export feature you can create and test Maple T A content To export the document 1 From the File menu select Export As 2 Inthe Export As dialog specify a filenam and the Maple T A zip fil type The zip fil containing your questions and assignment can be uploaded to Maple T A as a course module Any document content outside Maple T A sections indicated by green section markers is ignored by the export process For more details refer to the exporttoMapleTA help page 11 5 Connectivity Translating Maple Code To Other Programming Languages Code Generation The CodeGeneration package is a collection of commands and subpackages that enable the translation of Maple code to other programming languages Languages currently supported include C C Fortran 77 Java MATLAB and Visual Basic For details on Code Generation refer to the CodeGeneration help page Accessing External Products from Maple External Calling External calling allows you to use compiled C C Fortran 77 or Java code in Maple Functions written in these languages can be linked and used as if they were Maple procedures With external calling you can use pre written optimized algorithms without the need to translate them into Maple commands Access to the NAG library
48. Axis range to Pi to Pi and then click Plot 212 e 5 Mathematical Problem Solving Add the firs and second derivatives to the plot 10 Select and then Ctrl drag the derivative of the expression onto the plot region Do the same for the second derivative Enhance the plot by adding a legend using context menus 11 Right click in the plot region and select Le xcos x Curve 2 gend Show Legend 12 In the legend double click Curve 1 Notice that the Text icon is selected in the toolbar Delete the text and select the Math icon in the toolbar 5 This allows you to enter 2 D Math in a text region Enter the original expression x cos x 13 Repeat for Curve 2 and Curve 3 5 8 Clickable Math 213 Add a title 14 Right click in the plot region and select Title Add Title 15 In the legend replace the text New title with the text Plot the expression 16 Click the Math icon and enter the expression x cos x Click the Text icon once again and enter and its derivatives a CHS cos x xsin x 2 sin x xcos x Solution by Tutor The Student Calculus 1 package contains a tutor called Derivatives which displays a plot of the expression along with its derivatives In this example we solve the same problem as previously using this tutor Load the Student Calculus 1 package Loading Student Calculus1 From the Tools menu select Load Package Student C
49. Components of an Expression The components of an expression are called its operands To count the number of operands in an expression e Use the nops command For example construct a list of solutions to an equation 2 P gt solutions solve 6 xX x 7 x solutions 1 119 l Iy 119 Using the nops command count the number of solutions gt nops solutions 3 For more information on the nops command and operands refer to the nops help page Indeterminates To fin the indeterminates of an expression e Use the indets command The indets command returns the indeterminates as a set Because the expression is expected to be rational functions such as sin x f x and sqrt x are considered to be indeterminate 348 e 8 Maple Expressions gt indets 3 2 x sin J 1 y x y y 1 y sin y I y To return all subexpressions of a particular type specify the type as the second argument For information on types see Testing the Type of an Expression page 344 gt indets 3 7 x sin 1 y radical 1 y To test whether an expressions has subexpressions of a specifi type without returning them use the has command For more information see Testing for a Subexpression page 345 Manipulating Expressions This section introduces the most commonly used manipulation commands For additional manipulation commands see terative Commands page 374 Simplifying To simplify an expressio
50. Example Determine a basis for the space spanned by the set of vectors 2 13 15 7 2 13 5 4 9 Express the vector 25 4 9 with respect to this basis 5 3 Linear Algebra 171 gt with LinearAlgebra gt vyl lt 2 15 15 gt v2 lt 7 2 13 gt v3 lt 5 4 9 gt Find a basis for the vector space spanned by these vectors and then construct a matrix from the basis vectors gt basis Matrix Basis vl v2 v3 2 7 5 basis 13 2 4 15 13 9 To express 25 4 9 in this basis use the LinearSolve command gt LinearSolve basis lt 25 4 9 gt 170 9 _ 285 9 786 9 Numeric Computations You can very efficient perform computations on large matrices and vectors that contain floating poin data using the built in library of numeric linear algebra routines Some of these routines are provided by the Numerical Algorithms Group NAG Maple also contains portions of the CLAPACK and optimized ATLAS libraries For information on performing efficien numeric computations using the LinearAlgebra package refer to the EfficientLinearAlgebr help page See also Creating Matrices and Vectors with Specifi Properties page 162 and Reading from Files page 409 Student LinearAlgebra Package The Student package contains subpackages that help instructors teach concepts and allow students to visualize and explore ideas These subpackages also contain computational commands 1
51. Executable standard Executable Maple notation This is also re math notation This is also referred to as 2 D ferred to as 1 D Math Input or Maple Input Math Input gt int x 2 2 x 1 x gt Fs 2x ldx l 3 3 i 3 xX x x z x x x Access from the Insert 2 D Math menu Access from the Insert Maple Input menu When using 2 D Math the Math mode icon is When entering Maple Input or text in a text region highlighted in the toolbar MA the Text mode icon is highlighted in the toolbar Math In Document Mode or a document block input In Document Mode or a document block input is entered in a document block with a slanted is entered with a vertical cursor as plain text Cursor 2 lt l lt Enter some text In Worksheet Mode input is made at an input In Worksheet Mode input is made at an input prompt with a slanted cursor gt prompt with a vertical cursor gt l To convert a 2 D Math expression to 1 D Math To convert a 1 D Math expression to 2 D Math right click the expression Command click right click the expression Command click Macintosh and select 2 D Math Convert To Macintosh and select Convert To 2 D Math 1 D Math Input Input No termination symbol is required All input must end with a semi colon ora colon Palettes make entering expressions in familiar Using palettes while in 1 D Math teaches you the notation easier than entering foreign s
52. FPS system the foot pound and second are used to measure the dimensions of length mass and time The unit of speed is the foot second In SI the meter kilogram and second are used to measure the dimensions of length mass and time The units of speed magnetic flux and power are the meter second weber and watt respect ively Unit Conversions To convert a value measured in a unit to the corresponding value in a different unit use the Units Calculator e From the Tools Assistants menu select Units Calculator The Units Calculator application Figure 4 6 opens 4 5 Units Scientifi Constants and Uncertainty 129 Manitesolt Units Calculator Convert between over 500 units of measurement See Units help index for details First select a dimension from the drop down box Then select the units to convert from and to Click the Perform Umit Conversion button The Convert Back button converts in the opposite direction Convert Result 2 831684659 cubic Feet Ft ka cubic meters m 3 ne From io Dimension Ferform Unik Conversion Convert Back Figure 4 6 Units Calculator Assistant To perform a conversion 1 In the Convert text field enter the numeric value to convert 2 In the Dimension drop down list select the dimensions of the unit 3 In the From and To drop down lists select the original unit and the unit to which to convert 4 Click Perform Unit Conversion The same
53. Fitting Assistant Enter a data sample and use the Curve Fitting Assistant to fin the best approximation of a function to fi the data 1 From the Tools menu select Assistants Curve Fitting The firs dialog in the Curve Fitting Assistant appears 2 Enter data as Independent Values and De pendent Values Alternatively you could import a fil containing data If you have more data than the space provided click the Next Page button for more space For this example enter the data as shown Ed Curve Fitting Assistant Enter data points below Independent Values x Dependent Values f x Current Page 1 Previous Page Next Page Fit Cear Import Help Cancel Ei Curve Fitting Assistant Enter data points below Independent Values x Dependent Values f x 0 176777 0 044194 0 0 44194 0 176777 0 397748 707107 1 104854 next Page _ Ge Gee Got Gea Gemet Current Page 1 1 4 Point and Click Interaction 35 3 Once you have entered the data click the Fit Tumm button The second dialog of the Curve Fit ting Assistant appears In this dialog you can plot the data and sev eral types of interpolations including Polyno mial Spline and Least Squares For ex ample click the Plot button in the Polynomi al Interpolation section The polynomial is plotted with the data and the interpolating function is displayed below You can choose to return either the interpol at
54. Graphical Interface Components You can remove an embedded component by e Using the Delete key e Using the Backspace key e Placing the cursor at the component and selecting from the document menu Edit Delete Element Integrating Components into a Document Use embedded components to display information from calculations obtain input from a reader or perform calculations at the click of a button all without your readers having an understanding of Maple commands They can be entered in any part of a Maple document including a document block or table For details on each component see its help page This simple example inserts a slider with a label that indicates the current value of the slider 1 Place the cursor in the location where the embedded component is to be inserted 2 In the Components palette click the Slider item A slider is inserted into the document 3 In the Components palette click the Label item A label is inserted next to the slider pi Label 4 Right click Control click for Macintosh the label component Select Component Properties The Label Properties dialog opens See Figure 10 2 10 3 Creating Embedded Components 391 Label Properties Slider Properties Name SliderLabel Name Slider1 Tooltip Caption Label Value at Lowest Position Tooltip Value at Highest Position Image none selected A Current Position Spacing of Major Tick Marks Spacing of Minor Tick
55. Launch the Interactive Plot Builder and enter an expression 1 Add the expression 1 4 cos 4 theta Change the x axis range 2 In the Select Plot Type window a With 2 D polar plot selected change the Angle of theta to 0 8 Pi In the Plot Options window 3 From the Color group box select Magenta Plot the expression 4 Click Plot To see the Maple syntax used to generate this plot see Maple commands from Creating Plots Interactive Plot Builder page 249 244 6 Plots and Animations Example 6 Interactive Plotting Using the Interactive Plot Builder you can plot an expression with several of its variables set to numeric values The Interactive Parameter window allows you to interactively adjust these numeric values within specifie ranges to observe their effect To access this window enter an expression with two or more variables and select Interactive Plot with x parameter from the Select Plot Type and Functions drop down menu Interactive Parameter Maplet File Help Plot Window plot sin 5 000000000 x x 2 6 x 2 Pi 2 Pi labels x Figure 6 1 Interactive Parameter Window Launch the Interactive Plot Builder and enter an expression 1 Add the expression x 3 sin x t 6 2 Creating Plots 245 In the Select Plot Type window 2 From the Select Plot group box select Interactive Plot with 1 parameter 3 Change the range of the x axis to 0 2 Pi 4 Change the t range to 0
56. Options e The animate Command Options Exporting page 280 Methods for exporting plots Saving Plots to File Formats Code for Color Plates page 280 Information on Accessing Code for the Color Plates color plates 6 2 Creating Plots Maple offers several methods to easily plot an expression These methods include e The Interactive Plot Builder e Context menus e Dragging to a plot region e Commands Each method offers a unique set of advantages The method you use depends on the type of plot to display as well as your personal preferences Interactive Plot Builder The Interactive Plot Builder is a point and click interface to the Maple plotting function ality The interface displays plot types based on the expression you specify The available plot types include plots interactive plots animations or interactive animations Depending on the plot type you select you can create a e 2 D 3 D plot e 2 D polar plot e 2 D 3 D conformal plot of a complex valued function e 2 D 3 D complex plot e 2 D density plot e 2 D gradient vector fiel plot e 2 D implicit plot 6 2 Creating Plots 239 Using the Interactive Plot Builder you can 1 Specify the plotting domain before you display the graph 2 Specify the endpoints of the graph as symbolic such as Pi or sqrt 2 3 Select different kinds of graphs such as animations or interactive plots with slider control of a parameter that is customize and display a pl
57. Options window and return the plot command syntax to the document 4 Click Command Display the actual plot 5 Execute the inserted command to display the plot by using the context menu item Evaluate gt plots interactive By default Maple displays each plot in a plot region using a different color You can also apply a line style such as solid dashed or dotted for each expression in the graph For more information refer to the plot options help page To see the Maple syntax used to generate this plot see Maple commands from Creating Plots Interactive Plot Builder page 249 Example 3 Display a plot of a multi variate expression Maple can display three dimensional plots and offers numerous plot options such as light models surface styles and shadings to allow you to customize the plot Launch the Interactive Plot Builder and enter an expression 1 Add the expression 1 sin x y x 2 y 2 In the Select Plot Type window 2 Notice the available plot types for an expression with 2 variables as well as the plot objects for each type 3 Click Options In the Plot Options window 4 From the Variables column at the top of the dialog change the Range from fiel to 0 0 05 5 From the Label column enter z 6 From the Style group box select surface 7 From the Color group box in the Light Model drop down menu select green red 8 From the Color group box in the Shading drop down menu select z grayscal
58. P packages 81 accessing commands 47 definition 45 help 53 loading 83 top 86 unloading 84 page break 286 page headers and footers 296 palette custom 28 Snippets 28 palettes 63 67 87 354 categories 23 Components 389 favorites 21 managing 24 Matrix 156 162 overview 21 symbol recognition 27 Units 72 130 paragraph styles creating 292 description 287 parameters 379 parametric solutions 116 partial derivative entering 63 partial differential equations solving 124 paste 283 examples 56 PDEs 124 pdsolve command 124 pencil sketch pad 317 Physics package description 85 pie chart 192 piecewise command 190 Planck constant 134 Plot Builder description 36 plot command 179 Plot component 386 Index 431 plot3d command 341 plots analyzing 269 pan 269 point probe 269 rotate 269 scale 269 code for color plates 280 creating 261 context menu 245 displaying multiple plots 261 insert plot 248 Interactive Plot Builder 238 plot command 249 plot3d command 249 plots package 257 creating animations animate command 271 Interactive Plot Builder 271 plot3d viewpoint command 274 customizing 267 context menu 264 Interactive Plot Builder 263 plot options 267 plot3d options 267 customizing animations 279 command line options 278 context menu 277 Interactive Plot Builder 277 data 270 exporting 280 functional operators 341 gradient 200 line integra
59. Pel Figure 4 8 Units SI Palette To insert a unit Ina Units palette click a unit symbol 4 5 Units Scientifi Constants and Uncertainty 131 gt 3 ft 3 ft To insert a unit that is unavailable in the palettes 1 In a Units palette click the unit symbol Lz Maple inserts a Unit object with the placeholder selected 2 In the placeholder enter the unit name or symbol For example to enter 0 01 standard the default context miles you can specify the unit name mile or symbol mi gt 0 01 milel 0 01 mi The context of a unit is displayed only if it is not the default context Important In 1 D Math input the quantity and unit entered using the top level Unit command are a product not a single entity The following calling sequences defin different expressions gt 1 Unit m 2 Unit s gt 1 Unit m 2 Unit s 1 m 1 2 sl gt Im s Some units support prefixe For more information refer to the Units prefixe help page gt 1 5 kms 1 5 km Performing Computations with Units In the default Maple environment you cannot perform computations with quantities that have units You can perform only unit conversions For more information about the default environment refer to the Units default help page To compute with expressions that have units you must load a Units environment Natural or Standard It is recommended that you use the Standard environment gt w
60. Popups Smart Popups are menus that are invoked when you select an output equation expression or a subexpression With Smart Popups you can e select operations to apply to just one part of your equation or mathematical expression leaving the rest unchanged e Preview the result of the operation before going ahead e Explore your expression to deepen your understanding of the problem e Easily determine if your subexpression can be factored what its plot looks like what mathematical identities could be applied and more Drag to Solve The Drag to Solve feature enables you to solve your equations step by step by dragging terms to where you want them to be With Drag to Solve you can e Easily take complete control over each individual step of your calculation e Let Maple apply the appropriate addition subtraction division or multiplication operation to both sides of your equation to avoid mechanical errors e Keep the full record of steps produced by Maple to document your work For more information on Smart Popups and Drag to Solve as well as examples see the worksheet expressions clickablemath help page Examples This chapter is designed to show several ways to solve the same problem in Maple Throughout these examples you will need to insert new document block regions This is done through the Format menu by selecting Create Document Block Also these examples only use the keyboard keys needed for a Windows ope
61. Problem Solving Adjust the x and y axis ranges 8 Right click the plot and select Axes Properties In the Axis Properties dialog de select Use data extents and change the range to 0 to 2 10 Click the Vertical tab and repeat step 9 Click OK to apply these settings and close the dialog Solution by Tutor Load the Student Calculus 1 package Loading Student Calculus1 From the Tools menu select Load Pack age Student Calculus 1 Enter the expression x 1 ina blank document block Right click and select Tutors Calculus Catcutus 1 Function inverse Single Variable Function Inverse The Function Inverse Tutor displays Plot Window Enter a function and an interval Fix x 2 1 a 0 Adjust the domain to 0 2 Formula of the Inverse x 1 1 2 x 1 1 2 Plot Options Maple Command InversePlot x 2 1 x 0 2 5 8 Clickable Math 229 5 When you are finished click Close The plot of the function its inverse and the line inverse tutor eee 1 y x is returned to the document Example 5 Methods of Integration Trig Substitution dx by making the substitution x 2 sin w o l J4 We solve this problem using the following methods Evaluate the integral e Immediate Evaluation of the Integral page 229 Solution by Integration Methods Tutor page 230 e Solution by First Principles page 231 I
62. Seguente S ecrin s e a a DN 334 DE aea a a a a tose aha aes 334 E EEE AA E A I E Masta E E E A INT 335 ATIVO ea O E a A 336 TD Sa E access bceaatn eaten 338 Matrees and VECUOLS cinner e AE 338 Fonciona Operator fe cust caaea aE ETEEN EEE ERTA S 339 aE a E EE E A A O NE A nae ade 342 vill Contents 8 3 Working with Maple Expressions s Ai0545s0he0ntencddtigockornbaacied ae beenkenadiovieus 343 Low Level Operations niire tiera oae TE ENEE ETT TA ieee 343 Manipulating Expressions oe niiden a T ae adele 348 Evahiatino EXpresSIOns yc hos sesteactilectcatAe E a a a 353 Basie Programmi lal i ouch non becadalt auc hut moat aaa ana Once beath aoa hnabieneahocubaweds 365 9 L A tS CMA pter neroian Sea ET TEE nang ened Sane etna elena 365 2 OW CONTO kiesne Se eset A chert ce cbs AN ee ate Otc 366 Conditional Execution if Statement ccc cece cece eee ceeeee eee eeeeaeneneeaens 366 Repetition LOR SEALING ueis e E EA 369 9 MELA Y COMM ANS sa raer e TE E T E A 374 Creatina SCOUCI Ennii a heed e E a achat 375 Adding and Multiplying Expressions cccccececeneececeaeeeeeeneeeeeeneenees 375 Selecting Expression Operands 4 03 5 4c0 ibooh reeds e ae E A 376 Mapping a Command over a Set or List ccc ccc cece ec ec eeeee eae eeeeseeeneeaens 377 Mapping a Binary Command over Two Lists or Vectors cececeeeeeeees 377 Additional Intonation reiasa e a a a i aerideaiakesas 378 OW OC UIE Scent bitte
63. This is the most common use of the eval command For example substitute x 3 in the following polynomial gt X 4 7x 2 ve 4 7x4 2 gt evall x 427 7x4 2 x 3 44 To substitute a value for a variable using palettes 1 In the Expression palette click the evaluation at a point item x a 2 Specify the expression variable and value to be substituted 8 3 Working with Maple Expressions 355 For example V17 Substitutions performed by the eval function are syntactical not the more powerful algeb raic form of substitution If the left hand side of the substitution is a name Maple performs the substitution It eval cos abec a r os nbe cos 6 c If the left hand side of the substitution is not a name Maple performs the substitution only if the left hand side of the substitution is an operand of the expression gt eval cos ab ab als Maple did not perform the evaluation because ab is not an operand of cos a b c For in formation on operands refer to the op help page gt eval cos abc ab cos abc For algebraic substitution use the algsubs command or the simplify command with side relations 356 8 Maple Expressions T gt algsubs a b 6 cos a b o l OSS CT os 6 c gt simpli cos a be a b A l l OS ctl cos C To compute an approximate numerical value of an expression Numerical Approximation e Use the evalf comman
64. Units help page Scientific Constants and Element Properties Computations often require not only units see Units page 127 but also the values of sci entifi constants including properties of elements and their isotopes Maple supports com putations with scientifi constants You can use the built in constants and add custom con stants Overview of Scientific Constants and Element Properties The ScientificConstant package provides the values of constant physical quantities for example the velocity of light and the atomic weight of sodium The ScientificConstant package also provides the units for the constant values allowing for greater understanding of the equation as well as unit matching for error checking of the solution The quantities available in the ScientificConstant package are divided into two distinct categories e Physical constants e Chemical element and isotope properties 134 4 Basic Computations Scientific Constants List of Scientific Constants You have access to scientifi constants important in engineering physics chemistry and other fields Table 4 5 lists some of the supported constants For a complete list of scientifi constants refer to the ScientificConstants PhysicalConstant help page Table 4 5 Scientifi Constants Name Newtonian constant of gravitation Planck constant elementary_charge Bohr radius deuteron magnetic moment Avogadro constant Faraday constant You can spe
65. Use data extents and change the Range min and Range max to 0 and 5 respectively Click the Vertical tab and de select Use data ex tents Change the Range min and Range max to 5 and 10 respectively 8 Click OK to apply the changes and return to the plot The interception points of this graph with the x axis are 1 and 3 the same solutions that we found previously Example 3 Solve a Quadratic Trig Equation Find all of the solutions to the equation 6 cos x cos x 2 0 in the interval 0 2 7 We solve this problem using the following methods e Graphical Solution page 221 Solution by Task Template page 223 e Analytic Solution page 223 Graphical Solution 1 Ctrl drag the equation gt 6 cos x cos x 2 0 6 cos x cos x 2 0 to a blank docu ment block and press Enter 6cos x cos x 2 0 2 Right click the output and select Left hand Side gt left hand side cos x 2 0 gt 6 cos x 2 cos x cos x 2 222 e 5 Mathematical Problem Solving 3 Right click the output and select Plots Plot SS i ee Interactive Plot Builder Select Plot Select Plot Type and Functions Plot Edit Functions Select Plot 2 D plot 2 D polar plot 3 D conformal plot of a complex valued Function 2 D conformal plot of a complex valued Function 2 D complex plot 3 D complex plot Select Variabl
66. _ 1 x 4 x 7 x 1 4 x 1 x 4 to a new document block region and press Enter X 7 x 1 7 4 x 1 4 x 4 First manipulate the equation to become an x 7 j2 4 x 1 j2 4 x 4 expression l move to lefi 2 Right click the output and select Move to Left x 7 3 x 1 4 x 4 0 Note the difference in the alignment when using context menus on output rather than input The result is centered in the document with the self documenting arrow positioned at the left 220 e 5 Mathematical Problem Solving Action O O Rese Document 3 Right click the output and select Left hand m2 3 2 Side x 7 3 x 1 4 x 4 0 left hand side x 7 3 4 1 4 Right click the output and select Expand gt gt x 7 3 x 1 expand 62 24x 18 Now that the equation is in its simplest form 2 mae plot the result 6x 24x 18 5 Ctrl drag the output to a new document block 6 Right click the expression and select Plots 2 D Plot 5 8 Clickable Math 221 Change the x and y axis ranges using context menus 7 By default plots generated using the context menus have an x axis range of 10 to 10 To change the range right click the plot and select Axes Properties In the Horizontal tab of the Axes Properties dialog de select
67. a b option remember Copyright c 1990 by the University of Waterloo All rights reserved local q f if nargs 0 then l elif nargs 1 then t expand a sign t t elif 2 lt nargs then foldl procname args elif type a integer and type b integer then ilem a b else gcd a b q q b end if end proc Modules Maple procedures associate a sequence of commands with a single command The module a more complex programming structure allows you to associate related procedures and data A key feature of modules is that they export variables This means that the variables are available outside the module in which they are created Most Maple packages are implemen ted as modules The package commands are exports of the module For more information on modules refer to the module help page Objects Objects take the idea of associating data and procedures beyond what modules provide With objects multiple instances of a class of objects can be created Each individual object can have its own data yet share other values and procedures with the entire class objects A well implemented class of objects can be used in Maple as naturally as a built in Maple type For more information on objects refer to the object help page 382 e 9 Basic Programming 9 5 Programming in Documents To write Maple code you could simply open a Maple worksheet and start typing However if you want to create a readable document wit
68. a partial derivative use the same syntax Maple assumes that the derivatives commute gt diff xsin 3y W x x y l 2fx To enter higher order derivatives it is convenient to use the syntax diff f x n This syntax 3 cos 3 y can also be used to compute the symbolic n order derivative For example gt diff cos t Sn l 0S f AT cos 7 n Differentiating an Operator You can also specify a mathematical function as a functional operator a mapping For a comparison of operators and other expressions see Distinction between Functional Operators and Other Expressions page 340 176 5 Mathematical Problem Solving To fin the derivative of a functional operator e Use the D operator The D operator returns a functional operator For example fin the derivative of an operator that represents the mathematical function F x xcos x First defin the operator F 1 In the Expression palette click the single variable function definitio item 754 gt 2 Enter placeholder values e To move to the next placeholder press the Tab key Note If pressing the Tab key inserts a tab click the Tab icon in the toolbar gt F x gt xcos x Now defin the operator G that maps x to the derivative of x cos x gt G D F G x cos x xsin x F and G evaluated at gt return the expected values 1 1 gt F 5 c gt gr For more information on the D operator refer to the D help pa
69. a single index to select an entire column enter firs the entire range of rows 1 then the column index 5 3 Linear Algebra e gt M 2 l aI la 8 0 gt M 1 1 1 43 6 7 1 9 Similarly you can access submatrices Enter the indices as a list or range gt M 2 3 1 2 6 L2 1 9 9 6 Vectors To select an entry in a vector enter the vector name with a non zero integer index gt a lt 85 3 47 1 59 9 38 1 gt 85 3 47 1 59 9 38 1 a gt al 1 85 3 Negative integers select entries from the end of the vector gt al 1 38 1 165 To create a Vector consisting of multiple entries specify a list or range For more informa tion refer to the set and range help pages 166 5 Mathematical Problem Solving gt a 1 2 85 3 47 1 gt al2 4 47 1 59 9 38 1 Linear Algebra Computations Maple has extensive support for linear algebra You can perform many matrix and vector computations using context menus Matrix operations such as multiplication and inverses can be done with the basic matrix arithmetic operators The LinearAlgebra package provides the full range of Maple commands for linear algebra and vector space computations queries and linear system solving Matrix Arithmetic The matrix and vector arithmetic operators are the standard Maple arithmetic operators up to the following two differences e The scalar multiplication operator is the asterisk
70. and handouts You can e Copy cut and paste information e Format text for reports or course material e Add headers and footers e Insert images tables and symbols e Generate two and three dimensional plots and animations e Sketch in the document or on a plot e Insert hyperlinks to other Maple files web sites or email addresses e Place instructions and equations side by side e Bookmark specifi areas e Easily update revise and distribute your documents In this chapter we will create a document that demonstrates many of Maple s documentation features For further examples note that this guide was written using Maple 7 1 In This Chapter Section Copy and Paste page 283 various text formatting elements Quick Character Formatting page 283 Quick Paragraph Formatting page 285 Character and Paragraph Styles page 287 Sections page 294 Headers and Footers page 296 Show or Hide Worksheet Content page 297 Indentation and the Tab Key page 298 Commands in Documents page 299 e Document Blocks page 299 Format and display or hide commands in a document Typesetting page 302 Auto Execute page 302 281 282 7 Creating Mathematical Documents Tables page 304 Create tables and Creating a table modify their attributes Peleenens Navigating table cells Modifying Structural Layout Modifying Physical Dimensions Modifying Appearance Printing Options Execution Order Tables in the Class
71. as a document or worksheet e With the help page displayed in the right pane of the help system from the View menu select Open Page as Worksheet A new worksheet tab opens and displays the help page as an executable document Viewing Examples in 2 D Math You can choose to view the examples in most help pages in either 1 D Math Maple input or 2 D Math mode The default is 1 D Math To change the math mode In the Maple help system e From the View menu select or clear the Display Examples with 2D math check box x 2 e Click the 2 D Math icon x Note Some input in help pages displays as 1 D Math no matter which option you have chosen This is for Maple procedures and other code that is best input in 1 D Math For more information see the helpnavigator help page Copying Examples Instead of opening the entire page as a document you can copy the Examples section only To copy examples 1 With the help page displayed in the right pane of the help system from the Edit menu select Copy Examples 2 Close or minimize the Help Navigator and return to your document 3 In your document place the cursor at the location where you want to paste the examples 4 From the Edit menu select Paste The Examples section of the help page is inserted as executable content in your document 1 7 Available Resources Your work with Maple is supported by numerous resources 1 7 Available Resources 57 Resources Availabl
72. as you move the arrow indicator populates the Label caption field For details on this command refer to the DocumentTools Do help page Example 2 Creating Embedded Components In chapter 7 see Embedded Components page 326 you created a document that included embedded components imported from a task template Here we re create that configuratio of components This example takes two parameters and b as inputs then plots the function y bx a and calculates 1 Create the components The table layout is best done after the components are finished in case the configuratio of the components changes as you are working Create two DialComponents to set the parameters a and b one GaugeComponent to a b Component to display the function Note that you do not need to use the dial and gauge components here there are others such as the slider that could also be used display the result one PlotComponent to display the plot and one MathContainer 10 3 Creating Embedded Components 393 Embedded Plot window Figure 10 4 The Inserted Components 2 Edit the display of the components Open the Component Properties dialog for the firs DialComponent and notice that it already has a name This name is used to reference the component from other components and is unique Change the display of each of the components as follows e Dial0 no changes e Diall change the Value at Highest Position to 10 the
73. assignment modes determine what the user sees when opening your document e If you save the document in authoring mode task template contents visible the user sees this content when opening the document e If you save the document in assignment mode the user sees only the assignment layout 332 7 Creating Mathematical Documents In both cases the View Assignment menu is accessible As such users students can switch between the original document contents and the displayed assignment 7 10 Worksheet Compatibility Maple provides users with two worksheet interfaces the Standard Worksheet and the Classic Worksheet Both have access to the full mathematical engine of Maple and take advantage of the new functionality in Maple The Classic Worksheet has the traditional Maple worksheet look and uses less memory If you create a document in the Standard Worksheet interface of Maple and then open it in the Classic Worksheet interface you should note possible changes to your file For example a bulleted list in the Standard Worksheet will not be displayed with bullets in the Classic Worksheet Many of the graphical features in this manual especially those in this chapter are not available in the Classic Worksheet interface If you are creating documents for distribution refer to the Compatibility help page 8 Maple Expressions This chapter provides basic information on using Maple expressions including an overview of the basic d
74. carat E O 378 Definin and Running Simple Procedures ccc ccc cece eee eeeeeeceeeeeaees 378 PROCS COUPES with TANPINAR 379 Procedure Return Valles nsaisan e panels teetena sana paacns 379 Displaying Procedure Definition 33555 capt oie okadaic bAebmetieaitbenticedhs 380 Displaying Maple Library Procedure Definition ccc ce cece sees ee eeeee es 380 Modules escent cat ae ies bec tert al tN outer ele eA edn ele aed le athe 381 O10 oo kc Serene ee ene RES OT ERT Ie RENEE Ree SORT PREIS eet oT REENES ICT At oe RT RRES Te To 381 9 5 Programming in DOCUMENLS saskes iether n E tin aieuhavealoniews 382 Code Edit RESIO noeros Enee ss ta alae ETT A E E e TAE 382 SORP COIE corki t a a a a e 383 10 Embedded Components and Maplets cccccecec esc ec eee neeeeceeeeeeseneneesenenes 385 WOT Ti Bis CW Apter eiae a r tenherathabsnse duet A a 385 LO 2 Using Embedded Components recimi rsin o Ea se maces 385 a a 2 61 HNO eee ana tee ee Semen tore eee nite nor ee Ne meee eae ene ee 385 Printing and Exporting a Document with Embedded Components 388 10 3 Creating Embedded Components io sind decca lca nscheonl atabhatdnieaieuheccabebieans 388 Inserine COMIPONENUS gicnasnshcrrme nioe a E neue Rete TOA EETA S 389 Editing Component Properties General Process cccceeeecec ee eeeenee sees 389 Removing Graphical Interface Component cccccecececeeeeeeceeeeeaens 390 Integ
75. clauses Maple evaluates the conditional expressions in order until one returns true Maple executes the corresponding statement sequence and then exits the if statement If no evaluation returns true Maple exits the if statement oe f 2h gt if not type x integer then printf Sa is not an integer x elif x gt 10 then printf a is an integer with more than one digit x elif x gt 0 then 368 9 Basic Programming printf a is an integer with one digit x end if 11 is an integer with more than one digit Order of elif Clauses An elif clause s statement sequence is executed only if the evaluation of all previous conditional expressions returns false or FAIL and the evaluation of its conditional expression returns true This means that changing the order of elif clauses may change the behavior of the if statement In the following if statement the elif clauses are in the wrong order gt if not type x integer then printf Sa is not an integer x elif x gt 0 then printf a is an integer with one digit x elif x gt 10 then printf a is an integer with more than one digit x end if 11 is an integer with one digit elif and else Clauses In an if statement with elif and else clauses Maple evaluates the conditional expressions in order until one returns true Maple executes the corresponding statement sequence and then exits the if statement If no evaluation returns true
76. color 3 Select Color Z Grayscale Change the axes style 4 Select Axes Boxed 6 3 Customizing Plots 267 Alter the glossiness 5 Select Glossiness and then select Set Using the slider adjust the level of glossiness The plot and plot3d Options If you are using commands to insert a plot you can specify plot options as arguments at the end of the calling sequence You can specify the options in any order Applying plot options in the command syntax offers a few more options and greater control than what is available in the Interactive Plot Builder and context menus Table 6 3 Common Plot Options sridlines D lightmodel 3 D Controls the light model to illuminate the plot one of none light1 light2 light3 or light4 linestyle Define the dash pattern used to render lines in the plot one of dot dash dashdot longdash solid spacedash and spacedot egend 2 D Define a legend for the plot i Controls the minimum total number of points generated scaling Controls the scaling of the graph one of constrained or unconstrained shading 3 D Define how the surface is colored one of xyz xy z zgrayscale zhue or none style Define how the surface is to be drawn one of line point polygon or polygonoutline for 2 D plots contour point surface surfacecontour surfacewireframe wireframe or wireframeopaque for 3 D plots symbol Define the symbol for points in the plot one of asterisk box
77. complicated integer computations such as factoring an integer testing whether an integer is a prime number and determining the greatest common divisor GCD of a pair of integers Note Many integer operations are available as task templates Tools Tasks Browse under Integer Operations You can quickly perform many integer operations using context menus Selecting an integer and then right clicking for Macintosh Control clicking displays a context menu with in teger commands For example the context menu item Integer Factors applies the ifactor command to compute the prime factorization of the given integer See Figure 4 1 9469629 9469629 Copy Special b Numeric Formatting Explore 4poly a Command 45519n to a Mame Integer Factors Next Prime e Plots b Test Primality Integer Functions b Units b Number Theory Functions t Figure 4 1 Context Menu for an Integer 4 3 Integer Operations 107 The result of applying Integer Factors is shown gt 9469629 9469629 4 1 gt ifactor 4 1 3 13 17 23 4 2 Maple inserts the command ifactor using an equation label reference to the integer 946929 For more information on equation labels see Equation Labels page 95 For more information on using context menus in Worksheet mode see Context Menus page 88 For information on using context menus in Document mode see Context Menus page 68 Maple has many other integer commands inclu
78. conversion can be done with the convert units command gt convert 1 0 units Ibffit radius N m radius 1 355817948 Using the Units Calculator you can convert temperatures and temperature changes e To perform a temperature conversion in the Dimension drop down list select temper ature absolute e To perform a temperature change conversion in the Dimension drop down list select temperature relative To convert temperature changes the Units Calculator uses the convert units command For example an increase of 32 degrees Fahrenheit corresponds to an increase of almost 18 degrees Celsius 130 4 Basic Computations gt convert 32 0 units degF degC LTT TTTTTTS To convert absolute temperatures the Unit Converter uses the convert temperature command For example 32 degrees Fahrenheit corresponds to 0 degrees Celsius gt convert 32 temperature degF degC 0 Applying Units to an Expression To insert a unit use the Units palettes The Units FPS palette Figure 4 7 contains im portant units from the foot pound second system of units The Units SD palette Figure 4 8 contains important units from the international system of units W Units FPS W Units ST eil LAI Lei lel LI is ponndai WI ks Fe i WI VI KI poundforce IFI 4 I jach Ic e FI HF poundal j A red sr ee Tel mol ix Li Figure 4 7 Units FPS Palette 1 Tl
79. decreasing order of the next unknown in the list option specify the plex option gt sort p2 x y plex Pr x p gt For information on enclosing keywords in right single quotes see Delaying Evaluation page 361 The firs term contains x to the power 3 the second x to the power 2 and the third x to the power 0 Using context menus you can perform operations such as sorting for polynomials and many other Maple objects To sort a polynomial 1 Right click Control click for Macintosh the polynomial 2 The context menu displays From the Sorts menu select e Single variable and then the unknown e Two variable or Three variable Pure Lexical or Total Degree and then the sort priority of the unknowns 152 5 Mathematical Problem Solving See Figure 5 1 F i y 3 ety x Copy Special Paste Evaluate and Display Inline Ctrl Explore Apply a Command Assign to a Mame Coefficients Collect Combine Differentiate Evaluate at 4 Point Factor Integrate Limit Plots Series Simplify Solve Complete Square Complex Maps Constructions Conversions Integer Functions Integral Transforms Language Conversions Optimization Sequence Sorts Units 2 D Math FT F F F FT F F F Single variable F Two variable P Figure 5 1 Sorting a Polynomial Using a Context Menu Pure Lexical P X Y Total Degree b YX 5 2 Algebra 153 Maple sorts the polynomial In Wor
80. enter input at the Maple input prompt gt The default mode for input is Math mode 2 D Math To evaluate input e Press Enter Maple displays the result output below the input 3 2 Input Prompt 79 T For example to fin the value of sin 3 enter the expression and then press Enter 2 3 TT gt sin Z Zy 3 3 1 For example compute the sum of two fractions i gt I w b 85 99 3 2 Suppressing Output To suppress the output enter a colon at the end of the input 2 7 9 1 gt A set of Maple input and its output are referred to as an execution group 1 D Math Input You can also insert input using Text mode D Math The input is entered as a one dimen sional sequence of characters 1 D Math input is red To enter input using 1 D Math e At the input prompt press F5 or click the Text button in the toolbar Math to switch from 2 D Math to 1 D Math gt 1232 29857 120 1785623 120 Important 1 D Math input must end with a semicolon or colon If you use a semicolon Maple displays the output if you use a colon Maple suppresses the output gt 1232 29857 120 80 3 Worksheet Mode To set the default input mode to 1 D Math 1 From the Tools menu select Options The Options dialog is displayed 2 On the Display tab in the Input display drop down list select Maple Notation 3 Click Apply to Session to set for only the curre
81. equaten the solve command competes all real solutions U Cvetaded Infermanan gt polynomia ely lt 1 ESTES ETET O Sour gt frolvel polynomial pee 1334385488 0 5 929222024 ALM pomore O Ofhrerctgadors O Aegirchsns Y Other Equations Roots B re Fee mere complicated equations the solve command computes one real sousca r N gt _ O rgis L gt pxynomias s 3x y 17x ye Say 2yel Dame gt folvel polynomials pranaree te 2118203038 y 05305528403 42 1 ayn a oe O lewod hutera gt ove tan an x 1 e lvoe OMS 1108 42 2 ores Prono P n E Comer ik gt Figure 1 17 Sample Help Page Every help page in Maple lists the command s calling sequence parameters and a description with examples of the command at the end of the page Some help pages also contain hyper links to related help pages and hyperlinks to dictionary definitions Hyperlinks to help pages display in green while hyperlinks to dictionary definition display in dark red 1 6 The Maple Help System 55 Using the Help Navigator The Help Navigator contains a fiel for topic or text based searches The Table of Contents tab provides a structured list of all topics in the help system To search the help system 1 In the left pane enter a string in the search field 2 By default a topic search is performed To perform a text search select the Text radio button 3 Enter the term and click Search Topic searches
82. expression from the end of a sequence gt S 2 sin x You can select multiple expressions by specifying a range using the range operator gt 2 2 Y sin x Note This syntax is valid for most data structures Sets A set is an expression sequence enclosed in curly braces 127 si 2 gt o 4 2 sin 3 A Maple set has the basic properties of a mathematical set e Each element is unique Repeated elements are stored only once e The order of elements is not stored 8 2 Creating and Using Data Structures 335 For example gt c a a a b c a a b c Using Sets To perform mathematical set operations use the set data structure gt 2 6 5 1 U 2 8 6 7 1 2 5 6 7 8 Note The union operator is available in 1 D Math input as union For more information refer to the union help page For more information on sets refer to the set help page Lists A list is an expression sequence enclosed in brackets gt L 2 3 3 1 0 L 2 3 3 1 0 Note Lists preserve both the order and repetition of elements Accessing Entries To refer to an element in a list e Use square brackets For example gt L 2 1 1 0 For more information see Accessing Elements page 334 Using Lists Some commands accept a list or set of expressions 336 8 Maple Expressions For example you can solve a list or set of equations using a context menu or the solve command
83. finance communications graphics and more To access a free application for volume of revolution 1 Go to the Maplesoft web site http www maplesoft com 2 In the menu of the main web page click Community and then Application Center 5 8 Clickable Math 209 3 In the Application Search section enter Calculus 2 in the Keyword or phrase field Application Search Calculus 2 Any Application Typel Search Advanced Search 4 Click Search 5 From the search results page under Displaying applications click the Click here link 6 From the list of archived applications select Calculus I Complete Set of Lessons 7 Click on the Download Maple Document link Toolkit Download Maple amp Document EQ view HTML Version Ss Tell a Colleague about this Application ea Contact the Author Contribute Your work GL Evaluate Maple 8 Download the zip file 9 Extract the L2 volumeRevolution mws file 10 Execute the worksheet and examine the results 5 8 Clickable Math For years Maple has led the way in making math software easy to use With its collection of Clickable Math tools including palettes interactive assistants context sensitive menus tutors and more Maple has set the standard for making it easy to learn teach and do mathematics Two key features of the Clickable Math tool collection are Drag to Solve and Smart Popups 210 e 5 Mathematical Problem Solving Smart
84. from by and to clauses are optional and can be in any order between the for clause and the do keyword Table 9 1 lists the default clause values Table 9 1 Default Clause Values troma o 1 byme i Examples The following loop returns the square root of the integers 1 to 5 inclusive 370 9 Basic Programming gt for n to 5 do evalf sqrt n end do l 1 414213562 1 732050808 ie 2 23606 977 When the value of the counter variable n is strictly greater than 5 Maple exits the loop gt n 6 The previous loop is equivalent to the following for from statement gt for n from 1 by 1 to 5 do evalf sqrt n end do l 1 414213562 1 732050808 rA 2 236067977 The by value can be negative The loop repeats until the value of the counter variable is strictly less than the fina value gt for n from 10 by 1 to 3 do if isprime n then print n end if end do 9 2 Flow Control 371 5 3 gt n 2 for in Loop The for in loop statement repeats a statement sequence for each component operand of an expression for example the elements of a list Syntax The for in loop has the following syntax For variable in expression do BLalenent sequence end do The for clause must appear first The behavior of the for in loop 1s 1 Assign the firs operand of expression to the name variable 2 Execute the statement sequence 3 Assign the next operand of expression to vari
85. icon is disabled when using 2 D Math Math mode and as such the Tab key allows you to move between placeholders Tab icon on Allows you to indent in the document using the Tab key ru 7 3 Commands in Documents 299 7 3 Commands in Documents Document Blocks With document blocks you can create documents that present text and math in formats similar to those found in business and education documents In a document block an input prompt or execution group 1s not displayed By hiding Maple input such that only text and results are visible you create a document with better presentation flo Before using document blocks it is recommended that you display Markers A vertical bar is displayed along the left pane of the document Icons representing document blocks are displayed in this vertical bar next to associated content To activate Markers e From the View menu select Markers For further details on document blocks see Document Blocks page 50 in Chapter 1 Working with Document Blocks In document mode each time you press Enter a new document block appears Documents consist of a series of document blocks 1 Create a new document block after the last section of the pasted example either by pressing Enter or by selecting from the Format menu Create Document Block 2 Enter text and an expression to evaluate For example enter Plot the expression sin x and its derivative T sin x For detailed instru
86. max command 107 430 Index maximize 184 maximum 107 Mean command 191 Meter component 386 min command 107 minimize 184 minimum 107 mod command 107 mod operator 109 modes Document 61 Worksheet 61 modify table 305 modp command 109 mods command 109 modular arithmetic 107 109 modules 381 MPS X files 188 msolve command 125 mul command 375 multiplication implied 6 N names 63 93 adding assumptions 142 and symbols 28 assigned 361 assigning values to 93 logical 366 previously assigned 361 protected 94 removing assumptions 144 reserved 94 unassigning 94 144 362 valid 95 versus equation labels 99 with assumptions 143 nops command 347 norm command 155 169 normal command 352 normal form 352 not operator 366 numbers 63 exact 102 floating point 102 non base 10 108 numer command 346 numeric approximation 356 computation 102 numtheory divisors command 107 O objects 381 ODE Analyzer Assistant 36 120 online help 60 operands 347 selecting 376 operators 63 functional 339 logical 366 relational 366 Optimization package description 85 optimization 187 efficienc 187 plotting 186 point and click interface 184 Optimization Assistant 32 36 184 Plotter 186 Options dialog 20 or operator 366 Order environment variable 179 ordinary differential equations plotting solution 123 solving 120 orthogonal matrix 170 output suppressing 79
87. on plotting see Plots and Animations page 237 Integration Maple can perform symbolic and numeric integration 180 5 Mathematical Problem Solving To compute the indefinit integral of an expression 1 In the Expression palette click the indefinit integration item 4 i 2 Specify the integrand and variable of integration and then evaluate it For example to integrate x sin a x with respect to x gt x sin a x dx sin ax xcos ax a P a Recall that you can also enter symbols including and d using symbol completion e Enter the symbol name or part of the name for example int or d and then press the completion shortcut key For more information see Symbol Names page 28 You can also compute an indefinit integral using context menus For more information see Context Menus page 39 To compute the definit integral of an expression aw ie dx 1 In the Expression palette click the definit integration item a 2 Specify the endpoints of the interval of integration integrand expression and variable of integration and then evaluate it For example to integrate e In t over the interval 0 22 gt e In r dt 0 e In t Ei 1 at y In a it e Emro d Maple treats the parameter a as a complex number As described in Assumptions on Variables page 142 you can compute under the assumption that a is a positive real number using the assuming command 5 4 Calculu
88. page 95 Note Through the Variable Manager you can manage the top level assigned variables currently active in your Maple Session For more information about the Variable Manager see the Variable Manager help page 3 9 Names 93 Assigning to Names You can assign any Maple expression to a name numeric values data structures procedures a type of Maple program and other Maple objects Initially the value of a name is itself gt a a The assignment operator associates an expression with a name gt a ai Recall that you can enter 7 using the following two methods e Use the Common Symbols palette e Jn 2 D Math enter pi and then press the symbol completion shortcut key See Shortcuts for Entering Mathematical Expressions page 6 When Maple evaluates an expression that contains a name it replaces the name with its value For example gt cos a For information on Maple evaluation rules see Evaluating Expressions page 353 Mathematical Functions To defin a function assign it to a name For example defin a function that computes the cube of its argument 3 gt cube x gt y For information on creating functions see Example 2 Defin a Mathematical Function page 64 94 e 3 Worksheet Mode gt cube 3 cube 1 666 27 4624076296 Note To insert the right arrow enter the characters gt In 2 D Math Maple replaces gt with the right arrow symbol In 1 D Math the chara
89. placeholder selected Alternatively select the square root symbol from the Expression palette Enter x then press the right arrow to leave the square root region 10 Enter 3 and then press the Space bar 11 Select the n th root symbol from the Ex n pression palette va 12 Enter 3 then press Tab 13 Enter x then press Tab 14 Enter x for the integration variable 15 Click the Text icon in the toolbar then enter the rest of the sentence and write in simplest terms 1 3 Entering Expressions 31 Result in Document Text ET th Dra C 20 Math a a dx n Evaluate Tet nOD Drawing C 2D Math Times Me 5 Evaluate ix al dx gil io Drawing Plot Anim Tet GE C 20 Math 7 Times New Roman San 30 42 sort dx 1 grt Evaluate i Text WP Drawing Plot Anima C 2D Math Times Hew Roman 5 3x I Sk a dx a Evaluate A 1 Po Drawing Plot Animal i Times New Roman 7 ra a Evaluate 3 432 jx ae dx A l Math Drawing Plot Animation C Text w Times New Roman D haida 5 Evaluate 3 2 Vx 3Vx dx and write in simplest terms A ih 32 Getting Started 1 4 Point and Click Interaction Maple contains many built in features that allow you to solve problems quickly without having to know any commands Assistants Maple offers a set of assistants in the form of graphical user interfa
90. plots package contains a changecoords command Maple also contains a top level changecoords command gt with plots After the plots package is loaded the name changecoords refers to the plots changecoords command To use the top level changecoords command unload the package or use the restart command For alternative methods of accessing the top level command see the rebound help page 3 3 Commands 85 Top Packages Here are a few of the most frequently used Maple packages A complete list of packages is available in the Maple help system at Help Manuals Resources and more List of Packages Table 3 2 Top Packages CodeGeneration The Code Generation package is a collection of commands and subpack ages that enable the translation of Maple code to other programming lan guages such as C C Fortran MATLAB Visual Basic and Java LinearAlgebra The Linear Algebra package contains commands to construct and manip ulate Matrices and Vectors and solve linear algebra problems LinearAl gebra routines operate on three principal data structures Matrices Vectors and scalars Optimization The Optimization package is a collection of commands for numerically solving optimization problems which involve findin the minimum or maximum of an objective function possibly subject to constraints Physics The Physics package implements computational representations and related operations for most of the objects us
91. refer to the expression For more information see Equation Labels page 48 To collapse a Document Block e With your cursor inside the document block select View Collapse Document Block You can use this process of expanding document blocks to view and edit Maple commands within a document block Changing the Display You can specify which parts of the input and output are displayed when the document block is collapsed For each execution group in the block you can choose to display either the input or the output e Place the cursor in the execution group e From the View menu select Toggle Input Output Display Also you can choose to display output either inline or centered on a new line e From the View menu select Inline Document Output Example 9 Creating a Document Block in Worksheet Mode In Worksheet mode you can create the content using commands and then use a document block to choose how much information to display Enter the following sentence using text and 2 D Math input and output The answer to sin x dx is cos x At an input prompt click the text icon T to The answer to enter plain text Enter The answer to Note these instructions are for Worksheet mode Click the input prompt icon gt to enter Maple The answer to i in x dx commands Enter sin x dr and then press Enter pata cos x to execute the command L gt 1 6 The Maple Help System 53 A
92. reveal a list of matching topics sorted by the precision of the match e Text searches reveal a list of topics based on keyword frequency e You can search all of the help system or specifi Resources such as Help Pages Tasks Tutorials and Manuals by selecting the Resources drop down menu Search results are displayed as a list in the Search Results tab of the left pane Click the Table of Contents tab to view a structured list of all topics in the help system To display potential matches in the right pane click a topic preceded by an icon Table 1 9 describes the different icons Table 1 9 Help Page Icons A folder icon in the Table of Contents tab indicates that a topic can be expanded into subtopics 7 Question mark icon indicates a help page and displays the associated help page in the right pane when selected WS icon indicates an example worksheet Example worksheets open in a new tab in the Maple document D icon indicates a definitio and displays the associated dictionary definitio in the right pane when selected T icon indicates a Task template and displays the associated Task Template in the right pane when selected a M icon indicates a manual Manuals open in a new tab in the Maple document Viewing Help Pages as Documents In the help system examples are not executable The Maple help system allows you to open help pages as documents that you can execute 56 1 Getting Started To open a help page
93. routines and other numer ical algorithms is built into Maple using the external calling mechanism External calling can also be applied to functions other than numerical algorithms Routines exist that accomplish a variety of non mathematical tasks You can use these routines in Maple to extend its functionality For example you can link to controlled hardware via a serial port or interface with another program The Database package uses external calling to allow you to query create and update databases in Maple For more information refer to the Database help page 11 5 Connectivity 417 For more information on using external calling refer to the ExternalCalling help page Mathematica Translator The MmatTranslator package provides translation tools for converting Mathematica ex pressions command operations and notebooks to Maple The package can translate Math ematica input to Maple input and Mathematica notebooks to Maple documents The Mma subpackage contains commands that provide translation for Mathematica commands when no equivalent Maple command exists In most cases the command achieves the translation through minor manipulations of the input and output of similar Maple commands Note The MmaTranslator package does not convert Mathematica programs There is a Maplet interface to the MmaTranslator package For more information refer to the MmaToMaple help page Matlab Package The Matlab package enables you to trans
94. solution in 4 9 z 98 98037599 found using the starting value z 100 gt assign 4 9 4 4 Solving Equations 119 98 98037599 Creating a Function from a Solution The assign command assigns a value as an expression to a name It does not defin a function To convert a solution to a function use the unapply command Consider one of the solutions for q to the equation q rs teas 7 gt solutions solvel q rs pa a 1 J 14 4rs 20 1 J 1 4rPs 20 huti l solutions 2 2 gt f unapply solutions 1 r s 1 1 14 4rs 20 f 1 8 gt gt Here solutions 1 selects the firs element of the list of solutions For more information on selecting elements see Accessing Elements page 334 You can evaluate this function at symbolic or numeric values gt flxy 1 4xy 20x 2 x ae TZ 14 11 J2 I 2 gt f 5 7 2 1 4 032680522 For more information on definin and using functions see Functional Operators page 339 120 4 Basic Computations Other Specialized Solvers In addition to equations and inequations Maple can solve other equations including e Ordinary differential equations ODEs e Partial differential equations PDEs e Integer equations e Integer equations in a finit fiel e Linear systems e Recurrence relations Ordinary Differential Equations ODEs Maple can solve ODEs and ODE systems including initial value and bo
95. specifying the package as an argument The with command displays a list of the package commands loaded unless you suppress the output by entering a colon at the end of the calling sequence After loading a package you can use the short form names of its commands That is you can enter the commands without specifying the package name 84 3 Worksheet Mode For example use the NLPSolve command from the Optimization package to fin a local minimum of an expression and the value of the independent variable at which the minimum occurs gt Optimization NLPSolve to 15 0 0913252028230576718 x 10 9041216700744900 gt with Optimization ImportMPS Interactive LPSolve LSSolve Maximize Minimize NLPSolve OPSolve gt NLPSolve Sm y Led s 0 0913252028230576718 x 10 9041216700744900 For more information on optimization see Optimization page 184 To unload a package e Use the unwith command specifying the package as an argument gt unwith Optimization Alternatively use the restart command The restart command clears Maple s internal memory The effects include unassigning all names and unloading all packages For more information refer to the restart help page Note To execute the examples in this manual you may be required to use the unassign or restart command between examples Some packages contain commands that have the same name as a top level command For example the
96. table cell including other sections and tables Table cells can contain a mix of e Input commands e 2 D Math e Embedded components buttons sliders check boxes and more e Plots 7 4 Tables 305 e Images Enter a heading in both columns of the firs row in 2 D Math You can use any text formatting features within each cell for example bold and center the headings Navigating Table Cells Use the Tab key to move to the next cell Ensure that the Tab toolbar icon is off H Tab icon off Allows you to move between cells using the Tab key m Tab icon on Allows you to indent in the table using the Tab key j Tab between the cells of the table and enter the following expressions in the firs column For each function from the context menu select Differentiate With respect to x Cut and paste the resulting expression into the second column Sx cos x we Ssin wx e gt 8 sin x cos x Modifying the Structural Layout of a Table The number of rows and columns in a table are modifie using the Insert and Delete sub menus in the Table menu or by using the Cut and Copy Paste tools Inserting Rows and Columns Row and column insertion is relative to the table cell that currently contains the cursor If the document has an active selection insertion is relative to the selection boundaries e Column insertion can be to the left or right of the document position marker or selection 306
97. take up space and distract readers from the message of the document To enter startup code for a document 1 From the Edit menu select Startup Code Alternatively click the startup code icon in the toolbar 2 Enter commands to be run each time the worksheet is opened or restart is called 3 Click Syntax to check the syntax of the entered code before closing 4 Click Save to save the contents and close the dialog gt Startup Code For Chapter09 mw BAF Fie Syntax Save Syntax Figure 9 3 Startup Code Editor For more information refer to the startupcode help page 384 9 Basic Programming 10 Embedded Components and Maplets These graphical components help you to create documents to use and share with colleagues or students that interact with Maple code within the document without needing the reader to understand that Maple code Other methods of interaction with Maple are described throughout this guide 10 1 In This Chapter Using Embedded Components page 385 Basic interact Interacting with Components ing with Maple documents containing embedded compon ents Printing and Exporting Creating Embedded Components page 388 Methods Inserting Components for creating embedded components that work together Editing Components and with your document G i Removing Components Integrating into a Document Using Maplets page 396 Methods for launching a Maplet File Maplet Maple Document Aut
98. the Insert Matrix button 158 5 Mathematical Problem Solving 3x 3 ShiFE x10 Control x100 Figure 5 3 Matrix Palette Choosing the Size After inserting the matrix 1 Enter the values of the entries To move to the next entry placeholder press Tab 2 After specifying all entries press Enter l et 7 sin t 0 0 L se 2 5 3 Linear Algebra 159 Creating Vectors You can create a Vector using angle brackets lt gt To create a column vector specify a comma delimited sequence lt a b c gt The number of elements is inferred from the number of expressions gt 1 2 3 To create a row vector specify a vertical bar delimited sequence lt a b c gt The number of elements is inferred from the number of expressions gt 1 2 3 123 For information on the Vector command options refer to the Vector help page You can also create vectors using the Matrix palette If either the number of rows or number of columns specifie is 1 then you have the option of inserting a matrix or inserting a vector of the appropriate type See Figure 5 4 W Matrix Rows 1 Columns 2 Choose Type Custom values v Shape Any Data type Any v s Insert Vector row U Insert Vector row aun Figure 5 4 Insert Matrix or Insert Vector 160 5 Mathematical Problem Solving Viewing Large Matrices and Vectors Matrices 10 x 10 and smaller and vectors with 10 or fewer
99. the Target drop down list contains the define elements to which Target Option you can send information in this case Plotter1 a value Plotter1 and TextField1 The Lit group box located below the Expres o mans Form Argument Form sion group box displays the define Expression A elements to which you can retrieve in plot TextFieldl x 10 10 formation in this case TextField1 Evaluate Expression a In the Target drop down LEB list select Plotter1 TextField Inthe Command Form tab enter plot TextField1 x 10 10 in the Expression group box Note Do not include a semicolon at the end of the plot command You can also double click TextField in the List group box to insert this element in the command syntax c Click Ok Run the Maplet 11 From the File menu select Run You are prompted to save the Maplet Maplets created with the Maplet Builder are saved as maplet files 12 Click Yes and navigate to a location to save this Maplet For further information on the Maplet Builder see the MapletBuilder help page For more examples of designing Maplets using the Maplet Builder see examples MapletBuilder Maplets Package When designing a complicated Maplet the Maplets package offers greater control The Maplets Elements subpackage contains the elements available when designing a Maplet application After you defin the Maplet use the Maplets Display command to launch the Ma
100. the previous action 2 x 9 0 and select Solve Isolate Expression for x Input move to lett jr 9354 Ix 3 0 Result move to left Sx 7 3x4 2 2x Copy Special Numeric Formatting Explore pply a Command Differentiate Evaluate at a Point Integrate Left hand Side Manipulate Equation Map Command Onta Move to Right Negate Relation Plots Right hand Side Simplify Solve Test Relation Conversions Integral Transforms Sequence isolate for x 9 0 A m 5 Isolate Expression For p x Numerically Solve b Numerically Solve af cormples Numerically Solve From point Obtain Solutions For b Solve Solve rexplicit Solve general solution Solve For ariable b 1 2 Introduction to Maple 15 Now that we have solved the equation we can plot it To do this we will copy the equation 2x 9 0 to a new document block and use context menus again 4 From the Format menu select Create Document Block 5 To copy the expression 2 x 9 0 highlight only this expression from the previous result Press and hold the Ctrl key and drag the expression to the new document block region Result move to left isolate for x y Sx 7 3x 2 te c a move to left isolate for x 424 733 x m 8 2 M ea x f A NA to left isolate fi Sx FSaxet ee T fp ee pai gt ex 9 0 16 1 Getting Started To plot the expression 6 Righ
101. to Clipboard button Place the cursor where you want to insert the task and then paste the task Maple inserts the default content Use this method to quickly insert a task multiple times Note You can view the history of previously inserted tasks From the Tools menu select Tasks Previously selected task names are displayed below the Browse menu item Before inserting a task Maple checks whether the task variables have assigned values in your document If any task variable is assigned the Task Variables dialog opens to allow you to modify the names Maple uses the edited variable names for all variable instances in the inserted task By default the Task Variables dialog is displayed only if there is a naming conflict You can set it to display every time you insert a task To specify that the Task Variables dialog be displayed every time you insert a task 1 From the Tools menu select Options 2 Click the Display tab 3 In the Show task variables on insert drop down list select Always 4 Click Apply to Session or Apply Globally as necessary Updating Parameters and Executing the Commands In inserted Task Templates parameters are marked as placeholders in purple text or spe cifie using sliders or other embedded components 1 Specify values for the parameters in placeholders or using graphical interface components You can move to the next placeholder by pressing Tab 2 Execute all commands in the task by e Placi
102. to move to the next placeholder For example gt lim l x gt 0 sin x The limit Command By default Maple searches for the real bidirectional limit unless the limit point is or o0 To specify a direction include one of the options left right real or complex in a call to the limit command See Table 5 8 5 4 Calculus 173 Table 5 8 Limits Command Syntax on Using the limit command you can also compute multidimensional limits 9 gt limit m x y Y 0 For more information on multidimensional limits refer to the limit multi help page Numerically Computing a Limit To numerically compute a limit e Use the evalf Limit arguments calling sequence Important Use the inert Limit command not the limit For more information refer to the limit help page The Limit command accepts the same arguments as the limit command For example ttl Faas sin x i gt evalf Limit ee EP EET aE x 1 225 0 3020605357 For information on the evalf command see Numerical Approximation page 356 The Limit command does not compute the limit It returns an unevaluated limit sin x os x tan x gt Limit x 1 225 C sin x x gt 1 225 cos x tan x 174 5 Mathematical Problem Solving For more information on the Limit command refer to the Limit help page Differentiation Maple can perform symbolic and numeric differentiation To differentiate an
103. vertical alignment of rows 310 7 Creating Mathematical Documents For column alignment the current selection is expanded to encompass all rows in the selected columns The alignment choice applies to all cells within the expanded selection If the document does not contain a selection the cursor position 1s used to identify the column Similarly the selection is expanded to include all columns in the selected rows for vertical alignment options The following table illustrates the vertical alignment options The baseline option is useful for aligning equations across multiple cells within a row of a table Center Baseline 7 4 Tables 311 For example set the Row alignment to Baseline for all rows and set the Column alignment to Center for all columns A x f x Plot of f x and a l E l i y TE 1 i A lt 1 i a x x sinf wx el cos x ae Ssin wx e gt sin x 8 sin x cos x dx Cell Color You can set the background color of any cell or collection of cells to be any color This coloring is independent of any highlighting or text color that may also be applied To change the color of a cell place the cursor in the cell then from the Table menu select Cell Color In the Select A Color dialog choose a color from the swatches the color wheel or RGB See the DrawingTools help page for details on color selection 312 7 Creating Mathematical Documents For exam
104. www maplesoft com maplesim MaplePlayer for iPad The Maple Player is a free application for the iPad that uses the Maple computation engine to enable you to view and interact with documents created in desktop Maple For more information on the Maple Player for 1Pad visit http www maplesoft com products MaplePlaver Sharing and Storing Maple Worksheet Content The MapleCloud You can use the MapleCloud to share worksheet content with other users view content shared by other users and store entire standard Maple worksheets or selected content from standard Maple worksheets Through the MapleCloud palette you can upload standard Maple worksheet content and allow other users to download a copy of that content You can also upload and store content in a user specifi area that only you can access A list of shared worksheets that you have permissions to view are displayed in the Maple Cloud palette To share content with specifi users you can either create a user group or select an existing group and allow only those group members to access your content For more information about groups refer to the worksheet cloud groups help page Users need an internet connection to use the MapleCloud To share worksheet content create manage and join user groups and view group specifi content you must log in to the MapleCloud using a Maplesoft com Gmail or Google Mail account name and password A Maplesoft com membership account gives
105. your own by clicking the Custom Header or Custom Footer tab For more information on header and footer options refer to the headerfooter help page Show or Hide Worksheet Content You can hide document elements of a specifi type so that they are not visible This does not delete them but hides them from view Hidden elements are not printed or exported but they can be copied and pasted In a document use the Show Contents dialog to hide all spreadsheets input output or graphics plus markers for section boundaries execution group boundaries hidden table borders on mouse pointer roll over and annotations The dialog is accessed from the View Show Hide Contents menu Using the Show Contents Dialog A check mark beside the item indicates that all document elements of that type are displayed for the current document See Figure 7 9 Show Contents Components Spreadsheets Input Output Graphics Markers Section Boundaries Execution Group Boundaries Hidden Table Borders Annotation Markers Figure 7 9 Show Contents Dialog 298 7 Creating Mathematical Documents 1 From the View menu select Show Hide Contents The Show Contents dialog opens with all items selected for display 2 Clear the check box associated with the document components or markers to hide them Note By clearing the Input check box only Maple Input and 2 D Math input that is 2 D Math content that has been evaluated are hidden Clearing
106. 0 0 0 gt Vector 3 shap zero To create a row vector using the Vector constructor include row as an index gt Vector row 3Vfill 1 1 11 gt Vector row 127 0 34 J datatype integer 1 127 0 34 The Matrix palette does not support some properties To set all properties use the Matrix constructor To defin a matrix using the Matrix constructor specify e The number of rows and columns If you explicitly specify all element values these ar guments are not required e A list of lists that defin the element values row wise e Parameters such as shape datatype and fil that set properties of the matrix 164 5 Mathematical Problem Solving For example gt Matrix 1 2 3 4 5 6 123 456 The Matrix palette cannot fil the matrix with an arbitrary value Use the fil parameter gt Matrix 3 4 1 2 3 4 5 6 l 2 J l 2 3 etl 4 5 6 2 I Sr lLeoti gti For more information on the constructors including other calling sequence syntaxes and parameters refer to the storage Matrix and Vector help pages See also Numeric Computations page 171 Accessing Entries in Matrices and Vectors Matrices To select an entry in a Matrix enter the matrix name with a sequence of two non zero integer indices row first gt M 4 3 6 7 1 9 2 9 1 2 9 6 9 3 8 0 9 2 4 3 2 9 93 M 6 7 1 2 8 0 L9 90 92 gt M 1 3 9 3 To select an entire row enter
107. 08 Figure 6 1 Interactive Parameter Window ccccececeeeecec eee ee eee eeeeeeeeeeenen snes 244 Fieu eE Solec C olor Dilo Sah dsascarernoma ce sergio tian eaadotranenuee Rean neato 284 Figure 7 22 Character oly le alOO virescens Grete sete ad A 285 Pigure 3 Paragraph Style Dialog t sssccetntoceractheidei Sweetest lade detouoagciadaceiai estates 286 Figure 7 4 Style Manacement Dialo f po siccih aa chiain n e E EENE 288 Fioure 7 5 Definim a Character Style mrersiomirr annes e ees aea TEE EEE RAE 290 Figure 7 0 Definin a Paragraph Style encrena i a 293 Figure 7 7 Style Set Management Dialog sssessisiresriseisrresiniirersisiisressrasrresiena 294 Figure 7 8 Header and Footer Dialog Custom Header ccecececec eee eeees 296 Figure 7 9 Show Contents Dialog eorroteriii irria ti eea e eT REEE EE ETA TT 297 Figure 7 10 Working with Document Blocks cccecececcceneceneeeeeeeneeeeeenenenens 300 Figure 7 11 Delete Table Contents Verificatio Dialog oc sosoesssessessesseesseese 307 Figure 7 12 Table Paste Mode Selection Dialog cccececcceeeececeeeceeenenenenens 307 YOURS 7 DIWO Celli airera a To T A E AE Ta anaes 307 Fiere 7 UA Merced CIS ernea E a ate codbeasiceteod aaered 307 Figure 7 15 Drawing Tools and Canvas sssseesensseessresessseseessesssreseeseessessees 316 Figure 7 16 Drawing Outline Color Icon o nsonnsonnssnnssnnsssressressenssersssreseresen 317 Fig
108. 141 solving procedures 116 sort lists 353 polynomials 150 353 sort command 150 353 plex option 151 spacing format 286 Special Functions Assistant 36 spellcheck 328 American spelling 328 dictionary 330 sqrfree command 155 Standard Document Interface xvii starting 3 Standard Units environment 131 Standard Worksheet Interface xvii startup code 9 Startup Code 383 statements multiple lines 378 Statistics package 193 continuous distributions 190 description 85 discrete distributions 190 plots 192 strings 342 StringTools package 343 Student package description 86 Student Help Center 59 Student package 177 195 196 calculus subpackages 183 LinearAlgebra subpackage 171 Maplets 195 Tutors 195 student resources 207 students portal for 195 study guides 196 style set management 293 subscripts entering 7 format 283 substitute 353 sum command 376 superscript format 283 Sylvester matrix 170 symbol completion 7 symbolic computation 102 objects 103 symbols entering 28 names 28 system of units 128 controlling 132 systeme international SI 72 128 T Tab icon 87 inserting 87 key 87 Tab icon 9 table of contents Index 435 help system 55 tables 338 alignment 309 and Classic worksheet 313 appearance 308 borders 308 contents 304 execution order 313 physical dimensions 308 printing 312 using 304 visibility of cell content 312 Task Browser 90
109. 2 4 Basic Computations Figure 4 2 Context Menu for an Equation Lig Copy Spectal Mimer Formatting Expbre Appi 4 Command Approcimate Combine Cross Multioly Ciferentiate Ewsliabs at a Font integrate Left hand Sida Manipulate Equation Map Command Onto Mowe bo Left Mara bo Right Megete Relation Plots Right hand Side Simplify aqra Test Relation complete Square Conversions Integra Tromscorms Sequence T FF Tsolate Expression for F Mumericaky Sohre Numerically Solve ty comples Numerically Solve from point Obtan Solutions For F Save Solva Cexplcit lag Solve general solution Solve For Vsrishle F In Worksheet mode Maple inserts a calling sequence that solves the equation followed by the solutions If you select Solve Maple computes exact solutions 4 4 Solving Equations 113 gt 2 x 12 r n ee 4 3 gt solve 4 3 3 3 3 3 y 3h lye 3 4 4 X 4 t 14 11 l fx 14 14 11 A If you select Solve Numerically Maple computes floating poin solutions gt gt x 12 ae x 12 4 5 gt fsolve C4 5 x 2 063602674 x 2 492174103 4 6 For information on solving equations and inequations symbolically using the solve command see the following section For information on solving equations numerically using the fsolve command see Numerically Solving Equations page 116 Symbolically Solving Equations and Inequ
110. 4 Q QPSolve command 188 QR factorization 170 quadratic programs 188 quantities with uncertainty 139 accessing error 139 accessing value 139 computing with 140 constructing 139 element properties 140 rounding the error 139 scientifi constants 140 with units 140 quick character formatting 283 paragraph formatting 285 quit statement 374 quo command 148 quotes double 342 left single 95 right single 94 361 unevaluation 361 quotient integer 107 R Radio Button component 386 random matrices 160 variables 190 randpoly command 155 range in plots 265 operator 165 rank 168 rational expressions entering 6 read from files 411 RealDomain package description 85 recurrence relation solving 126 reference equation labels 99 names 93 relational operators 366 rem command 148 remainder integer 107 remove command 376 repetition statements 369 reserved names 94 resources in help system 55 Index 433 restart command 84 95 resultant command 155 return statement 374 values 379 rhs command 345 right single quotes 94 361 right click expressions 40 right hand side 345 RootOf structure 115 roots command 155 of equations 115 Rotary Gauge component 387 row vector creating 163 rsolve command 126 running documents 9 worksheets 9 S saving a Maple Document 18 scatter plot 192 scientifi constants 133 list 134 name 134 symbol 134 un
111. 5 components adding GUI elements 326 palette 326 computations assistants 90 commands 85 context menus 89 errors 105 avoiding 105 integers 109 interrupting 374 linear algebra 166 mathematics 147 numeric 105 palettes 87 performing 101 147 Real number system 141 symbolic 105 syntax free 75 task templates 91 tutors 90 under assumptions 142 single evaluation 144 updating 66 with uncertainty 140 with units 131 conditional execution 366 constants 63 content command 154 context of unit 128 context menus 68 89 168 customizing animations 277 equation 111 integer 88 106 overview 39 tutors 74 using 39 424 Index convert command 351 base option 108 373 degrees option 351 mathematical functions 351 polynom option 179 set option 351 temperature option 130 units option 129 351 copy 283 examples 56 copy expressions 12 correlation 140 coulditbe command 144 covariance 140 cross product 168 Curl command 183 Curve Fitting package PolynomialInterpolation command 155 Curve Fitting Assistant 34 155 cut and paste in tables 306 D D operator 176 Data Analysis Assistant 35 194 data structures 63 333 creating 341 Data Table component 386 Database Integration 416 datatype option 163 degree command 154 polynomials 153 demonstrations 195 denom command 346 derivatives 174 directional 176 partial 63 174 prime notation 302 Tutor 196 Dial comp
112. 6 Pelta VES aa e a T E hu abate an 369 WMeTatiy e O T jcc tess cass a a E a a 374 Lieseg C OTA pact aena T ENa TO OA 375 The add and mul Commands svare a e N E ia ae 375 The select remove and selectremove Commands c cccceeeeeeeeeees 376 Tioman Omman au a a eA E eemenaiaaue ee eece 377 TING Alpe Om ae RE EEE EA OE EEE O E 378 Table 10 1 Embedded Component Descriptions ccc cece ec ec ene ee eee eeeeeeneeeees 385 Table 11 1 Summary of Content Translation When Exporting to Different Formats 414 XV xvi List of Tables Preface Maple Software Maple software is a powerful system that you can use to solve mathematical problems from simple to complex You can also create professional quality documents presentations and custom interactive computational tools in the Maple environment You can access the power of the Maple computational engine through a variety of interfaces Standard default A full featured graphical user interface that helps you create electronic documents to show all your calculations assumptions and any margin of error in your results You can also hide the computations to allow your reader to focus on the problem setup and fina results The advanced formatting features lets you create the customized document you need Because the documents are ive you can edit the parameters and with the click of a button compute the new results The Standard interface has two mod
113. 72 5 Mathematical Problem Solving In the Student LinearAlgebra subpackage the environment differs from that of the Lin earAlgebra package in that floating poin computations are generally performed using software precision instead of hardware precision and symbols are generally assumed to represent real rather than complex quantities These defaults and others can be controlled using the SetDefault For more information refer to the Student LinearAlgebra SetDe fault help page For information on using Maple as a teaching and learning tool see Teaching and Learning with Maple page 194 5 4 Calculus The Task Browser Tools Tasks Browse contains numerous calculus task templates For a list of tasks navigate to one of the related folders such as Calculus Differential Equations Multivariate Calculus or Vector Calculus This section describes the key Maple calculus commands many of which are used in task templates or available in the context menus For a complete list of calculus commands refer to the Mathematics including Calculus Differential Equations Power Series and Vector Calculus subfolders and Student Package sections of the Maple Help System Table of Contents Limits To compute the limit of an expression as the independent variable approaches a value 1 In the Expression palette click the limit item ns 2 Specify the independent variable limit point and expression and then evaluate it Press Tab
114. 88 paragraph styles 291 approximation 103 least squares 170 numeric 356 arguments 379 arithmetic 66 finite precision 102 interval 138 matrix and vector 166 modular 107 109 polynomial 148 Arrays 336 indexing 336 large 337 arrow operator 94 assign command 118 assigned command 361 421 422 Index assignment operator 93 security levels 304 Assistants Avogadro constant 113 134 Back Solver 35 CAD Link 36 B Curve Fitting 34 155 Data Analysis 35 194 eBook Publisher 36 Equation Manipulator 36 Import Data 36 410 Installer Builder 36 Library Browser 36 Maplet Builder 36 ODE Analyzer 36 120 Optimization 36 184 overview 32 Plot Builder 36 238 Scientifi Constants 36 Special Functions 36 Tools menu 32 Unit Converter 351 Units Calculator 36 128 Worksheet Migration 36 assume command 142 adding assumptions 143 and procedure variables 145 imposing multiple assumptions 143 removing assumptions 144 setting relationships between variables 142 setting variable properties 142 testing property 143 using with assuming command 145 viewing assumptions 143 assuming command 142 144 180 350 additionally option 145 and procedure variables 145 applying to all names 144 using with assume command 145 Attributes submenu character 285 paragraph 286 auto execute 302 repeating 304 Back Solver Assistant 35 bar chart 192 basis vector s
115. Approximate b Combine b Cross Multiply Differentiate b Evaluate at a Point Integrate b Left hand Side Manipulate Equation Map Command Onta Move to Left Move to Right Negate Relation Plots b Right hand Side Simplify Solve Isolate Expression For b Test Relation Numerically Solve More koo MNumerf slly Solve From point Obtain Solutions For b 2 D Math b Solve Solve texplicit Solve general solution Solve For Variable b Figure 2 3 Finding the Approximate Solution to an Equation T _ x se 3 T Viti2e 3 A y1i 2n 17 gt 1x 9 e P 3 m 14 z 14 T ES x x solve E 12 gt 2 200603 126 2 337021648 TU For more information on solving equations including solving inequations differential equations and other types of equations see Solving Equations page 111 72 2 Document Mode Using Units You can create expressions with units To specify a unit for an expression use the Units palettes The Units FPS palette Figure 2 4 contains important units from the foot pound second FPS system of units used in the United States The Units SI palette Figure 2 5 contains important units from the international system SI of units W Units FPS zit Lal ls ponndai 2 poundjorce iach HF poundai j frat sr Figure 2 4 FPS Units Palette W Units 51 wet el Ls LV kel el IF WI I I7 4 Ir Ic 2 TI L rad sr wot e
116. Builder is divided into four different panes e The Palette pane displays palettes which contain Maplet elements organized by category For a description of the elements see the MapletBuilder Palette help page The Body palette contains the most popular elements e The Layout pane displays the visual elements of the Maplet e The Command pane displays the commands and corresponding actions define in the Maplet e The Properties pane displays the properties of an instance of a define element in the Maplet Example 3 Design a Maplet Using the Maplet Builder In this example shown in Figure 10 8 the Maplet user enters a function and plots the result 400 10 Embedded Components and Maplets Enter a functionofx sin x ks Figure 10 8 Image of the Maplet Button element Label element Bady 4 z cal E Plot element Eee fh EAE He TextField element LA ke e i Figure 10 9 Body Elements Used to Defin This Maplet Result in MapletBuilder Defin the number of rows in the Maplet r oe 5 Box Colurin N 1 In the Properties pane haion a In the drop down list select om _ BoxColumn1 4 JE numrows 2 T z A b Change the numrows fiel re Te oem to 2 valign 10 5 Authoring Maplets 401 Add a plot region to row 1 2 From the Body palette drag the Plot ter element to the firs row in the Layout pane ETEEFEN KE Y Menu F be FB i SBox
117. Chapter 7 were created using Worksheet mode 3 1 In This Chapter Input Prompt page 78 Where you enter input The Input Prompt gt e Suppressing Output e 2 D and 1 D Math Input e Input Separators Commands page 80 Thousands of routines for The Maple Library performing computations and other operations Top Level Commands Package Commands Lists of Common Commands and Packages Palettes page 86 Items that you can insert by Using Palettes clicking or dragging Context Menus page 88 Pop up menus of e Using Context Menus common operations 71 78 3 Worksheet Mode Assistants and Tutors page 90 Graphical inter Launching Assistants and Tutors faces with buttons and sliders Task Templates page 90 Sets of commands Viewing Task Templates with placeholders that you can insert and use to f ner Inserting a Task Template perform a tas Performing the Task Text Regions page 92 Areas in the document Inserting a Text Region in which you can enter text Formatting Text Names page 92 References to the expressions Assigning to Names you assign to them Unassigning Names Valid Names Equation Labels page 95 Automatically gener Displaying Equation Labels ated labels that you can use to refer to expressions Referring to a Previous Result Execution Groups with Multiple Outputs Label Numbering Schemes Features of Equation Labels 3 2 Input Prompt In Worksheet mode you
118. Command Macintosh To execute 2 D Math you can use any of the following methods e Pressing Ctrl Command for Macintosh That is press and hold the Ctrl or Command key and then press the equal sign key This evaluates and displays results inline e Pressing the Enter key This evaluates and displays results on the next line and centered e Right click Control click for Macintosh the input to invoke a context menu item From the context menu select Evaluate and Display Inline See Context Menus page 39 for more details 1 2 Introduction to Maple 9 e Using the Edit menu items Evaluate and Evaluate and Display Inline Toolbar Options The Maple toolbar offers several buttons to assist you when interacting with Maple See Table 1 2 Table 1 2 Maple Toolbar Options Inserts plain text after the current execu From the Insert menu select Text tion group Inserts Maple Input after the current exe gt From the Insert menu select Execution cution group For details refer to Group and then After Cursor Execution Groups page 18 Encloses the selection in a subsection For details refer to Sections page 294 Removes any section enclosing the selec tion Executes all commands in the worksheet or document Executes a selected area From the Edit menu select Execute and then Selection a From the Format menu select Indent Clears Maple s internal memory For de Enter restart ta
119. Computations FJ Solve Humerically Parameters Output 8 Runge Kutta Fehlberg 4 5th order Show Function values at t 1 000000 Cash Karp 4 5th order cf q 1 30283200321421 Dverk 7 8th order 1 27526554583447 Plot Options Gear single step extrapolation Rosenbrock stiff 3 4th order gt Livermore stiff 0O Boundary Value Problem solver O Taylor series 2 Modified Extended BDF Implicit ene ie Show Maple commands ixed step methods Boll dsolve dittidiftftiq ti t tj qiti 4 cosfe t q O 0 Dig 0 0 numeric Absolute 1 000000e 07 default Snn E s011 1 000000 plots odeplot soll O 10 color red Relative 1 000000e 06 default Figure 4 4 ODE Analyzer Assistant Solve Numerically Dialog To solve a system symbolically using the ODE Analyzer Assistant 1 Click the Solve Symbolically button 2 Inthe Solve Symbolically window Figure 4 5 you can specify the method and relevant method specifi options to use for solving the problem 3 To compute the solution click the Solve button 4 4 Solving Equations 123 IM Solve Symbolically Method Output Default timelimit s 60 i mep j Use Lie Methods alt cas t cos 22 Use Classification Methods Integrate auto a Explicit auti O Transforms I J Plot Options C Truncated Series order Expansion point 1 Show Maple commands
120. E 53 Usno mhe Help NaI aaO eea E E E N 55 Viewing Help Pages as Doc ments osea e E teers E a 55 Viewing Examples m 2 D Math arnein EE A TE eE N 56 Copy ime examples aiaa a aS 56 TO NV dla kc RESOU E ees ououaabmaddremmmncuee undies 56 Resources Available through the Maple Help System cccceceeeee ee ees 57 Maple Tourand Quick RESOuUrCES i555 205 a a a a a a sled ioes 58 VCD Site RCSOUNCCS ai25 x ober giaralecsohs dasaiatetes toh mbalidancenntiness dhanatatatesiabuatatienns 58 DMD OCU CI IMIOUS pak ca hictaas balsa ctouantacaranitancdt usa E 61 2T EE C apr e tn adda eesti e rade een aa nee eae nace wea em ae 61 DD MMO GUCHOI erent aE E E Veuciog twee ananck ge EEA 61 2S Pere PX DLCSS1O0S esnin a teaateoulaaty bie taaarenn Taa annie anes 62 ili iv Contents Example 1 Enter a Partial Den yativescoiaisset anil coneluti cont anubasedcanieeenaenbeacaeos 63 Example 2 Defin a Mathematical Function cccccceceeeececeeeeeeeenenes 64 2 Ae Evaline Expressi OMS mee ai ale ees ere ath eee sana oe hod eee Gane 65 2 5 Editing Expressions and Updating Output c cece cc cc ccc ce ee ee ee eeeeeeneeeees 66 2 6 Periormin oC OmpuUtatOns isos hel coche brcusbubl naa Nouba hnabieneehncebauedeat don a a ates 67 Compune with Palettes rriren eE ETE E eee eine 67 COPTER MENUS eoit at aed eee a A E E 68 ASSN dnd TUOS caa a a S 13 3 Work beet Mode eriein E E TI SEE EMSC Da 0 cd merme i AEEA T AET 77 IL DUC
121. Er orAnalysis rules help page 140 4 Basic Computations gt GetError ApplyRule 4 18 round 2 3 2 Units Quantities with errors can have units For example the scientifi constants and element and isotope properties in the ScientificConstant packages are quantities with errors and units To construct a new quantity with units and an uncertainty include units in the Quantity calling sequence For an absolute error you must specify the units in both the value and error gt with Units Standard with ScientificErrorAnalysis gt Quantity 3 5 m 0 1 m Quantity 3 5 m 0 1 m For a relative error you can specify the units in only the value gt Quantity 3 5 m 0 1 relative Quantity 3 5 m 0 35 m For information on the correlation between variance of and covariance between quantities with uncertainty refer to the ScientificEr orAnalysis help page Performing Computations with Quantities with Uncertainty Many Maple commands support quantities with uncertainty gt ql Quantity 31 2 gt q2 Quantity 20 1 Compute the value of the derivative of q1 x sin q2 x at x sin 7 4 gt dl diff g1 x sin g2 x x dl 2 Quantity 31 2 x cos Quantity 20 1 x Quantity 20 1 gt d2 eval di x sin r 4 6 Restricting the Domain 141 To convert the solution to a single quantity with uncertainty use the combine errors command gt result c
122. FAA ASN IWS HZ x y 2y 2x 2 0 2x 0 8 9 You can use values in one data structure type to compute values in another data structure type as long as both data structures are dimensional and contain the same number of ele ments In the following example the values in an Array are compared to the values in a Matrix that contains the same number of elements gt 12 88 20 gt 3 100 25 312 100 lt 88 8 10 25 lt 20 For more information refer to the elementwise help page 360 e 8 Maple Expressions Levels of Evaluation In a symbolic mathematics program such as Maple you encounter the issue of levels of evaluation If you assign y to x z to y and then 5 to z what is the value of x At the top level Maple fully evaluates names That is Maple checks if the name or symbol has an assigned value If it has a value Maple substitutes the value for the name If this value has an assigned value Maple performs a substitution recursively until no more substitutions are possible For example gt xXS y gt V I z ol Maple fully evaluates the name x and returns the value 5 gt x 5 To control the level of evaluation of an expression e Use the eval command with an integer second argument If passed a single argument the eval command fully evaluates that expression If you specify an integer second argument Maple evaluates the expression to that level gt eval x gt eval x 1 gt eval
123. IMPLONS ONVAtlaDIGS apnar denea eaa a ed Godbatiacuss 142 gt Mathematical Probleni SOlyine 54462 i5ccenchtncneesincieants Lathse ueceintalesniesaealeentlaces 147 od Nia This C hapten ie aed ccd boc bench beat delicate oe ealt Sag r hele 147 DD Alo EDIT orohia Ea eta cl eae el nna Sa Be Snel Rea ERE Caen 148 Polynomial AOC Dra oii S ste tee tale e deg tiie relented Shon ihe eta Dhaeiee 148 Sel ENa Alee Da Ree epee Peete a a Mere teen n ST Tir Dene nee ea EaCT 155 Creatine Matrices and Vectors s iou cccl ailose cain baie dunner aioli e e aei 156 Accessing Entries in Matrices and Vectors cccccccececeeeeeeceneeeeeeneeeenes 164 Linear Als ebra GomputaHOns nosio ted tine e a ied ebb 166 Student LinearA locbra Package oecacraiese tiie thtadene a a a hades 171 SACE lUS anan e a E N 172 ESen e a T A T 172 Din orena E LO ec aS atest a a Na E e a N 174 Die Hck A OE E T A AE EA A E E 178 TPC OL ALIOU eaaa a a A S 179 Diferential Egations veirino re i eTA e ERAAN 182 Calc uns Packa tes nuirir a a a a ind a a 182 5 9 PUI ZIU O aea a a E A 184 Pointand Click nite Prd Ce araa a e E bast nea heos 184 Large Optimization Probles jg sarecaiane dear a EE TE NE A ceils 187 MPSA VPIS SUD DOI satis iin ioe teehee A N eee Ohad 188 Optimization Package Commands picichccc6 in ihe oscncaeedidedaiguhase a biel 189 Di SCAMS ICS EE ties anceed ree nace a ranma tessa nelelia cent ante NE A hae 189 Probability Distributions and Random Variables
124. If palettes are not visible use the following procedure 1 From the View menu select Palettes 2 Select Expand Docks 3 If the Components palette is not displayed right click Control click for Macintosh the palette dock From the context menu select Show Palette and then Components For more information see Palettes page 21 You can embed the following items e Button Toggle Button e Combo Box Check Box List Box Radio Button e Text Area Label e Slider Plot Mathematical Expression e Dial Meter Rotary Gauge Volume Gauge e Data Table 7 7 Embedded Components 327 OW Components Toggle Button Combo Box i Check Box Radio Button Text Area Label List Box J flax Figure 7 21 Components Palette Task Template with Embedded Components In your document you can add components that have already been configure to work to gether by using a task template Here we use the Interactive Application template For details on how to create and modify components see Creating Embedded Components page 388 To insert the task template from the Tools menu select Tasks Browse In the table of contents expand Document Templates and select Interactive Application Click Insert Minimal Content The following is inserted into your document 328 7 Creating Mathematical Documents Title author Exolanatory text describing the application use the Dials to set parameters use the
125. Like any symbolic expression you can convert RootOf structures to a floating poin value using the evalf command 116 4 Basic Computations gt evalf 4 7 1 0 984001051867989 1 52659083388421 I 0 484001051867989 0 609947140486231 I 0 484001051867989 0 609947140486231 I 0 984001051867989 1 52659083388421 I Some equations are difficul to solve symbolically For example polynomial equations of order fiv and greater do not in general have a solution in terms of radicals If the solve command does not fin any solutions it is recommended that you use the Maple numerical solver fsolve For information see the following section Numerically Solving Equations For more information on the solve command including how to solve equations define as procedures and how to fin parametric solutions refer to the solve details help page For information on verifying and using solutions returned by the solve command see Working with Solutions page 118 Numerically Solving Equations The fsolve command solves equations numerically The behavior of the fsolve command is similar to that of the solve command gt equation2 zcos z 2 gt fsolve equation2 z 23 64662473 4 8 Note You can also numerically solve equations using the context menus See Solving Equations and Inequations page 111 It is recommended that you verify the solutions returned by the fsolve command For details see Working with Solutions
126. List Box component 386 lists 165 335 returning solutions as 113 local variables 379 logical operators 366 loops 369 general 373 infinite 374 Macintosh command complete 7 context menus 39 manipulate equation 216 map command 377 Maple Application Center 196 Maple library 45 Maple Portal 57 195 Maple Student Help Center 196 MapleCloud 419 MaplePrimes 59 Maplet Builder description 36 launching 398 Maplet authoring 398 Maplets adding hyperlink to 323 authoring 405 Maplet Builder 398 Maplets package 403 launching Maple worksheet 397 Maplet fil type 396 Maplets package Display command 403 Elements subpackage 403 Maplet authoring 403 saving Maple worksheet 405 Index 429 maplet file 405 using 396 markers bookmarks 324 displaying 51 for document blocks 299 math dictionary description 57 math educators portal for 195 Math Expression component 386 Math mode 19 shortcuts 7 mathematical functions list 81 mathematics computations 147 teaching and learning 207 matrices 338 arithmetic 166 context menus 168 data type 162 163 defining 156 efficienc 162 filling 163 Hermitian transpose 168 image 161 large 160 multiplication 167 operations 168 random 160 scalar multiplication 167 selecting submatrices 165 shape 162 163 transpose 168 type 162 Matrix Browser 160 338 constructor 163 data structure 155 palette 126 156 162 Matrix command 156
127. Maple User Manual Copyright Maplesoft a division of Waterloo Maple Inc 2012 Maple User Manual Copyright Maplesoft Maple MapleSim Maple Application Center Maple Student Center Maplet Maple T A MapleNet and MapleCloud are all trademarks of Waterloo Maple Inc Maplesoft a division of Waterloo Maple Inc 1996 2012 All rights reserved No part of this book may be reproduced stored in a retrieval system or transcribed in any form or by any means electronic mechanical photocopying recording or otherwise Information in this document is subject to change without notice and does not represent a commitment on the part of the vendor The software described in this document is furnished under a license agreement and may be used or copied only in accordance with the agreement It is against the law to copy the software on any medium except as specificall allowed in the agreement Adobe and Acrobat are either registered trademarks or trademarks of Adobe Systems Incorporated in the United States and or other countries Java and all Java based marks are trademarks or registered trademarks of Oracle and or its affiliates MATLAB is a registered trademark of The MathWorks Inc Microsoft and Windows are registered trademarks of Microsoft Corporation NAG is a registered trademark of The Numerical Algorithms Group Ltd All other trademarks are the property of their respective owners This document was produced using Maple and Do
128. Maple has a powerful set of solvers for ordinary differential equations ODEs and partial differential equations PDEs and systems of ODEs and PDEs For information on solving ODEs and PDEs see Other Specialized Solvers page 120 Calculus Packages In addition to top level calculus commands Maple contains calculus packages VectorCalculus Package The VectorCalculus package contains commands that perform multivariate and vector calculus operations on VectorCalculus vectors vectors with an additional coordinate system attribute and vector field vectors with additional coordinate system and vectorfiel attributes for example Curl Flux and Torsion gt with VectorCalculus gt BasisFormat false gt SetCoordinates cartesian x y z 5 4 Calculus 183 gt VectorField VectorField y x z VectorField x Note For information on changing the display format in the VectorCalculus package see the VectorCalculus BasisFormat help page Find the curl of VectorField1 gt Curl VectorField bW oo amp Find the flu of VectorField1 through a sphere of radius r at the origin gt Flux VectorField1 Sphere 0 0 0 1 4 3 i 3 TT Compute the torsion of a space curve The curve must be a vector with parametric function components gt simplify Torsion t r P t assuming t real gt 9f 9 For information on the assuming command see The assuming Command page
129. Maple s embedded components to create your own For more information on how the Demonstrations were created refer to the Demonstrations Details help page The Demonstrations are connected to more complete teaching material provided in the Teacher Resource Center The Maple Teacher Resource Center contains resources and tips for teachers using Maplesoft products to help in the classroom Available resources include e Classroom content for subjects including Precalculus Calcu lus and Engineering e Training videos e E books http www maplesoft com teachercenter The Maple Portal includes material designed for all Maple users as well as specifi portals for students and educators The Maple Portal includes e How Dol topics that give quick answers to essential ques tions Tutorials that provide an overview of topics from getting started to plotting and working with matrices Navigation to portals with specialized information for stu dents math educators and engineers Access the portal from the Help menu Help Manuals Re sources and More Maple Portal The Maple Help System has an integrated dictionary of over 5000 mathematics and engineering terms You can search the dictionary by entering a term in the Help System search field 196 5 Mathematical Problem Solving Resource Description Maple Application Center The Maple Application Center contains tutorials and applications that help instructors beg
130. Marks 10 Options Enabled Visible Options Enable Input visible Show Track C Orient Vertically C Show Axis Labels Show Axis Tick Marks C Snap to Axis Tick Marks L Use Specified Text Width Figure 10 2 Label Properties Dialog Update Continuously while Dragging Figure 10 3 Slider Properties Dialog Name the component SliderLabel and click Ok Right click Control click Macintosh the slider component Select Component Properties The Slider Properties dialog opens See Figure 10 3 Name the component Slider 8 9 Enter the value at the lowest position as 0 and the highest as 100 Enter major tick marks at 20 and minor tick marks at 10 10 To defin an action click the Edit button for the Action When Value Changes The dialog that opens allows you to program the action of displaying the slider value in the label component The dialog includes instructions on how to program embedded com ponents The use in end use statement allows you to specify routines using the short form of accessing a package command without invoking the package For details on this command refer to the use help page 11 Before the end use statement at the bottom of the dialog enter the following command Do SliderLabel caption Slider1 value 12 Click OK 13 Make sure that the Update Continuously while Dragging check box is selected 392 10 Embedded Components and Maplets The value from the slider
131. Overview of Solution Methods for Important Equation Types 111 Sample DME MS1O MS sce reae aa EEE Ea EAEAN 128 Seren CONSTA 25 7 cee eaten e E a E 134 Polynomial Arithmetic Operators cccc cece ese neeeec ee eneeseeeneeseaenenees 149 Polynomial Coefficien and Degree Commands cccceeeeee eee es 153 Select Other Polynomial Commands ccc cece eee ceeeeeeeeeeeeeneeeees 154 Additional Polynomial Help iera na saws daresehebie ER 155 Matrix and Vector Arithmetic Operators ccccc cece eee eeeeec ee eeeeeenenes 166 Select Matrix and Vector Operators ic ic tacos od gace teninew AEE ieaeacaats EARE 168 Select LinearAlgebra Package Commands cceccecececeeeeeneneees 170 NC ASIDES E E E EE na els Weedon Sedan EE E E E E 173 Table 5 9 Optimization Package Commands ccccececeeeec ee eeeeeeeeeeeeenenenees 189 Table 5 10 Student and Instructor Resources nnonnnonnssnnssnnesrnesseessressrresere gt 195 Table 6 1 Windows of the Interactive Plot Builder c ccc cccce ec ec ec eeeeeneeenes 239 Table 6 2 The plot and plond Commands e n E 249 Tablet Common PIOC OMUOUS sossen an ea EE AE 267 Table 6 4 Table 6 5 Table 6 6 Table 9 1 Table 9 2 Table 9 3 Table 9 4 Table 9 5 Table 9 6 Table 9 7 PIOCANN RODIO ae a a ceo 269 The animate Command orea ara AEE E E E Oa 212 Animato OPMOUS rain ei E A 27
132. PROM D e alle a a tat a a nunieiouatnee 78 SUP Pies silo OQUP eea R a cea Wane aioaiee 79 PD Wath TD edie dlati ce a aaea A A hata ae hund 79 Papur Separators eeren T E T Ge seiecainsemetatnts 80 ZI OMA ANOS easa a e ia 80 Te Maple LIBI geet nem re Renn a a E a ne Neer rey 81 Top Level Commands ss igs cat ates rob senl mua tarinsabiabnarce hasan e A EOR 81 Package Commands ascosi eTa conga A ng Hola RAW Aue ioe patel TEE Hae Rela 83 Oar PIC Ue E EE E E vod delve aati env E A aman tefees 86 D0 CONTEXT Meni pi sree acts ace asians a Quien Saha tide ca a a paaateaes 88 Exainple Usine Context Menus c2i 0c cich nb ncc alah ourhedibasediabieee ieoberctlevi gether 89 30 Assistants and PULOES sises ieii TTE ESEE E EEE E TTE E AE TEE 90 Launching a Assistant or Tutor stadia cto cok encode see vated e ah 90 Se BS cael ho 01 0 12 Ree Oe Ee a OOe PORNE TACT RE Meee ROR TYE oe stort ene 90 OO Tet RENON aieea toh heise daar roi noes aaeta ended area hana a pom neon neato nanenhs 92 Dee NIOS e aera a ncaa oad Reve E S a patame meets 92 ASSN ONIME Smaa a a a a a a 93 Winassionine NaMe aers a i a E ERN 94 Vand NAMES aaant a e a a a E 95 JATE GUA on Labe kieren a E TTA TAT TATT 95 Display ite Equation Labels renec eoi a eel aa eat 96 Reterring to a Previous RESUM ahaa ti sicutatoneeceh acetal Suter E 96 Execution Groups with Multiple Outputs cc ccccc cece ec eceneececeeeeeesenenen 97 abel Number o Scheme S ccnccausn ss sesutolnsesttn
133. Page Break Before and Linebreak 6 To add or modify a font style click Font The Character Style dialog opens For detailed instructions see Creating and Modifying Character Styles page 289 7 2 Document Formatting 293 7 To save the style click OK or to abandon click Cancel If you are modifying an existing style all text in your document that uses the altered style is updated to reflec the changes Paragraph Style Properties Units Spacing Indent Line 0 0 Left Margin Above 0 0 Right Margin Below 0 0 First Line Alignment Bullets and Numbering Style Linked to Previous List Iker Initial List Value Bullet Suffix Page Break Before Linebreak Figure 7 6 Definin a Paragraph Style Style Set Management Saving Styles for Future Use You can use the style set of a particular document as the default style for all documents 294 e 7 Creating Mathematical Documents Style Set Management Current Style Sek User defined Style Set Style Set Operations Revert to Style Set Soply style definitions From the current style set Apply Style Set Load style definitions From another worksheet Mew Style Set Create a new style set File Cancel Figure 7 7 Style Set Management Dialog For information on creating and managing style sets see the worksheet documenting styles help page Sections You can organize your document into sections either before or after
134. Plot and Math Components to display the results parameter 1 parameter Plat of y Figure 7 22 Interactive Application Task Template This configuratio of components plots a linear function with slope and y intercept given respectively by the two dials parameter and parameter and displays the function ameter2 ee ona gauge For details on how these components work together see Embedded parameter Components and Maplets page 385 7 8 Spell Checking The Spellcheck utility examines all designated text regions of your document for potential spelling mistakes including regions that are in collapsed sections It does not check input output text in execution groups or math in text regions See Figure 7 23 Note The Spellcheck utility uses American spelling 7 8 Spell Checking 329 The CodeGeneration package is a collection of comands and subpackages that enable the translation of Maple code to other programming languages Spellcheck Mot Found comands Change To cormmanda Suggestions Ignore All Change All Figure 7 23 Spellcheck Dialog How to Use the Spellcheck Utility 1 From the Tools menu select Spellcheck Alternatively press F7 The Spellcheck dialog appears It automatically begins checking the document for potential spelling mistakes 2 If the Spellcheck utility find a word that it does not recognize that word is displayed in the Not Found text box You have six choices e To i
135. Row2 3 In the Properties pane haii Art SL Humcolumns a In the drop down list select numrows B oxRow2 s reference BoxRow2 Add columns to row 2 valign b Change the numcolumns fiel to 3 Add a label to row 2 4 From the Body palette drag the Label element to the left column in the Lay out pane In the Properties pane z a In the drop down list select a321 21 3 Labell a Entar a function ox T Ter b Change the caption fiel to Enter a function of x 402 e 10 Embedded Components and Maplets Add a text region to row 2 Body v 24 2 al ie lle f EE a 6 From the Body palette drag the Text Field element to the middle column The TextField element allows the Maplet user to enter input that can be 28 _ u4 i l T E H kK e retrieved in an action JE Ra Ifnecessary resize the Maplet Builder Y Menu to display the entire Layout pane By 2 E Y ToolBar Enter a function of x oe Add a button to row 2 8 From the Body palette drag the But ton element to the right column in the Y Dialog Layout pane TEELT 9 In the Properties pane z a In the drop down list select 5 Es Bi Buttonl Enter a function of x Y Tooter b Change the caption fiel to Plot c Inthe onclick property drop down list select lt Evalu ate gt 10 5 Authoring Maplets 403 10 In the Evaluate Expression dialog that displays
136. Spacing of Major Tick Marks to 1 and the Spacing of Minor Tick Marks to 1 e RotaryGauge0 change the Value at Highest Position to 40 the Spacing of Major Tick Marks to 5 and the Spacing of Minor Tick Marks to 1 e Plot0 no changes 394 e 10 Embedded Components and Maplets e MathContainer0 change the Width in Pixels to 200 and the Height in Pixels to 45 Note the names of all of the components and close each dialog before moving on 3 Create actions for the components Components can perform actions when their values are changed so the code to execute needs to be in the dials That way whenever one of them is changed the other components are updated to reflec that change The following Maple commands retrieve the values of the parameters and display them in the other three components gt parameter1 Do Dial0 gt parameter2 Do Diall gt Do SRotaryGauge0 parameterl1 parameter2 gt Do Plot0 plot parameter2 x parameterl1 x 50 50 y 50 50 gt Do sMathContainer0 y parameter2 x parameterl1 4 Test the actions To test these commands firs load the DocumentTools package with the following command gt with DocumentTools Execute the commands in the document and verify that the components you inserted are updated the gauge should change to the computed value a plot should appear in the plot component and the function should display in the math container 5 Troubleshootin
137. The image is displayed in the document Ifthe source fil is altered the embedded image does not change because the original object is pasted into the document 320 7 Creating Mathematical Documents To resize an inserted image 1 Click the image Resizing anchors appear at the sides and corners of the image 2 Move the mouse over the resize anchor Resizing arrows appear 3 Click and drag the image to the desired size Note To constrain the proportions of the image as it is resized press and hold the Shift key as you drag You can also draw on images 1n the same way as the drawing canvas For more information refer to the worksheet documenting drawingtools help page ImageTools Package You can manipulate image data using the ImageTools package This package is a collection of utilities for reading and writing common image fil formats and for performing basic image processing operations within Maple Within Maple images are represented as dense rectangular Arrays of 64 bit hardware floating poin numbers Grayscale images are 2 D whereas color images are 3 D the third dimension representing the color channels In addition to the commands in the ImageTools package many ordinary Array and Matrix operations are useful for image processing For details about this feature refer to the ImageTools help page 7 6 Hyperlinks Use a hyperlink in your document to access any of the following e Web Page URL e Email e W
138. able 4 Repeat steps 2 and 3 for each operand in expression If there are no more operands exit the loop This is the loop bound test Example The following loop returns a floating poin approximation to the sin function at the angles measured in degree in the list L gt L 23 4 87 2 43 0 99 7 372 9 Basic Programming gt for iin L do evalf sin i Pi 180 end do 0 3971478907 0 9988061374 0 6819983602 0 9857034690 while Loop The while loop repeats a statement sequence until a boolean expression does not hold Syntax The while loop has the following syntax gt While conditional expression do statement sequence end do A while loops repeats until its boolean expression conditional expression evaluates to false or FAIL For more information on boolean expressions see Conditional Execution if Statement page 366 Example The following loop computes the digits of 872 349 in base 7 in order of increasing signi ficance gt x 872349 gt while x gt 0 do irem x 7 x 1iquo x 7 end do 9 2 Flow Control 373 2 x 124621 0 x 17803 2 x 2543 2 x 363 6 t 2 r 0 r l x 0 To perform such conversions efficientl use theconvert base command gt convert 872349 base 7 2 0 2 2 6 2 0 1 For information on non base 10 numbers see Non Base 10 Numbers page 108 General Loop Statements You can include a while statement in a for
139. adding hyperlink to 322 help system accessing 53 description 57 Edit menu 56 Help Navigator 54 manuals 55 search 55 table of contents 55 tasks 55 topic search 55 tutorials 55 View menu 56 Hermitian transpose matrix and vector 168 Hessenberg form 170 hexadecimal numbers 108 hide worksheet content 297 highlight color 283 Hilbert Matrix 170 histogram 192 How Do I topics 57 hyperlinks in worksheet 320 Index 427 entering 29 110 icons open as example worksheet 56 if statement 366 ifactor command 106 107 349 igcd command 107 images adding hyperlink to 321 fil format 319 inserting 319 imaginary unit entering 29 110 implied multiplication 6 implies operator 366 Import Data Assistant 36 410 indent format 286 indeterminates 347 indets command 347 indices 81 165 inequations solving 111 for real solutions 141 symbolically 113 infinit loops 374 infolevel command 124 input 1 D Math 79 2 D Math 78 prompt 78 separating 80 setting default mode 80 insert bookmark 324 hyperlink 321 images 319 section 295 sketch pad 317 table 304 Installer Builder Assistant 36 instructor resources 207 428 Index int command 181 Int command 181 integers commands 107 computations 109 context menu 88 factoring 106 Gaussian 110 modulo m 109 solving equations 125 solving modular equations 125 integration 67 87 179 def
140. agement Figure 7 4 and Character Style Figure 7 5 dialogs To apply a character style to text in your document 1 Select the text to modify 2 In the styles drop down list in the context bar of your document select an appropriate character style All character styles are preceded by the letter C The selected text now reflect the attributes of the character style you have chosen C code E C Dictionary Hyperlinl C Equation Label C Hyperlink C Maple Input C Maple Input Placehe Page Number C Text PA 3 Optional If necessary you can remove this style From the Edit menu select Undo 7 2 Document Formatting 289 Creating and Modifying Character Styles You can create custom character styles to apply to text or change existing character styles New styles are automatically added to the styles drop down list in the context bar of your document 1 From the Format menu select Styles The Style Management dialog opens See Figure 7 4 To create a character style e Click Create Character Style The Character Style dialog opens See Figure 7 5 e Inthe firs row of the dialog enter a style name in the blank text region To modify a character style e From the style list select the character style to modify Recall that all character styles are preceded by the letter C while paragraph styles are preceded by the letter P e Click Modify The Character Style dialog opens with the current attributes displaye
141. alculus 1 Ctrl drag the expression x cos x to a blank document block region 214 5 Mathematical Problem Solving Right click the expression and select I takuu 1 Derivative Tutors Calculus Single Variable Fie Hep Derivatives Note The Tutors menu Piot Window Enter a function and an interval a b is now available in the context menu because we loaded the Student Calculus l a 1 package in step 1 ia Derivatives In the Derivative Tutor the color swatch shown beside the original expression is the 1 re eA color used for the curve in the plot region Z Display f x in the plot ae vf wi F 2 sin x x costx Similarly for f x and f x Sipe r Gna 4 Change the lower endpoint to P1 Select the check box to display x in the om i z aple Comman plot Click Display to make these ina i DerivativePlot xtcos x Pi Pi order 1 changes take effect 2 view 3 14 3 14 3 77 3 77 You can change the expression and modify plot options from within this tu derivative tutor tor For each change made click Display xcos x to view the altered plot When complete click Close to display the resulting plot in the document 5 8 Clickable Math 215 Access the Tutor from a Task Template Maple also comes with a Task Template to solve this problem without using any commands Launch the Task Template Browser by select 5 Calculus
142. alling sequence use the value command gt value 5 7 27 5 8 By default the LineInt command returns the value of the integral gt Linelnt VectorField lt y x x y gt Circle lt 0 0 gt r 20 For more information on the Student package refer to the Student help page 5 7 Teaching and Learning with Maple 203 Calculus Problem Solving Examples Maple is a powerful application with many resources to guide you The following examples provide you with scenarios to learn about using Maple resources and the Maple program When using Maple to solve a problem consider the following process 1 Formulate your problem 2 Obtain Maple resources that allow you to solve it Problem Scenario A Your company is designing a bottle for its new spring water product The bottle must contain 18 ounces of water and the height is fixed The design includes an undulating curved surface You know the amplitude and equation of the curve but you must fin the radius You require the Volume of Re volution Scenario B You want to teach your students the concept of a Volume of Revolution Specificall you want to plot and compute the volume ofa solid generated by rotating f x a lt x lt b about an axis or a line parallel to an axis 204 e e 5 Mathematical Problem Solving __ Tutors Check for Existing Tools __ 9 Task Templates __ Help Pages Probl Check for roblem
143. aluation of a quoted expression removes one set of right single quotes gt i 4 gt 1 i 1 8 11 gt 8 11 i 8 12 gt 8 12 5 8 13 For information on equation labels and equation label references see Equation Labels page 95 Enclosing an expression in unevaluation quotes delays evaluation but does not prevent automatic simplification gt q i 3q 4q i 8 14 Unassigning a Name Using Unevaluation Quotes To unassign a name e Assign the name enclosed in unevaluation quotes to itself gt 8 3 Working with Maple Expressions 363 i You can also unassign a name using the unassign command For more information see Unassigning Names page 94 364 8 Maple Expressions 9 Basic Programming You have used Maple interactively in the previous chapters sequentially performing oper ations such as executing a single command Because Maple has a complete programming language you can also use sophisticated programming constructs In Maple you can write programs called procedures and save them in modules These modules can be used and distributed in the same way as Maple packages Important It is strongly recommended that you use the Worksheet mode and 1 D Math input when programming or using programming commands Hence all input in this chapter is entered as 1 D Math 9 1 In This Chapter constructs Conditional Execution if Statement Repetition for Statement Iterative Command
144. an introduction to entering simple expressions in 2 D Math see Entering Expressions page 18 It is also easy to enter mathematical expressions such as x x lt 0 e Piecewise continuous functions 0 x 0 x 0 lt x e Limits d x lim dxi ai pE 2 3 Entering Expressions 63 e Continued fractions J2 and more complex expressions Mathematical expressions can contain the following objects e Numbers integers rational numbers complex numbers floating poin values finit fiel elements i 0 e Operators Jim R Pera ay e Constants T T e Mathematical functions sin x cos 3 i Pee e Names variables x y z B e Data structures sets lists Arrays Vectors Matrices Maple contains over a thousand symbols For some numbers operators and names you can press the corresponding key for example 9 gt or x Most symbols are not available on the keyboard but you can insert them easily using two methods palettes and symbol names Example 1 Enter a Partial Derivative To insert a symbol you can use palettes or symbol names 2 Enter the partial derivative a e using palettes fi 1 In the Expression palette click the partial differen a tiation item x f Maple inserts the partial deriv ative The variable placeholder is selected 2 Enter t and then press Tab The expression place holder is selected
145. aple Cormmand gradienti x 3 x 2 y 241 s 2 1 output plot axes boxed scaling unconstrained Figure 5 13 Multivariate Calculus Gradient Tutor Showing x y Plane When you close the tutor Maple inserts the 3 D plot 5 7 Teaching and Learning with Maple 201 gt Student MultivariateCalculus GradientTutor Many Student package commands can return a value mathematical expression plot or animation This allows you to compute the fina answer see the general formula applied to a specifi problem or visualize the underlying concepts For example the Student VectorCalculus LineInt line integral command can return the following e Plot that visually indicates the vector field path of integration and tangent vectors to the path e Unevaluated line integral e Numeric value of the line integral gt with Studenti VectorCalculus 202 e 5 Mathematical Problem Solving gt Linelnt VectorField lt y x gt Circle lt 0 0 gt 1 output plot z Ea Pa Fi i Hi i l N x K w ms a I ea ea e A A F ie ri 7 j 1 i F y N N i w The path of integration vector s tangent to the path and vector field arrows gt Linelnt VectorField lt y x gt Circle lt 0 0 gt 1 output integrat 2 sin 1 cos t dt 5 7 0 To evaluate the integral returned by the output integral c
146. ar ODEs with polynomial coefficient To access all available functionality use the dsolve command directly For more information refer to the dsolve help page Partial Differential Equations PDEs To solve a PDE or PDE system symbolically or numerically use the pdsolve command PDE systems can contain ODEs algebraic equations and inequations For example solve the following PDE symbolically For help entering a partial derivative see Example 1 Enter a Partial Derivative page 63 0 gt x f x y y 7 x v 0 Oy Ox 9 F UZ ae 414 X dy x F y ax x y gt pdsolve 4 14 The solution is an arbitrary univariate function applied to y Maple generally prints only the return value errors and warnings during a computation To print information about the techniques Maple uses increase the infolevel setting for the command To return all information set infolevel to 5 4 4 Solving Equations 125 gt infolevel pdsolve 5 gt pdsolve 4 14 Checking arguments First set of solution methods general or quase general solution Second set of solution methods complete solutions Trying methods for first order PDEs Second set of solution methods successful P 4 f x y FI y For more information on solving PDEs including numeric solutions and solving PDE sys tems refer to the pdsolve help page Integer Equations To fin only integer solutions t
147. aragraph menu provides access to the following quick alignment features Align Left Center Align Right and Justify 286 7 Creating Mathematical Documents To modify a paragraph 1 In the document select the paragraph to modify 2 From the Format menu select Paragraph and then the appropriate feature Attributes Submenu Spacing Indent Alignment Bullets Line Break and Page Break You can change various paragraph attributes in one dialog e From the Format menu select Paragraph and then Attributes The Paragraph Style dialog opens See Figure 7 3 e When changing spacing you must indicate units inches centimeters or points in the Units drop down list Paragraph Style Properties Units Spacing Indent Line 0 0 Left Margin 0 0 Above 0 0 Right Margin 0 0 Below 0 0 First Line 0 0 Alignment Bullets and Numbering Initial List Value Bullet Suffix Page Break Before Linebreak Figure 7 3 Paragraph Style Dialog For example in the pasted text select all of the items under Parameters then open the Paragraph Style dialog Notice that the spacing has already been set In the Indent section change the Left Margin indent to 10 0 pt 7 2 Document Formatting 287 In the Bullets and Numbering section click the Style drop down and select Dash Click OK to close the dialog and apply the styles Result plot create a two dimensional plot Calling Sequence plot x plot
148. ard Maple arithmetic operators excluding the division operator The division operator accepts polynomial arguments but does not perform polynomial division Polynomial division is an important operation The quo and rem commands fin the quotient and remainder of a polynomial division See Table 5 1 The iquo and irem commands fin the quotient and remainder of an integer division For more information see Integer Operations page 106 5 2 Algebra 149 Table 5 1 Polynomial Arithmetic Operators Addition gt 7 1 32 5x 2 F 343 5x Multiplication gt 7 1 32 5x 2 7 1 3x 5x 2 Division Quotient and uo 7 E i Q a gt quol2 x x 3 3x 5 x Remainder rem A F Exponentiation Ea You can specify multiplication explicitly by entering which displays in 2 D Math as In 2 D Math you can also implicitly multiply by placing a space character between two expressions In some cases the space character is optional For example Maple interprets a number followed by a name as an implicit multiplication In 2 D Math exponents display as superscripts To expand a polynomial use the expand command gt expand 3x 3x 5 X 2 9x 142 2 If you need to determine whether one polynomial divides another but do not need the quotient use the divide command The divide command tests for exact polynomial division 150 5 Mathematical Problem Solving gt di vide x4 Hoy
149. arkers c wesedosnxeuaastorarsedavanassaiuatleavabanadvorateetoabe 51 Figure 1 16 Expanded Document BlOCK ersi dreiinn a ene aE EEA 5I Heure sl Sampe HEP Pi Eae TEE A 54 Foire ir COMEM onnea a E SN Re Tr eee ee RP AS 68 Figure 2 2 Approximating the Value of a Fraction cccecececeeeeeeeeeeeeeeeenenenees 69 Figure 2 3 Finding the Approximate Solution to an Equation cccceeee eee ee es 71 Paiute 2APPS UNMIS PIENE eei a N T2 Pome 2a SLU ANCL a E E F2 Peurred I Expression Pale oem Ee E AE EE EEEO R 87 Piire o2 neter C Onex MeMa a E AEAN 88 higure 3 5 ODE Analyzer Assistant eaa obanaquiwaiashvabetianiusadtwe oheviasdeated bens 90 MPU re FAS ok OW Se wo at act rasan catacmtecalas E pia vena nam E as 9 Pacure lt 3 5 lt Insert Label Dialob 3 6 Ader are E An tameneeweuan derma nudadss sar An inwmhade ued 96 Figure 3 6 Format Labels Dialog Adding a Prefi ccc cece cece cece ee ee ene eeeenens 98 Figure 4 1 gt Context Menu tor an cInte Ger unesie na E ET 106 Figure 42 ontext Menu for an Eg ation 2c eis e ae a EEEE 112 Fiewe4 o ODE AndlyzerASSistant seeren E E ETA AE 120 Figure 4 4 ODE Analyzer Assistant Solve Numerically Dialog ccee eens 122 Figure 4 5 ODE Analyzer Assistant Solve Symbolically Dialog c ee 123 Figure 4 6 Units Calculator Assistant discs acconyeauisavarsimiabenspnddedsaes Aa 129 Peura y UM FPS PIENE ei ans terest dir ng tse ET EASA EE A 130 Fiore 4 6
150. ata structures Many of the commands described in this chapter are useful for programming For information on additional Maple programming concepts such as looping conditional execution and procedures see Basic Programming page 365 8 1 In This Chapter Creating and Using Data Structures page 333 Expression Sequences How to defin and use basic data structures Seti Lists Tables Arrays Matrices and Vectors Functional Operators Strings Working with Maple Expressions page 343 Tools Low Level Operations for manipulating and controlling the evaluation of expressions Manipulating Expressions Evaluating Expressions 8 2 Creating and Using Data Structures Constants data structures mathematical expressions and other objects are Maple expressions For more information on expressions refer to the Maple Help System This section describes the key data structures e Expression sequences e Sets e Lists e Tables e Arrays e Matrices and Vectors e Functional operators e Strings 333 334 e 8 Maple Expressions Expression Sequences The fundamental Maple data structure is the expression sequence It is a group of expressions separated by commas gt 2 y sin x I Accessing Elements To access one of the expressions e Enter the sequence name followed by the position of the expression enclosed in brackets I For example gt 2 i Using negative integers you can select an
151. ath in one or more execution groups 1s selected then a document block is created that contains those execution groups If not anew document block is created after the current execution group For more information see the next example Document block regions are identifie using markers that are located in a vertical bar along the left pane of the document See Figure 1 15 In addition to document block boundaries these markers icons indicate the presence of hidden attributes in the document such as annotations bookmarks and numeric formatting To activate markers From the View menu select Markers See Figure 1 15 Figure 1 15 Document Block Markers To view code in a document block 1 Place the cursor in a document block to be expanded 2 From the View menu select Expand Document Block C 2D Math w Times Hew Roman 12 v E U Mis ste mra xk Tk 1 Q 0 pea y 2 Figure 1 16 Expanded Document Block With the Document Block expanded you can see the Maple command that was used to perform this calculation In Figure 1 16 the solve command was used 52 1 Getting Started Also notice a red prompt gt before the original expression and the solve command Entering commands outside of a document block region is done at this input region To insert an input region click the gt button in the toolbar menu In Figure 1 16 an equation label was used to
152. ations The solve command 1s a general solver that determines exact symbolic solutions to equations or inequations The solutions to a single equation or inequation are returned as an expression sequence For details see Creating and Using Data Structures page 333 If Maple does not fin any solutions the solve command returns the empty expression sequence gt solve 3x 14 0 l to u ESN oS MEN AET 2 2 2 In general solve computes solutions in the fiel of complex numbers To restrict the problem to only real solutions see Restricting the Domain page 141 It is recommended that you verify the solutions returned by the solve command For details see Working with Solutions page 118 To return the solutions as a list enclose the calling sequence in brackets 114 4 Basic Computations gt solve x x 256y x 14 2 1 1024y lF 1024 y ied 2 2 Expressions You can specify expressions instead of equations The solve command auto matically equates them to zero gt solvel e z LambertW 1 Multiple Equations To solve multiple equations or inequations specify them as a Creating and Using Data Structures page 333 gt solve xy y 5 x gt 0 gt 9 gt _ J 5 gt 5 lt y y y y y 2 y J f J f NM as yrs _ yts o lt po ytS yt5 lt 0 gt solve x47 y 5 x lt 0 2 a T SD y y j Ca x yt5 y 5 y 5 ah Solving fo
153. atrix or set of linear equations to be solved Load the Student LinearAlgebra Loading Student LinearAlgebra package From the Tools menu select Load Package Student Linear Algebra This makes the tutors in that package available For details see Package Commands page 47 Right click the matrix and select Tu tors Linear Algebra Linear 2 Linear Algebra Linear System Solving System Solving The Linear Sys tem Solving dialog appears where Gaussian Elimination Gauss Jordan Elimination you can choose the solving method Gaussian Elimination reduces the Boel matrix to row echelon form then performs back substitution to solve the system Gauss Jordan Elimina tion reduces the matrix to reduced row echelon form where the equa tions are already solved For this ex ample choose Gaussian Elimination 2 6 Performing Computations 75 The Gaussian Elimination dialog __ fjg jhear Algebra Gaussian Elimination opens You can specify the Gaussian Fie Edt Help elimination step by step or you can i 5 7 3 4 n Seis a use the Next Step or All Steps but 145 34 10 2 Click on any button to tons to have Maple perform the steps 1 o 3 23 10 een ee ce for you 42 17 131 5 Add multiple Once the matrix is in row echelon row 1 upper triangular form click the sal Solve System button to move to the next step Multiply row 1 Multiply
154. beta beta beta beta l n H l 20 n gt gt binomial 7 B 2B B P B 2P gt 19 gt 5 102493 7361666644598071 114328769317982974 11 8 For more information refer to the read and interface help pages 11 4 Exporting to Other Formats Exporting Documents You can save your documents by selecting Save or Save As from the File menu By selecting Export As from the File menu you can also export a document in the following formats HTML LaTeX Maple input Maplet application Maple text plain text PDF and Rich Text Format This allows you to access your work outside Maple HTML The html fil that Maple generates can be loaded into any HTML browser Exported mathematical content can be displayed in one of the following formats GIF MathML 2 0 Presentation MathML 2 0 Content or Maple Viewer and is saved in a separate folder MathML is the Internet standard sanctioned by the World Wide Web Consortium W3C for the communication of structured mathematical formulae between applications For more information about MathML refer to the MathML help page Maple documents that are exported to HTML translate into multiple documents when using frames If the frames feature is not selected Maple creates only one page that contains the document contents LaTeX The tex fil generated by Maple is ready for processing by LaTeX All distributions of Maple include the necessary style files By default the LaTeX st
155. ble the add in 2 From the View menu select Toolbars and then Maple 3 On the Maple toolbar click the Maple help icon Re OpenMaple OpenMaple is a suite of functions that allows you to access Maple algorithms and data structures in your compiled C C Java or Visual Basic programs This is the reverse of external calling which allows access to compiled C C Fortran 77 and Java code from Maple To run your application Maple must be installed You can distribute your application to any licensed Maple user For additional terms and conditions on the use of OpenMaple refer to the extern OpenMapleLicensing txt fil in your Maple installation For more details on using OpenMaple functions refer to the OpenMaple help page MapleSim MapleSim is a complete environment for modeling and simulating multidomain engin eering systems During a simulation MapleSim uses the symbolic Maple computation engine to generate the mathematical models that represent the system behavior Because both products are tightly integrated you can use Maple commands and technical document features to edit manipulate and analyze a MapleSim model For example you can use Maple commands and tools to manipulate your model equations develop custom components based on a mathematical model and visualize simulation results 11 5 Connectivity 419 MapleSim software is not included with the Maple software For more information on MapleSim visit http
156. brary contains the most frequently used Maple commands Packages contain related commands for performing tasks from disciplines such as Student Calculus Statistics or Differential Geometry For example the Optimization package contains commands for numerically solving optimization problems For details on top level and package commands see Commands page 80 Entering Commands If you want to interact with Maple using commands simply enter the command using 2 D math Notice that commands and variable names display in italics Maple commands are constructed in a format similar to command arguments based on the command you are using 46 1 Getting Started For example to factor an expression enter factor 2x 1 x 1 To differentiate an expression enter diff sin x x cos x To integrate an expression on the interval 0 2 T enter int 2x cos x x 0 21 To plot an expression enter plot sin x xx 10 10 For a list of the top commands in Maple see Top Commands page 82 1 5 Commands 47 Package Commands There are two ways to access commands within a package using the long form of the package command or the short form Long Form of Accessing Package Commands The long form specifie both the package and command names using the syntax package com mand arguments LinearAlgebra RandomMatrix 2 44 31 92 67 Short Form of Accessing Package Commands The sh
157. c and numeric quantities Maple can perform computations with units and uncertainties Maple supports hundreds of units for example miles coulombs and bars and provides facilities for adding custom units Maple has a library of hundreds of scientifi constants with units including element and isotope properties To support computations with uncertainties Maple propagates errors through computations Units The Units package in Maple provides a library of units and facilities for using units in computations It is fully extensible so that you can add units and unit systems as required Note Some unit operations are available as task templates see Tools Tasks Browse and through context menus Overview of Units A dimension is a measurable quantity for example length or force The set of dimensions that are fundamental and independent are known as base dimensions In Maple the base dimensions include length mass time electric current thermodynamic temperature amount of substance luminous intensity information and currency For a complete list enter and execute Units GetDimensions Complex dimensions or composite dimensions measure other quantities in terms of a combination of base dimensions For example the complex dimension force is a measurement mass length of eae lime Each dimension base or complex has associated units Base units measure a base dimension Complex units measure a complex
158. cBook Printed in Canada ISBN 978 1 926902 23 4 Contents PEC IAC e ELT IE E ET h alata EE I T E EE E E xvii EEE A 16 E E A E E E E E ae STA EE en ee Pe ee l A EE REE EE A OEI N A OE S AA EN l 1 2 IntrOductiOn 10 Maple serrana vy ah ane eee T aoa eee A E A 2 WV OR KUM 1 Wi AOC inte aks hate raced aaet etn E a 2 Starting the Standard Document Interface 2 2 0 0 cece cece ec ene ee ee eeeeeeeenenenees 3 I Tt 2 D M ar sca E E E au mierda ward elnanie som anode ane 5 TOON at OOS x ess han Stein on deck erst Sa cata oi ieee ated ewan mae eee 9 Context Monus and Copy A amp A DraT soassa ana EEN a aaa 11 Savna a Via ples Oe Wiis eian E EE E ENR 18 Lo Entenno TEX OLCSSIONS senare Ae ra EE A AEA A T 18 Execul on CLOUDS erra a aa E a A woe AE 18 Math Mode VS TOXEMOd esete E aA 19 POO e E E E E 21 SYMON P21 1 ok e EA TA A A TAE AEAEE 28 Toolbar Teon Sa rsu ne A E N 30 LA Pomt and C lick linteraciOn nae E E E EAA 32 PS A E E E N 32 iR S SAE 4 teers E ER E E EE ON OE S E EN 31 MUNAD Sos se E E ca gate eats ET A ae i 38 COMTEX MENUS Deneire n sant aban aan wnediedanosbas tamed E SAN 39 TEE F210 a 0 cil okie eee SE E E RR Rr 40 EXPIOraTIOM ASSISTANT arera lea A EE E AEAEE E TA S 43 NS OMAN ae a a a e EN 45 The Maple Tr Dr ary siamrecean an ian a EEES 45 Re Tae tt Gina E E A ae een eon 45 Docum or BOCK Scree ee AC awarl aaa heuer darneeaduentaba tar A S 50 1G The Maple Hen oy Enie E ac eal aaa Heal A E 53 Accessing ING ICI Syste iaaa A a
159. cd see nteger Operations page 106 and Mathematical Problem Solving page 147 generally use only symbolic computation to achieve their results Exact Computations In Maple integers rational numbers mathematical constants such as z and and mathem atical structures such as matrices with these as entries are treated as exact quantities Names such as x y my variable and mathematical functions such as sin x and LambertW k z are symbolic objects Names can be assigned exact quantities as their values and functions can be evaluated at symbolic or exact arguments l golt Important Unless requested to do otherwise see the following section Maple evaluates expressions containing exact quantities to exact results as you would do if you were per forming the calculation by hand and not to numeric approximations as you normally obtain from a standard hand held calculator gt sin 1 sin 7 sin x sin 1 0 sin x gt ftant di i In cos f 4 2 Floating Point Computations In some situations a numeric approximation of an exact quantity is required For example the plot command requires the expression it is plotting to evaluate to numeric values that can be rendered on the screen a cannot be so rendered but 3 14159 can be Maple distin 104 4 Basic Computations guishes approximate from exact quantities by the presence or absence of a decimal point a 19 1 9 is approximate whil
160. certainty 138 units 137 using 134 value 136 value and units 137 Scientifi Constants Assistant 36 ScientificConstant package description 85 ScientificConstant package 133 extensibility 138 objects 136 ScientificErrorAnalysi package description 85 ScientificErrorAnalysi package 138 434 Index extensibility 141 objects 139 search help system 55 sections in worksheet 294 security levels auto execute 304 security tab options dialog 304 select command 376 selection execute 9 selectremove command 376 semicolon 79 80 seq command 375 series 178 command 178 plotting 179 Taylor 178 type 179 sets 334 shape option 163 show worksheet content 297 show contents dialog using 297 significan digits 104 simplify command 348 355 sketch pad canvas style 298 slider embedding 326 Slider component 387 Snippets palette 28 solutions assigning as expression 118 assigning as function 119 details 124 formal 124 formal power series 124 integers 125 real 141 series 124 verifying 118 solve equations 111 for real solutions 141 numerically 116 symbolically 113 inequations 111 for real solutions 141 symbolically 113 integer equations 125 linear system 125 170 modular integer equations 125 ODEs 120 PDEs 124 recurrence relation 126 transcendental equations 115 solve command 113 336 findin all solutions 115 findin parametric solutions 116 real solutions
161. ces to perform many tasks without the need to use any syntax An example of an assistant is shown in Figure 1 4 M Optimization Assistant g Saver Probes Local Defaut Objective Function 3 F x y C Nonlinear Constraints and Bounds xe 0 5 y 0 5 Options TEA x y 6 gt Miremize E Maximize Feasidty Tolerance def au nil values Smuka Objective value 134 491161539748162 Optimality Tolerance Cet auk x 4 53555292535125 7 1 46440707460871 iteration Limi defy infinie Bound def aust On Quit Return Solution x Figure 1 4 Optimization Assistant Using the Tools Assistants menu you can access tools to help you accomplish various tasks See Figure 1 5 In some cases you can launch an assistant by entering an expression and selecting the assistant from the context menu that displays 1 4 Point and Click Interaction 33 Tools Window Help Assistants k Back Solver Tutors e Curve Fitting i l Tasks b Data Analysis ri Demonstrations Equation Manipulator Import Data Load Package b oiai ae Paia Installer Builder Spellcheck FF Library Browser Complete Command Ctrl 5pace Maplet Builder Help Database k ODE Analyzer Optimization Options Plot Builder Scientific Constants Special Functions Units Calculator Worksheet Migration CAD Link Figure 1 5 Accessing the Assistants from the Tools Menu 34 1 Getting Started Example 7 Curve
162. cify a constant using either its name or symbol Accessing Constant Definition The GetConstant command in the ScientificConstan s package returns the complete definitio ofa constant To view the definitio ofthe Newtonian gravitational constant specify the symbol G or its name in a call to the GetConstant command gt with ScientificConstants gt GetConstant G i er 11 Newtonian_constant_of_gravitation symbol G value 6 673 10 uncertainty E 1 0107 units 9 kgs For information on accessing a constant s value units or uncertainty see Value Units and Uncertainty page 136 Element Properties Maple also contains element properties and isotope properties 4 5 Units Scientifi Constants and Uncertainty 135 Elements Maple supports all 117 elements of the periodic table Each element has a unique name atomic number and chemical symbol You can specify an element using any of these labels For a complete list of supported elements refer to the ScientificConstants element help page Maple supports key element properties including atomic weight atomicweight electron affinit electronaffinit and density For a complete list of element properties refer to the ScientificConstants p operties help page Isotopes Isotopes variant forms of an element that contain the same number of protons but a different number of neutrons exist for many elements To see the list of supporte
163. circle cross diagonalcross diamond point solidbox solidcircle or soliddiamond for 2 D plots asterisk box circle cross diagonalcross diamond point solidsphere or sphere for 3 D plots Define a title for the plot Define the thickness of lines in the plot transparency 3 D Controls the transparency of the plot surface view Define the minimum and maximum coordinate values of the axes displayed on the screen For a complete list of plot options refer to the plot options and plot3d options help pages 268 6 Plots and Animations gt plot Si x x 20 20 title Plot of the Sine Integral titlefont HELVETICA 12 color Niagara 2 style point Plot of the Sine Integral To create a smoother or more precise plot calculate more points using the numpoints option 6 4 Analyzing Plots 269 y gt plot3d 10 10 y 10 10 axes boxed numpoints 1500 J P Hehimodii light3 shading zgrayscale orientation 160 20 style patchnogrid 6 4 Analyzing Plots Point Probe Rotate Pan and Zoom Tools To gain further insight into a plot Maple offers various tools to analyze plot regions These tools are available in the Plot menu menu Context Bar and in the context menu under Transform when the plot region is selected Table 6 4 Plot Analysis Options Point probe Display the coordinates corresponding to the cursor position on a two di 2 D mensional plot in the cont
164. ckly performing calculations You can enter a mathem atical expression and then evaluate manipulate solve or plot it with a few keystrokes or mouse clicks This chapter provides an overview of Document mode Document mode sample Find the value of the derivative of Inla at x 4 differentiate w r t x dy evaluate at point g 2 In x 1 cee T 6l 62 2 Document Mode T X 1 sinf dx sin x aif x Tt T 0 Integrate sin over the interval 0 z Worksheet mode is designed for interactive use through commands and programming using the Maple language The Worksheet mode supports the features available in Document mode described in this chapter For information on using Worksheet mode see Chapter 3 Worksheet Mode page 77 Note To enter a Maple input prompt while in Document mode click in the Maple toolbar Important In any Maple document you can use Document mode and Worksheet mode Interactive document features include e Embedded graphical interface components like buttons sliders and check boxes e Automatic execution of marked regions when a fil is opened e Tables e Character and paragraph formatting styles e Hyperlinks These features are described in Chapter 7 Creating Mathematical Documents page 281 Note This chapter and Chapter 1 were created using Document mode All of the other chapters were created using Worksheet mode 2 3 Entering Expressions Chapter 1 provided
165. completion it is inserted Otherwise a list of possible matches is displayed 3 Select the correct completion from the list fimear LinearAlgebra LinearA lzebra A Linear lgebra Add linear combination Lineardigebra Add Mul Mrz i Linear4lgebral add linear combination with scalars and constructor options Uneardicebra Add v i ve xl x2 Lin ardlgebral add linear combination with scalars OnearAlpebra Add i ivi Mve xl xe Linear dlgebral Add linear combination with scalars constructor options and overvrite TinearAlgebra Add Jiv Linear Algebra 4djoint square Matrix OneorAleedra Adjoint if Linear 4lgebraL adjoint square Matrix with constructor options Gneardigebra Adfotnt i oufpufopiions fst Linear Algebra BackwardSubstitute tupper row echelon OneardAlpebra Backward ubsttute Ji M Linear lgebra BackwardSubstituke upper row echelon OneorAleebra Backwardoubsttute J Jf M Linear Algebra BackwardSubstitute tupper row echelon with options and overwrite Lineardigebra Backhwardau Linear Algebra BackwardSubstitute upper row echelon with options OnearAlcebre Backward substitute Mv linear GloehralRandMatris Frac scalars MinaardAlcahral Randifatar ii iri r3 wil Mm gt 4 Some inserted commands have placeholders denoted by purple text The firs placeholder is highlighted after you insert it into the document Replace it with your parameter then move to the next placehold
166. cters are not replaced For example defin a function that squares its argument gt square x gt x 2 gt square 32 1024 For more information on functions see Functional Operators page 339 Protected Names Protected names are valid names that are predefine or reserved If you attempt to assign to a protected name Maple returns an error gt sin 2 Error attempting to assign to sin which is protected For more information refer to the type protected and protect help pages Unassigning Names The unassign command resets the value of a name to itself Note You must enclose the name in right single quotes gt unassign a gt a a Right single quotes unevaluation quotes prevent Maple from evaluating the name For more information on unevaluation quotes see Delaying Evaluation page 361 or refer to the uneval help page See also Unassigning a Name Using Unevaluation Quotes page 362 3 10 Equation Labels 95 Unassigning all names The restart command clears Maple s internal memory The effects include unassigning all names For more information refer to the restart help page Note To execute the examples in this manual you may be required to use the unassign or restart command between examples Valid Names A Maple name must be one of the following e A sequence of alphanumeric and underscore _ characters that begins with an alphabet ical character Note To enter an underscor
167. ction 2 Display the context menu See Figure 2 2 3 From the context menu select Approximate and then the number of significan digits to use 5 10 20 50 or 100 3 Copy Special b Paste Ctrl Evaluate and Display Inline Ctri Explore 4pply a Command Approximate RO 455i9gn to a Mame Denominator z Numerator a0 More ee ee 2 D Math Figure 2 2 Approximating the Value of a Fraction 70 2 Document Mode at 10 digits 0 6666666667 w N You can replace the inserted right arrow with text or mathematical content To replace the right arrow 1 Select the arrow and text Press Delete 2 Enter the replacement text or mathematical content Note To replace the right arrow with text you must firs press F5 to switch to Text mode For example you can replace the arrow with the text is approximately equal to or the 0 660666666667 w N Solving an Equation You can fin an exact symbolic solution or an approximate numeric solution of an equation For more information on symbolic and numeric computations see Symbolic and Numeric Computation page 102 To solve an equation 1 Enter an equation 2 Display the context menu See Figure 2 3 3 From the context menu select Solve or Numerically Solve in the Solve menu item 2 6 Performing Computations 71 Copy Special d Paste Ctrl V Evaluate and Display Inline Ctri Explore 4pooly a Command
168. ctions on entering this phrase see X Example 6 Enter Text and 2 D Math in the Same Line Using Toolbar Icons page 30 in Chapter 1 3 Select the expression Control click for Macintosh to display the context menu 4 Click the Evaluate and Display Inline menu item The expression is evaluated 5 Check that the input mode is Text then enter the rest of the sentence in the same plot See Figure 7 10 300 7 Creating Mathematical Documents 7 a M oe oe ee d Plot the expression sin x and its derivative a sin x x Before A Copy Special gt Paste Ctrl Evaluate and Display Inline Ctrl Explore Apply a Command Assign to a Name Collect gt Combine gt Differentiate gt Evaluate at a Point Integrate gt Limit Plots gt Series gt Simplify gt Solve gt More gt Help on Command 2 D Math gt After Plot the expression sin x and its derivative gt sin x cos x in the same plot Figure 7 10 Working with Document Blocks Result plot create a two dimensional plot Calling Sequence plot f x plottf x x0 x1 plotivl v2 Parameters f expression in independent variable x Z independent variable x0 x1 left and right endpoints of horizontal range x 2 coordinates and y coordinates Plot the expression sin x and its derivative res sin x cos x in the same plot Inline Document Output Document blocks can display content inli
169. custom help system consisting of almost 5000 reference pages The help system is a convenient resource for determining the syntax of Maple com mands and for learning about Maple features Accessing the Help System There are several ways to access the Maple help system e From the Help menu select Maple Help e Click 28 in the toolbar 54 1 Getting Started To get help on a specifi word e Ina document place the insertion point in a word for which you want to obtain help From the Help menu select Help on Alternatively press F2 Control for Macintosh to access context sensitive help e Ina document execute the command topic for example enter LinearAlgebra and press Enter The Maple help system opens in a separate window with two panes The left pane contains the Help Navigator where you initiate searches and browse the table of contents and the right pane displays the fina search result such as a specifi help page Didapte 14 Hedy foie Jo fre Cm Vew oy Heb n et Swe erg Sead For Tox Tew gt faia m row LSOIVE cotve one or meee equations edag Noating poist arithmetic Peearces At w Staates aan Y Calling Sequence ale of Corterts Seach Rents a i r fsolvel equations variables complies 4 QO attire Rated al UWr New y Crete Magee Wort heet Param eters Dare Worbaheet j n 2 meia P equations CFU IA AGUTIO EITEL idf eipweitiory Lil epucrion procer e Lil procedure n Ua
170. d The evalf command returns a floating poin or complex floating point number or expres sion gt evalf cos zi x 3 0 8660254040 gt eval 9 814954579 x x 23 14069264 gt evalf t 3 141592654 By default Maple calculates the result to ten digits of accuracy but you can specify any number of digits as an index that is in brackets gt evalf 40 z 3 141592653589793238462643383279502884 197 For more information refer to the evalf help page See also Numerically Computing a Limit page 173 and Numeric Integration page 181 8 3 Working with Maple Expressions 357 Evaluating Complex Expressions To evaluate a complex expression e Use the evale command If possible the evale command returns the output in the canonical form expr1 i expr2 In 2 D Math input you can enter the imaginary unit using the following two methods In the Common Symbols palette click the i or j item See Palettes page 21 e Enter i or j and then press the symbol completion key See Symbol Names page 28 gt evalc J Ll 1 gt evale sin 3 5j sin 3 cosh 5 Icos 3 sinh 5 In 1 D Math input enter the imaginary unit as an uppercase 1 I gt evalc 2 1 I 2 cos In 2 21 sin In 2 Evaluating Boolean Expressions To evaluate an expression involving relational operators gt lt lt and e Use the evalb command Note In 1 D Math input enter lt and
171. d See Figure 7 5 For either action continue 2 Select the properties for the new character style such as font size attributes and color In the font attributes the Superscript and Subscript check boxes are mutually exclusive When you select one of the two check boxes the other is disabled You must clear one before selecting the other Note A preview of the style is displayed in the last row of the Character Style dialog 3 To save the style click OK or to abandon click Cancel If you have modifie a style all text in your document that uses the altered style is updated to reflec the changes 290 7 Creating Mathematical Documents w Character Style a aa ne sb ro era Comm Bold js a C taic oO Underlined B Superscript Subscript Arial Rounded MT Bold a Arial Unicode MS Berlin Sans FE Demi Maplesoft p o Figure 7 5 Definin a Character Style For example in the pasted text suppose we want to create a character style for the bold purple parameter e From the Format menu select Styles then click Create Character Style e Enter the style name Placeholder and then select the character attributes In this case click the Bold check box Then click the Color button and choose a dark purple Click OK to create the character style Now you can apply the style to any text Under Calling Sequences select each list of parameters inside the command To apply
172. d isotopes for an element use the GetIsotopes command gt Getlsotopes element L1 kis bis io Lie Oe 6 a Maple supports isotopes and has a distinct set of properties for isotopes including abundance binding energy bindingenergy and mass excess massexcess For a complete list of isotope properties refer to the ScientificConstants p operties help page Accessing an Element or Isotope Property Definition The GetElement command in the ScientificConstan s package returns the complete definitio ofan element or isotope 136 4 Basic Computations gt GetElement L 3 symbol Li name lithium names lithium electronaffinity value 0 6180 uncertainty 0 0005 units eV atomicweight value 6 941 uncertainty 0 002 units amu boilingpoint value 1615 uncertainty undefined units K ionizationenergy value 5 3917 uncertainty undefined units eV density value 0 534 uncertainty undefined E 3 cm units electronegativity value 0 98 uncertainty undefined units meltingpoint value 453 65 uncertainty undefined units K gt GetElement Li 41 Li y Massexcess value 25320 173 uncertainty 212 132 units keV bindingenergy value 4618 058 uncertainty 212 132 units keV atomicmass value 4 027 182329 10 uncertainty 227 733 units uam u Value Units and Uncertainty To use constants or
173. dd the windows and doors Constructing a Maplet is no different First defin the rows and columns of the Maplet application and then proceed to add the body elements such as buttons text fields and plot regions Simple Maplet A Maplet application can be define using the commands in the Maplets Elements package and then launched using the Maplets Display command The following commands defin and run a very simple Maplet application that contains the text string Hello World gt with Maplets Elements gt MySimpleMaplet Maplet Hello World gt Maplets Display MySimpleMaplet FE Ed Maplet Hello World Figure 10 6 A Simple Maplet Maplet Builder To start the Maplet Builder e From the Tools menu select Assistants Maplet Builder 10 5 Authoring Maplets 399 Layout Pane B Maplet Builder Untitled Maplet BAX File Help A vw Y Body p r Buttont S ea aga background sl V y El aml E a a me caption Button a E le fe Ao enabled true c PS cy font Dialog imade ayaga g onclick clickButtont ke reference Button tooltip Y Menu visible true al gay g Y ToolBar fe T Di TEETE I E REAA Al e 3 z K gt Layout JA Tun A Action RuriWindow1 clickButtont gt Command Command Pane Properties Pane Palette Pane Figure 10 7 Maplet Builder Interface The Maplet
174. dimension Maple supports over 40 units of length in cluding feet miles meters angstroms microns and astronomical units A length must be measured in terms of a unit for example a length of 2 parsecs Table 4 4 lists some dimensions their corresponding base dimensions and example units 128 4 Basic Computations Table 4 4 Sample Dimensions Time time second minute hour day week month year millennium blink lune Energy a 7 joule electron volt erg watt hour ength Mass i f E calorie Calorie British thermal unit time Electric potential a a volt abvolt statvolt ength mass fo time electric current For the complete list of units and their contexts and symbols available for a dimension refer to the corresponding help page for example the Units length help page for the units of length Each unit has a context The context differentiates between different definition of the unit For example the standard and US survey miles are different units of length and the second is a unit of time and of angle You can specify the context for a unit by appending the context as an index to the unit for example mile US_ survey If you do not specify a context Maple uses the default context Units are collected into systems for example the foot pound second FPS system and in ternational system or syst me international SI Each system has a default set of units used for measurements In the
175. ding those listed in Table 4 1 Table 4 1 Select Integer Commands abs absolute value displays in 2 D math as a factorial displays in 2 D math as a ged dereatest common divisor quo dquotentofinteger division SSCS S mod modular arithmetic See Finite Rings and Fields page T09 numtheory divisors set of positive divisors 108 4 Basic Computations gt iguo 209 17 12 gt irem 209 17 5 gt igced 2024 4862 22 gt iroot 982523 4 31 For information on findin integer solutions to equations see Integer Equations page 125 Non Base 10 Numbers and Other Number Systems Maple supports e Non base 10 numbers e Finite ring and fiel arithmetic e Gaussian integers Non Base 10 Numbers To represent an expression in another base use the convert command gt convert 6000 binary 1011101110000 gt convert 34271 hex 385DF For information on enclosing keywords in right single quotes see Delaying Evaluation page 361 You can also use the convert base command gt convert 34271 base 16 15 13 5 8 3 4 3 Integer Operations 109 Note The convert base command returns a list of digit values in order of increasing signi ficanc Finite Rings and Fields Maple supports computations over the integers modulo m The mod operator evaluates an expression over the integers modulo m gt 27 mod 4 3 By default
176. display functions computations and theorems in various ways including stepping through important computations The Student package contains the following subpackages Calculus single variable calculus LinearAlgebra linear algebra MultivariateCalculus multivariate calculus NumericalAnalysis numerical analysis Precalculus precalculus VectorCalculus multivariate vector calculus The Units package contains commands for unit conversion and provides environments for performing calculations with units It accepts approxim ately 300 distinct unit names for example meters and grams and over 550 units with various contexts for example standard miles and U S survey miles Maple also contains two Units palettes that allow you to enter the unit for an expression quickly The Vector Calculus package is a collection of commands that perform multivariate and vector calculus operations A large set of predefine or thogonal coordinate systems is available All computations in the package can be performed in any of these coordinate systems It contains a facility for adding a custom but orthogonal coordinate system and using that new coordinate system for your computations Palettes are collections of related items that you can insert by clicking or dragging For ex ample see Figure 3 1 3 4 Palettes 87 Y Expression i e aE a N er ran fa 2J Ii af a i i lim f ath a b ab gt T g D dl a ja va a lal e I
177. dow or the zoom factor If the table exceeds the width of the document window the horizontal scroll bar can be used to view the rightmost columns Note Using this option tables may be incomplete when printed Modifying the Appearance of a Table Table Borders The style of exterior and interior borders is set using the Table Properties dialog From the Table menu select Properties e You can set all none or only some of the borders to be visible in a table Exterior borders are controlled separately e You can control the visibility of interior borders by using the Group submenu of the Table menu grouping rows or columns suppresses interior borders provided that the interior border style is set by row and column group 7 4 Tables 309 For example group the columns together and group rows 2 to 4 together Then in the Table Properties dialog select Exterior Borders Top and bottom and Interior Borders By row and column group fix E f x Plot of f x and i x l i 2 7 l ya PA a La 1 i 7 Es i ES ai x Ba E sin wx el5 cos x we 5 sin x e 2 sin x 8sin x cos x dx e Hidden borders are visible when the mouse hovers over a table Note You can hide the visibility of lines on mouse pointer roll over by using the View Show Hide Contents dialog and clearing the Hidden Table Borders check box Alignment Options The table alignment tools control the horizontal alignment of columns and
178. ds Command Description mul Compute numeric product Return operands that satisfy a condition Return operands that do not satisfy a condition 9 3 Iterative Commands 375 selectremove Return operands that satisfy a condition and separately return operands that do not satisfy a condition map o o o Apply command to the operands of an expression zip o Apply binary command to the operands of two lists or vectors Creating a Sequence The seq command creates a sequence of values by evaluating a specifie expression over a range of index values or the operands of an expression See Table 9 3 Table 9 3 The seq Command seq expression name initial fina gt seq exp x x 2 0 seq expression name in expression gt seq u u in Pi 4 Pi 2 2 1 Pi da 4 3 Adding and Multiplying Expressions The add and mul commands add and multiply sequences of expressions over a range of index values or the operands of an expression See Table 9 4 Table 9 4 The add and mul Commands add expression name initial fina gt add exp x x 2 4 2 3 4 e e e mul expression name initial fina gt mul 2 x x 1 10 3715891200 376 9 Basic Programming add expression name in expression gt add u u in Pi 4 Pi 2 Pil TT mul expression name in expression gt mul u u in Pi 4 Pi 2 Pi 3 n i 8 The endpoints of the index range initial and fina in th
179. e 9 From the Miscellaneous group box in the Grid Size drop down menu select 40 40 Plot the expression 10 Click Plot To see the Maple syntax used to generate this plot see Maple commands from Creating Plots Interactive Plot Builder page 249 6 2 Creating Plots 243 Example 4 Display a conformal plot Maple can display a conformal plot of a complex expression mapped onto a two dimensional grid or plotted on the Riemann sphere in 3 D Launch the Interactive Plot Builder and enter an expression 1 Add the expression z 3 In the Select Plot Type window 2 From the Select Plot group box select 2 D conformal plot of a complex valued function 3 Change the range of the z parameter to 0 2 2 I In the Plot Options window 4 From the Axes group box select normal 5 From the Miscellaneous group box select the Grid Size drop down menu option 30 30 Plot the expression 6 Click Plot Example 5 Display a plot in polar coordinates Cartesian ordinary coordinates is the Maple default Maple also supports numerous other coordinate systems including hyperbolic inverse elliptic logarithmic parabolic polar and rose in two dimensions and bipolar cylindrical bispherical cylindrical inverse elliptical cylindrical logarithmic cosh cylindrical Maxwell cylindrical tangent sphere and toroidal in three dimensional plots For a complete list of supported coordinate systems refer to the coords help page
180. e 10 8 exact Note An alternative representation of floating poin numbers called e notation may not include an explicit decimal point Je5 100000 3e 2 03 In the presence of a floating poin approximate quantity in an expression Maple generally computes using numeric approximations Arithmetic involving mixed exact and floating point quantities results in a floating poin result hee 4 3 2 166666667 If a mathematical function is passed a floating poin argument it normally attempts to produce a floating poin approximation of the result 1 0 gt sin 1 5 e dx 0 0 0 9974949866 1 718281828 Converting Exact Quantities to Floating Point Values To convert an exact quantity to a numeric approximation of that quantity use the evalf command or the Approximate context menu operation see Approximating the Value of an Expression page 69 v u gt evalf n evalf sin 3 evalf t 3 141592654 0 141 1200081 1 833333333 By default Maple computes such approximations using 10 digit arithmetic You can modify this in one of two ways e Locally you can pass the precision as an index to the evalf call gt evalf 20 exp 2 evalf r R 7 3890560989306502272 1 354117939 e Globally you can set the value of the Digits environment variable 4 2 Symbolic and Numeric Computation 105 gt Digits 25 gt eval tan 5 For more information see the evalf and Digits help pages
181. e Clickable Calculus e The help system e Online resources Preface xix e Performing computations e Creating plots and animations e The Maple programming language e Using and creating custom Maplet applications e File input and output and using Maple with third party products e Data structures For a complete list of manuals study guides toolboxes and other resources visit the Maplesoft web site at http www maplesoft com Audience The information in this manual is intended for first tim Maple users and users looking for a little more information Conventions This manual uses the following typographical conventions e bold font Maple command package name option name dialog menu or text fiel e italics new or important concept e Note additional information relevant to the section e Important information that must be read and followed Customer Feedback Maplesoft welcomes your feedback For suggestions and comments related to this and other manuals contact doc maplesoft com xx Preface 1 Getting Started Don t worry about your difficultie in Mathematics I can assure you mine are still greater Albert Einstein Mathematics touches us every day from the simple chore of calculating the total cost of our purchases to the complex calculations used to construct the bridges we travel To harness the power of mathematics Maplesoft provides a tool in an accessible and com plete form Tha
182. e Efficien Computation MPS X File Support Statistics page 189 Performing statistics compu Probability Distributions and Random Variables tations using the Statistics package Statistical Computations Plotting Teaching and Learning with Maple page 194 Table of Student and Instructor Resources Student and Instructor resources for using Maple j Student Packages and Tutors in an academic setting 147 148 5 Mathematical Problem Solving Clickable Math page 209 Solve math problems Step by Step examples using some of the interactive methods available in Maple 5 2 Algebra Maple contains a variety of commands that perform integer operations such as factoring and modular arithmetic as described in Integer Operations page 106 In addition it supports polynomial algebra For information on matrix and vector algebra see Linear Algebra page 155 Polynomial Algebra A Maple polynomial is an expression in powers of an unknown Univariate polynomials are polynomials in one unknown for example x 2x 13 Multivariate polynomials 4s 3 3 2 are polynomials in multiple unknowns such as xy gt VY 7x The coefficient can be integers rational numbers irrational numbers floating poin numbers complex numbers variables or a combination of these types Pj gt ax x N gt gt l ax 7x b ax x 7 Arithmetic The polynomial arithmetic operators are the stand
183. e Purposes Ranges and Plot Options On Plot return plot command Fi Select Variable Purposes Ranges and Flot Options 4 Modify the plot range to x 0 to 2 Pi On Plot return plot command 5 Click Plot to display the plot in the document 6 From the graph we can see all of the solutions within the interval 0 2 To approximate the values click the plot select the type of co ordinates that you want to view from the selec tion menu Cw in the toolbar and then use the point probe tool to view the coordinates of the mouse pointer 5 8 Clickable Math 223 Solution by Task Template 1 From the Format menu select Tasks 5 5 Algebra Browse Expand the Algebra folder and Complete the Square select Solve Analytically in a Specifie Complex Arithmetic Interval bbe Conic Analysis and Graph vee Solve a Set of Equations Symbolically se Salve an Equation Numerically sne Salve an Equation Symbolically Solve an Inequality be Solve Analytically in Specified Interval 2 Click Insert Minimal Content Solve Analytically in a Specified Interval Ent ion T n nter an expression gt 12 sin x as sin x 3 12 sina 5 sins 3 15 gt Student Calculus Roots 15 0 2 2 ope Ta 2 arcsin arcsin T arcsin 5 16 T arcsin 2 r Express the roots in gt evalf 16 i i gt 0 8480620790 2 293530575 3 481429564 17 5 943343398
184. e add and mul calling sequence must evaluate to numeric constants For information on symbolic sums and products refer to the sum and product help pages Selecting Expression Operands The select remove and selectremove commands apply a boolean valued procedure or command to the operands of an expression For information on operands refer to the op help page e The select command returns the operands for which the procedure or command returns true e The remove command returns the operands for which the procedure or command returns false or FAIL e The selectremove command returns two expressions of the same type as the input expres sion The firs consists of the operands for which the procedure or command returns true The second consists of the operands for which the procedure or command returns false or FAIL The structure of the output is the same as the structure of the input See Table 9 5 For information on Maple procedures see Procedures page 378 Table 9 5 The select remove and selectremove Commands select proc_cmd expression gt select issqr 198331 889249 11751184 9857934 89249 11751184 9 3 Iterative Commands 377 remove proc_cmd expression gt remove var gt degree var gt 3 2 x 3 y y S x Zz selectremove proc_cmd expression gt selectremove x gt evalb x gt round x sin 0O sin 1 sin 3 0 1411200081 0 0 8414709848 For info
185. e arie a TE AEEA e 98 Features of Equation LAD IS ates ie Coa itera eae ee Genwi ceatlel cclatteaca rccand 99 4 Basic COMPU CALIOMS cererii a has cia nen ates oud E Lana deeee 101 A Ta THis Chapter ohiact sock nankncetdatt n a a a a ee 101 4 2 Symbolic and Numeric Computation cccceccececeneeeeceeeeeeseneeeesenenes 102 Fact omputat ions einga a a N a a tel cea Darel 103 Floating Point Computations s sccescidacedesiwtceectainddaiaeviadie eh Me deloeeean hades 103 Converting Exact Quantities to Floating Point Values ccccceeeeee eee es 104 DOULC ESOL E TO opne Ta a ants ues nS Titan GE E 105 A Mite CCl Operation S ited od beet Salute Galatta e a als utente aluncenatenade Gee Ree 106 Contents v Non Base 10 Numbers and Other Number Systems ccccceseeeeeeeees 108 AA Solving EQUATIONS enine ea ETE ETRE sinha einen aume ae Rolo pine ei 111 Solving Equations and Inequations nsonnsonnesenssnnnssenssressrressresreesseesse 111 Other specialized Solver eiie e heath a a ieee eee 120 4 5 Units Scientifi Constants and Uncertainty cc cece cece ccec eee eeeeeeneees 127 OTa acetone ees tra E ese A ites et testes chan tania EAA Se wea tala eee E 127 Scientifi Constants and Element Properties c ccccccceeec ee eeeeeeneeeeees 133 Uncertainty Propatatio N eaii a tented 138 AO Resmen th WO aii ict ii eset eea a e aa 141 Real Number Donat cwasccma ma E a TA N E E 141 ASSU
186. e character in 2 D Math enter a backslash character followed by an underscore character that is _ e A sequence of characters enclosed in left single quotes C Important Do not begin a name with an underscore character Maple reserves names that begin with an underscore for use by the Maple library Examples of valid names ca e al e polynomial e polynomiall divided_by_polynomial2 e 2a xy 3 10 Equation Labels Maple marks the output of each execution group with a unique equation label Note The equation label is displayed to the right of the output gt dinta de cos x 3 4 Using equation labels you can refer to the result in other computations 96 3 Worksheet Mode gt 3 4 dx sin x 3 5 Displaying Equation Labels Important By default equation labels are displayed If equation label display is turned off complete both of the following operations e From the Format menu select Equation Labels and then ensure that Worksheet is selected Inthe Options dialog Tools Options on the Display tab ensure that Show equation labels is selected Referring to a Previous Result Instead of re entering previous results in computations you can use equation label references Each time you need to refer to a previous result insert an equation label reference To insert an equation label reference 1 From the Insert menu select Label Alternatively press Ctrl L Command L Mac
187. e following example a camera path is specifie to zoom into and view different sides of the plot surface 276 6 Plots and Animations gt plot3d sin x y x 1 1 y 1 1 shading xyz viewpoint path 50 x 90 cos x 100 sin x x 2 2 2 6 7 Playing Animations Animation Context Bar To run the animation click the plot to display the Animate context bar Table 6 6 Animation Options Name dieon SSS S i scription Frame ation a a Current caret 20 Slider control for viewing individual Frame frames of an animated plot 6 8 Customizing Animations 277 Forward a Forward Play the animation forward Oscillate Oscillate Play the animation forward and backward Backward Backward Play the animation back ward Single T Single Run the animation in single cycle mode The animation is dis Continuous played only once Continuous Run the animation in continuous mode The animation re peats until you stop it Frames per gt eE Set the animation to play at a faster or second gt slower speed Point probe i Determine the coordinates of a 2 D amp i plot at the position of the cursor Zoom Zoom into or out of the plot by chan ging the view ranges Pan aM Pan the plot by changing the view ranges Rotate 3 D uy Rotate a three dimensional plot to see it from a different point of view You can also run the animation using the context menu or the Plot m
188. e in the assistant refer to the Import Matrix help page 11 3 Reading from Files 411 Reading Expressions from a File You can write Maple programs in a text fil using a text editor and then import the fil into Maple You can paste the commands from the text fil into your document or you can use the read command When you read a fil with the read command Maple treats each line in the fil as a com mand Maple executes the commands and displays the results in your document but it does not by default insert the commands from the fil in your document For example the fil ks txt contains the following Maple commands S n gt sum binomial n beta 2 beta 2 beta beta beta beta 1 n S 19 Note that the fil should not contain prompts gt at the start of lines When you read the file Maple displays the results but not the commands B 1 102493736166664459807 1 1143287693 17982974 11 6 S 1 gt binomial 7 B Le p J 2 gt filename cat kernelopts datadir kernelopts dirsep ks txt gt read filename i 26 S 1 binomial n B 2B B p B 2P 1024937361666644598071 1 143287693 17982974 11 7 If you set the interface echo option to 2 Maple inserts the commands from the fil into your document 412 e 11 Input Output and Interacting with Other Products gt interface echo 2 read filename gt S n gt sum binomial n beta 2 beta 2
189. e plot or draw shapes and enter text on the plot region By clicking an animation region you have the same features available for a plot region in ad dition to tools for playing the animation in the Animation icon For details on plots and animations refer to Plots and Animations page 237 For the remaining icons hover the mouse over the icon to display the icon description Context Menus and Copy amp Drag Context Menus Maple dynamically generates a context menu of applicable options when you right click an object expression or region The options available in the context menu depend on the selected input region For example you can manipulate and graph expressions enhance plots format text manage palettes structure tables and more When using context menus 12 1 Getting Started to perform an action on an expression the input and output are connected with a self docu menting arrow or equal sign indicating the action that had taken place For more information see Context Menus page 39 Copy amp Drag With Maple you can drag input output or curves in a plot region into a new input region This is done by highlighting the input or selecting the curve and dragging it with your mouse into a new input region Dragging the highlighted region will cut or delete the original input To prevent this use the copy and drag feature e Ctrl drag Windows and UNIX e Command drag Macintosh That is highlight the region y
190. e pointer You can evaluate expressions using context menus The Evaluate and Display Inline op eration see Figure 2 1 is equivalent to pressing Ctrl Command for Macintosh That is it inserts an equal sign and then the value of the expression Alternatively press Enter to evaluate the expression and display the result centered on the following line For more information on evaluation see Evaluating Expressions page 65 From the context menu you can also select operations different from evaluation To the right of the expression Maple inserts a right arrow symbol and then the result 2 6 Performing Computations 69 For example use the Approximate operation to approximate a fraction 2 at 10 digits 0 6666666667 ww t You can perform a sequence of operations by repeatedly using context menus For example to compute the derivative of cosh use the Differentiate operation on the expression and then to evaluate the result at a point use the Evaluate at a Point operation on the output and enter 10 differentiate w r t x 7 evaluate at point x cos x 2 sinl 20 sin 100 The following subsections provide detailed instructions on performing a few of the numerous operations available using context menus Figures in the subsections show related context menus or palettes Approximating the Value of an Expression To approximate a fraction numerically 1 Enter a fra
191. e square onthe left sde w Reban Rest EJ Equation Manipulator x 7 x 1 4 x 1 4 x 4 x 7 3 x 1 4 x 4 0 C Show steps stacked vertically History El x 7 2 x 1 2 4 x 1 2 4 x 4 2 E2 lhs E1 rhs E1i 0 Undo Redo Power Square both sidas Take square root of both sides Addition Raise both sides to power 3 Group terms on left Miscellaneous Operations Apply to both sides Apply expand to leftside Do Complete the square on the left side exp 218 5 Mathematical Problem Solving Factor the equation i Apply to leftside w Do 5 From the same drop down menu select factor and click Do 6 Click Return Steps to close the dialog and re gt gt gt 3 x 7 x 1 4 x 1 x 4 turn all of the steps to the Maple document manipulate equation x 7 x 1 4 x 1 4 x 4 4 x 7 3 x 1 4 x 4 7 0 6x 24x 18 0 6 x 1 x 3 0 7 Ctrl drag the factored form of the original solutions for x j 6 x 1 x 3 0 gt 1 3 equation to a new document block region 8 Right click and select Solve Obtain Solu tions for x Instant Solution To apply an instant solution to this problem use context menus l a the ane x 7 x 1 _ 4 x _ 1 x 4 x 7 x 1 4 x 1 x 4 to a new document block
192. e through the Maple Help System Help Pages Use the help system to fin information about a specifi topic command package or feature For more information see The Maple Help System page 53 Dictionary More than 5000 mathematical and engineering terms with over 300 figure and plots 1 From the Help menu select Maple Help 2 Enter a search term Dictionary entries that match your query are displayed in the left pane with a 0 icon Tutorials and the Maple Portal The Maple Portal includes material designed for all Maple users from new users to users who want more advanced tutorials The Maple Portal also includes specifi sections for students math educators and engineers The Maple Portal includes e How Do I topics that give quick answers to essential questions e Tutorials that provide an overview of topics from getting started to plotting data manip ulation and interactive application development e Navigation to portals with specialized information for students math educators and en gineers Access the portal from the Help menu Help Manuals Resources and More Maple Portal Applications and Example Worksheets Applications Sample applications demonstrate how Maple can be used to fin and document a solution to a specifi problem Some applications allow for input or contain animations that you can run however their primary use is for demonstrations Topics include DC Motor Control Design Digital F
193. eb site resource for free applications related to mathematics education science engineering computer science statistics and data analysis finance communications and graphics Many applications are available in translations French Spanish and German You can also search for Education and Research PowerTools which provide free course curricula and are available as add on Maple packages and courses PowerTools are developed by experts in their field to help users configur Maple for research in specifi application areas http www maplesoft com applications Training Maplesoft offers a comprehensive set of complementary training materials From complete training videos to recorded training seminars to downloadable documentation you have many options to get familiar with Maplesoft products In addition whether you are an expert or someone who is considering a new license purchase a custom training session that 1s right for you and or your organization can be created http www maplesoft com support training MaplePrimes A web community dedicated to sharing experiences techniques and opinions about Maple and related products as well as general interest topics in math and computing 60 1 Getting Started http www mapleprimes com Online Help All of Maple s help pages are available online http www maplesoft com support help Technical Support A Maple web site containing FAQs downloads and service packs links to discus
194. ebra Linear algebra operations act on Matrix and Vector data structures You can perform many linear algebra operations using task templates In the Task Browser Tools Tasks Browse expand the Linear Algebra folder 156 5 Mathematical Problem Solving Creating Matrices and Vectors Creating Matrices You can create a Matrix using e The Matrix command e The angle bracket shortcut notation e The Matrix palette see Figure 5 2 When creating a Matrix using the Matrix command there are several input formats available For example enter a list of lists The dimensions of the matrix are inferred from the number of entries given gt Matrix 1 7 0 je sin ot 0 0 se l Tt 0 e sin t 0 0 Se Alternatively use the angle bracket shortcut lt gt Separate items in a column with commas and separate columns with vertical bars gt 1 m 0e sin s rat 0 se Il amp 0 m sin t 0 0 ka Se For information on the Matrix command options see Creating Matrices and Vectors with Specifi Properties page 162 5 3 Linear Algebra 157 Use the Matrix palette to interactively create a matrix without commands y Matrix Rows 2 a Columns 2 Choose Type Custom values v Shape Any 7 Data type any 7 HE Insert Matrix Figure 5 2 Matrix Palette In the Matrix palette you can specify the matrix size see Figure 5 3 and properties To insert a matrix click
195. ed in mathematical physics computa tions RealDomain The Real Domain package provides an environment in which Maple as sumes that the basic underlying number system is the fiel of real numbers instead of the complex number field ScientificConstant The Scientifi Constants package provides access to the values of various physical constants for example the velocity of light and the atomic weight of sodium This package provides the units for each of the constant values allowing for greater understanding of an equation The package also provides units matching for error checking of the solution ScientificEr orAnalysis The Scientifi Error Analysis package provides representation and con struction of numerical quantities that have a central value and an associated uncertainty or error which is a measure of the degree of precision to which the quantity s value is known Various first orde calculations of error analysis can be performed with these quantities Statistics The Statistics package is a collection of tools for mathematical statistics and data analysis The package supports a wide range of common statist ical tasks such as quantitative and graphical data analysis simulation and curve fitting 86 3 Worksheet Mode Package Name Student VectorCalculus 3 4 Palettes The Student package is a collection of subpackages designed to assist with teaching and learning standard undergraduate mathematics The many commands
196. ed you can display the plot or advance to the Plot Options window 240 3 Plot Options window r W 3 D Plot plot3d 6 Plots and Animations fx vd gt sink yi e y 1 Variables ne 2 Pj yl 2 Bj Range From Style default Line deat w Symbol Color none Custom none Light Model default Glossiness none Shading default kal Coordinate System cartesian wt Axes Preview Advanced Settings toa 2 Pj xX Label Orientation horizontal to z Fi y horizontal w horizontal Title Caption YEW Constrained Scaling Fi orthogonal Projection Orientation theta 45 phi 45 Miscellaneous Grid Size 25 25 Transparency default Fill to xy plane 3 Plot Options window Apply plot options Once finished you can display the plot or return the command that generates the plot to the document Example 1 Display a plot of a single variable expression Maple can display two dimensional graphs and offers numerous plot options such as color title and axis styles to customize the plot 6 2 Creating Plots 241 Launch the Interactive Plot Builder 1 Make sure that the cursor is in a Maple input region 2 From the Tools menu select Assistants and then Plot Builder Notes 1 In worksheet mode Maple inserts plots interactive in the Maple document Entering this command at the Maple prompt also opens the Plot Builder 2 Interaction with the document is d
197. element properties you must firs construct a ScientificConstant object To construct a scientifi constant use the Constant command gt G Constant G To construct an element or isotope property use the Element command gt LiAtomicWeight Element Li atomicweight LiAtomicWeight Element Li atomicweight Value To obtain the value of a ScientificConstant object use the evalf command 4 5 Units Scientifi Constants and Uncertainty 137 gt evalf G 1 068912061 10 gt evalf LiAtomic Weight 2 541006042 107 Note The value returned depends on the current system of units Units To obtain the units for a ScientificConstant object use the GetUnit command Ibs b For information on changing the default system of units for example from SI to foot pound second see Changing the Current System of Units page 132 gt GetUnit G gt GetUniLiAtomic Weight Value and Units If you are performing computations with units you can access the value and units for a ScientificConstant object by specifying the units option when constructing the object and then evaluating the object gt evalf Constant G units 3 1 068912061 0 Ib s gt evalf Element Li 5 atomicmass units 1 835022162 107 1b 138 4 Basic Computations Uncertainty The value of a constant is often determined by direct measurement or derived from measured values Hence it has an assoc
198. elements display in the docu ment Larger objects are displayed as a placeholder For example insert a 15 x 15 matrix In the Matrix palette 1 Specify the dimensions 15 rows and 15 columns 2 In the Type drop down list select a matrix type for example Random 3 Click Insert Matrix Maple inserts a placeholder 15 x 15 Matrix Data Type anything Storage rectangular Order Fortran order To edit or view a large matrix or vector double click the placeholder This launches the Matrix Browser See Figure 5 5 5 3 Linear Algebra 161 Browse Matrix x D O w plag vn lt cn O mo Pa ao I cn l m i ae I a PJ I F n wn pl I _ a 1 6 Ea EE a Ph cn at l Go igan L J i A Figure 5 5 Matrix Browser To modify the entries using the Matrix Browser 1 Select the Table tab 2 Double click an entry and then edit its value Press Enter 3 Repeat for each entry to edit 4 When you have finishe updating entries click Done You can view the matrix or vector as a table or as an image which can be inserted into the document For more information refer to the MatrixBrowser help page 162 5 Mathematical Problem Solving To set the maximum dimension of matrices and vectors displayed inline e Use the interface command with the rtablesize option For example interface rtablesize 15 For more info
199. elp pages For more information on matrices and vectors see Linear Algebra page 155 Saving Expressions to a File If you construct a complicated expression or procedure you can save them for future use in Maple If you save the expression or procedure in the Maple internal format Maple can retrieve it more efficient than from a document Use the save command to write the ex pression to a m file For more information on Maple internal fil formats refer to the fil help page 11 3 Reading from Files 409 i Il G i n k 1 Hi 4 i gt gbinomial n k gt In this example small expressions are used In practice Maple supports expressions with thousands of terms gt expr qbinomial 10 4 T _ 8 _ 9 _ 10 expr Ui q U q q U q U q i 4q U 11 3 a a a r aat gt nexpr normal expr nexpr P tq tet a a P i Pre 11 4 r 1 You can save these expressions to the fil qbinom m gt save gbinomial expr nexpr qbinom m Clear the memory using the restart command and retrieve the expressions using the read command gt restart gt read qbinom m gt expr f tao lig i T Q 1 1 1 11 5 For more information on writing to files refer to the save help page 11 3 Reading from Files The most common reason for reading file is to load data for example data generated in an experiment You can store data in a text file and the
200. en Input and Output 1 Place the cursor in the document block region 2 From the View menu select Toggle Input Output Display 302 e 7 Creating Mathematical Documents Input from any executable math or commands is displayed in one instance or only output is displayed Typesetting You can control typesetting and 2 D Math equation parsing options in the Standard Work sheet interface Extended typesetting uses a customizable set of rules for displaying expres sions The rule based typesetting functionality is available when the Typesetting level is set to Extended Tools Options Display tab This parsing functionality applies to 2 D Math editing Math mode only For example you can change the display of derivatives to suit the content and audience of your document fla Tools Options Display tab Typesetting level d n Maple Standard ay gt L ffa dx Tools Options Display tab Typesetting level Ex tended f x To specify rules use the Typesetting Rule Assistant e From the View menu select Typesetting Rules The Typesetting Rule Assistant dialog opens For more information see the Typesetting TypesettingRuleAssist and OptionsDialog Display help pages Auto Execute The Autoexecute feature allows you to designate regions of a document for automatic exe cution These regions are executed when the document opens or when the restart command is executed This is useful when
201. ent cells in a table select the cells you would like to merge From the Table menu select Merge Cells You can merge cells across row or column borders See Figure 7 13 The resulting cell must be rectangular The contents of the individual cells in the merge operation are concatenated in execution order See Figure 7 14 For details on cell execution order see Execution Order Dependency page 313 Figure 7 13 Two Cells Figure 7 14 Merged Cells 308 7 Creating Mathematical Documents Modifying the Physical Dimensions of a Table The overall width of the table can be controlled in several ways The most direct way is to press the left mouse button press mouse button for Macintosh while hovering over the left or right table boundary and dragging the mouse left or right Upon release of the mouse button the table boundary is updated This approach can also be used to resize the relative width of table columns Alternatively the size of the table can be controlled from the Table Properties dialog Select the Table menu and then Properties Two sizing modes are supported 1 Fixed percentage of page width Using this option the table width adjusts whenever the width of the document changes This option is useful for ensuring that the entire content of the table fit in the screen or printed page 2 Scale with zoom factor This option is used to preserve the size and layout of the table regardless of the size of the document win
202. enu 6 8 Customizing Animations The display options that are available for static plots are also available for Maple animations Interactive Plot Builder Animation Options Using the Interactive Plot Builder you can apply various plot options within the Plot Options window See nteractive Plot Builder page 271 Context Menu Options As with static plots you can apply plot options to the animation by right clicking Con trol click for Macintosh the animation output 6 2 278 6 Plots and Animations 0 5 Customize the animation using the context menu 1 To change the line style right click the plot region Select Style Point 2 To remove the axes select Axes None The animate Command Options The animate command offers a few options that are not available for static plots Refer to the animate help page for information on these additional options By default a two dimen sional animation consists of sixteen plots frames and a three dimensional animation consists of eight plots frames To create a smoother animation increase the number of frames using the frames option Note Computing more frames increases time and memory requirements x 5 920 gt sinewave sail dade e gt ball proe x y plots pointplot x y symbol circle symbolsize 20 end proc 6 8 Customizing Animations 279 t gt plots animate m t sin t e 3 t 0 20 frames 60 background
203. er by pressing the Tab key Equation Labels Equation labels help to save time entering expressions by referencing Maple output See Figure 1 11 By default equation labels are displayed If equation labels are not displayed 1 From the Tools menu select Options and click the Display tab Ensure that the Show equation labels check box is selected 2 From the Format menu select Equation Labels Ensure that both Execution Group and Worksheet are selected S sin x dx al f cos x 1 a 1 dx sin x 2 C Figure 1 11 Equation Label 1 5 Commands 49 To apply equation labels 1 Enter an expression and press Enter Note that the equation label is displayed to the right of the answer in the document 2 In anew execution group enter another expression that will reference the output of the previous execution group 3 From the Insert menu select Label Alternatively press Ctrl L Command L for Macintosh to open the Insert Label dialog Enter the label number in the Insert Label dialog and click OK The item is now a label See Figure 1 12 Y sin x dx ty all cos x a sire Insert Label Identifier 1 Figure 1 12 Inserting an Equation Label 4 Press Enter to obtain the result To change the format of equation labels e Select Format Equation Labels Label Display In the Format Labels dialog select one of the numbering schemes e Optionally enter an appro
204. er to the examples index help page Saving When saving a Maplet you can save the document as an mw fil or you can export the document as a maplet file Maple Document To save the Maplet code as an mw file 1 From the File menu select Save 2 Navigate to the save location 3 Enter a filename 4 Click Save If the document contains only Maplet code it is recommended that you export the document as a maplet file Maplet File To export the Maplet code as a maplet file From the File menu select Export As In the Files of Type drop down list select Maplet Navigate to the export location Enter the filename Click Save On A Q N e 406 10 Embedded Components and Maplets 11 Input Output and Interacting with Other Products 11 1 In This Chapter Section Writing to Files page 407 Saving to Maple Saving Data to a File a aoe Saving Expressions to a File Reading from Files page 409 Opening Maple Reading Data from a File file Reading Expressions from a File Exporting to Other Formats page 412 Export Exporting Documents ing documents in fil formats supported by MapleNet other software Maple T A Connectivity page 416 Using Maple with Translating Maple Code to Other Programming other programming languages and software Languages Accessing External Products from Maple Accessing Maple from External Products Sharing and Storing Maple Worksheet Content with the MapleCloud
205. erting 130 overview 127 prefixes 131 system of controlling 132 systems of 128 Units package description 86 Units Calculator 128 Units Calculator Assistant 36 Units package 127 environments 131 extensibility 133 UseSystem command 133 UsingSystem command 132 Units palettes 72 130 universal gravitational constant 134 UNIX command complete 7 context menus 39 unwith command 84 URL adding hyperlink to 322 V variables 63 variance 140 VariationalCalculus package 183 Vector constructor vectorfiel attribute 182 data structure 155 vector fields 182 vector spaces basis 170 VectorCalculus package description 86 VectorCalculus package 182 Student version 183 vectors 338 arithmetic 166 column 159 context menus 168 cross product 168 data type 163 defining 159 efficienc 162 filling 163 large 160 multiplication 167 row 159 163 scalar multiplication 167 selecting entries 164 shape 163 transpose 168 View menu in help system 56 markers 51 Volume Gauge component 387 W Web page adding hyperlink to 322 Web site access to Maple help pages 60 Application Center 59 196 MaplePrimes 59 Student Center 196 Student Help Center 59 Teacher Resource Center 59 Technical Support 60 Training 59 Welcome Center 58 Welcome Center 58 while loops 372 Windows command complete 7 context menus 39 with command 83 worksheet adding hyperlink to 322 Worksheet Environment 3 W
206. es Document mode and Worksheet mode An interactive version of this manual is available in the Standard Work sheet interface From the Help menu select Manuals Resources and more Manuals User Manual Classic A basic worksheet environment for older computers with limited memory The Classic interface does not offer all of the graphical user interface features that are available in the Standard interface The Classic interface has only one mode Worksheet mode Command line version A command line interface for solving very large complex problems or batch processing with scripts No graphical user interface features are available Maplet Applications Graphical user interfaces containing windows textbox regions and other visual interfaces which gives you point and click access to the power of Maple You can perform calculations and plot functions without using the worksheet Maplesoft Graphing A graphical calculator interface to the Maple computational engine Using Calculator it you can perform simple computations and create customizable zoomable graphs This is available on Microsoft Windows only This manual describes how to use the Standard interface As mentioned the Standard inter face offers two modes Document mode and Worksheet mode Using either mode you can create high quality interactive mathematical documents Each mode offers the same features and functionality the only difference is the defau
207. et your custom dictionary and clicked Apply to Session then this word will not be recognized in a new Maple session If you set your custom dic tionary and clicked Apply Globally then this new word will be recognized 7 9 Creating Graded Assignments You can use Maple to create graded assignments Question types include multiple choice essay true or false fill in the blanks and Maple graded Note This feature can be used to create questions for Maple T A an online automated testing and assessment system For details about Maple T A see Maple TA page 415 Creating a Question To create a question 1 Open the Task browser Tools Tasks Browser 2 From the Maple T A folder select the appropriate question type 3 Insert the question template into a document 4 Enter the question content as described in the template 5 Repeat steps 1 to 4 for each question to add to the document Viewing Questions in Maple To view and test your questions in Maple e From the View menu select Assignment This view displays all of the questions in your assignment with access to hints plotting and grading After answering your questions you can test the grading function by clicking the Grade button A Maplet dialog is displayed indicating if the question was answered correctly If hints were provided in the question these are also displayed Saving Test Content When you save a document with test content the authoring and
208. exponent press the right arrow key To enter a product 1 Enter the firs factor 2 Press the asterisk key which displays in 2 D Math as a dot 3 Enter the second factor Implied Multiplication In most cases you do not need to include the multiplication operator Insert a space character between two quantities to multiply them Note In some cases you do not need to enter the multiplication operator or a space character For example Maple interprets a number followed by a variable as multiplication Important Maple interprets a sequence of letters for example xy as a single variable To specify the product of two variables you must insert a space character or multiplication operator for example x y or x y For more information refer to the 2DMathDetails help page Shortcuts for Entering Mathematical Expressions Table 1 1 Common Keystrokes for Entering Symbols and Formats a implicit multiplication Space key 2 7xy 3y xy aa 1 2 Introduction to Maple 7 Symbolormats Rey Ramp 4 A _ _ B command symbol com Esc Macintosh Windows and g UNIX about 3 about about assumptions and properties abouti expr e Ctrl Space Windows i x e Ctrl Shift Space UNIX ae abselsol first order DETools abelsol ODE y pletion ba E3 square root sqrt and then command comple 35 tion lt ion enter exit 2 D Math e F5 key versu
209. expression d 1 In the Expression palette click the differentiation item dx j or the partial differentiation item x j 2 Specify the expression and independent variable and then evaluate it For example to differentiate x sin ax with respect to x d gt xsin ax dx sin ax xcos ax a You can also differentiate using context menus For more information see Context Menus page 39 To calculate a higher order or partial derivative edit the derivative symbol inserted For example to calculate the second derivative of x sin ax xX with respect to x gt L x sin ax 4 dx 2 cos ax a xsin ax w To calculate the mixed partial derivative of x sin 3 y yx 0 5 xsin 3y yx Ov Ox 3 cos 3 vy 5x Note To enter another symbol you can copy and paste the existing symbol or enter d and use symbol completion 5 4 Calculus 175 The diff Command Maple computes derivatives using the diff command To directly use the diff command specify the expression to differentiate and the variable gt xsin ax xsin ax x 5 1 gt diff CS 1 x sin ax xcos ax a 2x 5 2 For information on equation labels such as 5 1 see Equation Labels page 95 You can calculate a higher order derivative by specifying a sequence of differentiation variables Maple recursively calls the diff command gt diff CS 1 x x 2 cos ax a xsin ax ge 5 3 To calculate
210. ext pressing Enter inserts a line break You can use the basic algebraic operators such as and with most expressions includ ing polynomials see Polynomial Algebra page 148 and matrices and vectors see Matrix Arithmetic page 166 2 x 1 h 2x 12 x 3x 11 12 24 297 81 207 87 4 8 99 27 69 29 2 5 Editing Expressions and Updating Output One important feature of Maple is that your documents are live That is you can edit expres sions and quickly recalculate results To update one computation 1 Edit the expression 2 Press Ctrl Command for Macintosh or Enter The result is updated To update a group of computations 1 Edit the expressions 2 Select all edited expressions and the results to recalculate 3 Click the Execute toolbar icon f All selected results are updated To update all output in a Maple document e Click the Execute All toolbar icon M 2 6 Performing Computations 67 All results in the document are updated 2 6 Performing Computations Using the Document mode you can access the power of the advanced Maple mathematical engine without learning Maple syntax In addition to solving problems you can also easily plot expressions The primary tools for syntax free computation are e Palettes e Context menus e Assistants and tutors Note The Document mode is designed for quick calculations but it also supports Maple commands For
211. ext bar upper left hand corner amp Rotate uy Rotate a three dimensional plot to see it from a different point of view 3 D 270 6 Plots and Animations Pan the plot by changing the view ranges for 2 D plots smartplots re sample to reflec the new view Change the position of the plot in the plot region for 3 D plots Zoom into or out of the plot by changing the view ranges for 2 D plots smartplots re sample to reflec the new view Make the plot larger or smaller in the plot window for 3 D plots Use the Selection Tool to select the information displayed in the point probe tool tooltip You can choose to display coordinates derived from converted pixel coordinates or data points derived from the original data points Selection Tool 6 5 Representing Data The Live Data Plots palette has templates that allow you to represent your data in many different ways including e Area chart e Bar chart e Box plot e Bubble plot e Histogram e Line chart e Pie chart e Scatter plot Once you select a type of plot an interactive environment allows you to change a number of options to refin the look of your plot As you refin your plot Maple automatically up dates the plot command with your options If the Live Data Plots palette is not displayed in the palette dock from the main menu select View Palettes Arrange Palettes and then select Live Data Plots from the Arrange Palettes dialog 6 6 Creating Animation
212. ext fil by email and the recipient can import the Maple text into a Maple session and regenerate the computations in the original document PDF Export a Maple document to a Portable Document Format PDF fil so that you can open the fil in a reader such as Adobe Acrobat The PDF document is formatted as it would appear when the Maple worksheet is printed using the active printer settings Note Images plots and embedded components may be resized in the PDF file Plain Text Export a Maple document as plain text so that you can open the text fil in a word processor Rich Text Format RTF Export a Maple document to a rich text format fil so that you can open and edit the fil in a word processor Note The generated rtf format is compatible with Microsoft Word and Microsoft WordPad only 414 11 Input Output and Interacting with Other Products Summary of Translation Table 11 1 Summary of Content Translation When Exporting to Different Formats Content HTML LaTeX Maple Maplet Maple Plain PDF Input Applica Text Text Format tion Text aintained Maintained Pre Preceded Preceded Main Main Main ceded by by by tained tained tained i 1 D Math Maintained Maintained Main Main Preceded Preceded Static im Static im tained tained by gt by gt age age 2 D Math GIF or Either text MathML or shapes i i depending ter based ter based on option typeset selected ting aan
213. f x xQ x1 e Font Color Context Bar Icon Highlight Color Context Icon bai For font and highlight colors you can select from Swatches a color wheel RGB values or choose a color using the eye dropper tool See Figure 7 1 Figure 7 1 Select Color Dialog In this example choose a dark purple color as in the help pages To format this text as bold click the Bold toolbar icon R Also select the text Calling Sequence and format as bold Result plot create a two dimensional plot Calling Sequence plotte x plot f x x0 x1 plotil 72 Parameters f expression in independent variable z x independent variable X0 z1 left and night endpoints of horizontal range yl v2 x coordinates and y coordinates 7 2 Document Formatting 285 Attributes Submenu Setting Fonts Character Size and Attributes You can also change various character attributes such as font character size style and color in one dialog To modify text 1 In the document select text to modify 2 From the Format menu select Character and then Attributes The Character Style dialog opens See Figure 7 2 Character Style Underlined Superscript Subscript Arabic Transparent Arial Arial Black Arial Narrow Arial Rounded MT Bold Arial Unicode MS Baskerville Old Face Berlin Sans FB Demi Bernard MT Condensed Figure 7 2 Character Style Dialog Quick Paragraph Formatting The Format P
214. f x x0 x1 plotil 72 Parameters f expression in independent variable z E independent variable 0 zl left and night endpoints of horizontal range i v72 x coordinates and y coordinates For more information refer to the paragraphmenu help page Character and Paragraph Styles Maple has predefine styles for characters and paragraphs A style is a set of formatting characteristics that you can apply to text in your document to change the appearance of that text When you apply a style you apply a group of formats in one action e A character style controls text font size color and attributes such as bold and italic To override the character style within a paragraph style you must apply a character style or character formatting e A paragraph style controls all aspects of a paragraph s appearance such as text alignment line spacing and indentation In Maple each paragraph style includes a character style 288 7 Creating Mathematical Documents Style Management P Annotation Title Al Create Character Style P Author P Bullet Item P Dash Item f Modify P Diagnostic P Error P Heading 1 P Heading 2 P Heading 3 P Heading 4 Create Paragraph Style Delete Figure 7 4 Style Management Dialog Applying Character Styles By using the drop down list in the document context bar you can apply e Existing Maple character styles e New styles that you have created through the Style Man
215. formation on the plot options used in this section refer to the plot options and plot3d options help pages Display a Parametric Plot Some graphs cannot be specifie explicitly In other words you cannot write the dependent variable as a function of the independent variable y f x One solution is to make both the x coordinate and the y coordinate depend upon a parameter 256 6 Plots and Animations gt plot cos 3 t sin S f 0 2 t Display a 3 D Plot Maple can plot an expression of two variables as a surface in three dimensional space To customize the plot include plot3d options in the calling sequence For a list of plot options see The plot and plot3d Options page 267 6 2 Creating Plots 257 2 2 xy x y S c s X 2 2 y 2 2 glossiness 0 5 style patchnogrid a r d gt plot3d light 100 345 0 4 0 9 0 7 ambientlight 0 5 0 1 The plots Package The plots package contains numerous plot commands for specialized plotting This package includes animate contourplot densityplot fieldplo odeplot matrixplot spacecurve textplot tubeplot and more For details about this package refer to the plots help page gt with plots The pointplot Command To plot numeric data use the pointplot command in the plots package with the data organ ized in a list of lists structure of the form Es yy X Vo e 1 Y By default Maple does not connect the point
216. from or for in loop The general for from loop has the following syntax 374 9 Basic Programming For counter from initial hy increment to final While conditional expression do statement sequence end do The general for in loop has the following syntax For variable in expression while conditional expression do Statement sequence end do After testing the loop bound condition at the beginning of each iteration of the for loop Maple evaluates conditional_ expression e If conditional expression evaluates to false or FAIL Maple exits the loop e If conditional expression evaluates to true Maple executes statement sequence Infinite Loops You can construct a loop for which there is no exit condition for example a while loop in which the conditional_expression always evaluates to true This is called an infinit loop Maple indefinitel executes an infinit loop unless it executes a break quit or return statement or you interrupt the computation using the interrupt icon For more information refer to the break quit return and interrupt help pages Additional Information For more information on the for statement and looping refer to the do help page 9 3 Iterative Commands Maple has commands that perform common selection and repetition operations These commands are more efficien than similar algorithms implemented using library commands Table 9 2 lists the iterative commands Table 9 2 Iterative Comman
217. g The firs Do command gives an error because the second parameter is 0 One way to avoid this problem is to change the range of the second dial In the Component Properties dialog for the second DialComponent change the Value at Lowest Position from 0 to 1 Altern atively you could change the code to compensate with an if statement 6 Copy the actions to the components Once the commands work as expected you can copy them into the components e Open the Component Properties dialog for the firs DialComponent and click the Edit button for Action When Value Changes Copy and paste the commands into the space between the use statements 10 3 Creating Embedded Components 395 EJ Action When Value Changes use DocumentTools in parameterl Do s DialO parameterz Dol sDiall Do RotaryGauge0 parameterl parameter Do SPlotO plot parameterz x parameterl x 50 50 y 50 50 Do MathContaineroO y parameter3 x parametert end use Check syntax before saving Check Now Figure 10 5 DialComponent Action Dialog e Do the same for the second DialComponent 7 Create the layout for the components Create a table and then cut and paste the components into it along with explanatory text Important you must cut not copy the components or their names will be changed to avoid duplication For information on creating and modifying tables refer to Tables page 304 396 10 Embedded Componen
218. g a Maple object such as a function e creating a document such as an application Each task contains a description along with a collection of content that you can insert directly into your document Content consists of 2 D mathematics commands embedded components for example buttons and plots You specify the parameters of your problem and then execute the commands in the document See Figure 1 10 for an example of a Task Template 7g Browse Tasks File wiew H 6 Algebra EH Calculus Integral o E Integration Be Approximate Integration Approximate Definite Integral of a Function Numeric Integration E E Methods of Integration E E Applications E E Series Calculus Multivariate Calculus Vector T Convert Expression to Function Curve Fitting 0 Differential Equations 0 DocBook Metadata E Document Templates 0 Evaluating J A Geometry 0 Integers 9 Linear Algebra Ey Lists Maple T A Plots H E Polynomials Statistics Transformations Fela Units Constants and Errors ask 4pproxDefIntegralUnivariateFen Figure 1 10 Browse Tasks Dialog Previewing Tasks To preview Maple tasks 1 4 Point and Click Interaction 41 Sex Copy Task to Clipboard Insert Default Content Insert Minimal Content Insert into New Worksheet C Display task markers Approximate Definite Integral of a Function Description Approximate the definite integral of a
219. gain click the text icon to insert the rest of the The answer to Pra text 1s and then enter another input prompt gt sin x dx icon Make sure to put spaces around all of the l cos x text so the sentence displays properly K gt To display the same output again use the value The answer to command and an equation label This allows you gt sin x dx to insert text between the input and output of a l single command there are really two commands Lis P value 1 gt 5 To finis the sentence click the text icon in the The answer to last execution group and enter a period gt sin x dx cos x Enter and execute the command as shown cos x cos x is gt vaiue 1 L cos x Select the entire sentence then from the Format he answer to menu select Create Document Block By de cos x fault only the text and output remains visible and 5 cos x output is centered on a new line To display the text and output on one line place the cursor in the document block From the View menu select Inline Document Output gt lt The answer to cos x is cosl x To display input instead of output for the firs ex pression place the cursor in the firs expression From the View menu select Toggle Input Output Display Only the firs region displays input The answer to sin dx is cos x 1 6 The Maple Help System The Maple program provides a
220. ge For a comparison of the diff command and D operator refer to the diffVersusD help page Directional Derivative To compute and plot a directional derivative use the Directional Derivative Tutor The tutor computes a floating poin value for the directional derivative 5 4 Calculus 177 To launch the tutor e From the Tools menu select Tutors Calculus Multivariate and then Directional Derivatives Maple launches the Directional Derivative Tutor See Figure 5 7 Ei Multivariate Calculus Directional Derivative File Help Flot Window f Options F xt 2ye Point x Direction 1 of Frames 10 Values Actual Value 2 6833 Maple Command Directionalberivative x Z y 2 2 output plot Figure 5 7 Directional Derivative Tutor To compute a symbolic value for the directional derivative use the Student Multivariate Calculus DirectionalDerivative command The firs list of numbers specifie the point at which to compute the derivative The second list of numbers specifie the direction in which to compute the derivative 178 5 Mathematical Problem Solving For example at the point 1 2 the gradient of a y points in the direction 2 4 which is the direction of greatest increase The directional derivative in the orthogonal direction 2 1 is zero gt with Student MultivariateCalculus gt DirectionalDerivative x y x y 1 2 1 2 245 gt DirectionalDeriva
221. gnore the word click Ignore e To ignore all instances of the word click Ignore All e To change the word that is accept the suggested spelling that is in the Change To text box click Change e To change all instances of the word that is accept the suggested spelling to replace all instances of the word click Change All e To add the word to your dictionary click Add For details see the following User Dic tionary section e To close the Spellcheck dialog and stop the spelling check click Cancel 3 When the Spellcheck is complete a dialog containing the message The spelling check is complete appears Click OK to close this dialog 330 7 Creating Mathematical Documents Note when using the Spellcheck utility you can fi spelling errors in the dialog but you cannot change the text in document The Spellcheck utility does not check grammar Selecting a Suggestion To select one of the suggestions as the correct spelling click the appropriate word from the list in the Suggestions text box If none of the suggestions are correct highlight the word in the Change To text box and enter the correct spelling Click Change to accept this new spelling User Dictionary You can create and maintain a custom dictionary that works with the Maple Spellcheck utility Properties of the Custom Dictionary File e It must bea text file that is have the fil extension txt For example mydictionary txt e It isa list of words o
222. gt using the lt gt lt and gt operators The evalb command uses a three valued logic system The return values are true false and FAIL If evaluation is not possible an unevaluated expression is returned 358 e 8 Maple Expressions gt evalb x x true gt evalb x y false gt evalb 3 21 lt 2 31 FAIL Important The evalb command does not perform arithmetic for inequalities involving lt lt gt or and does not simplify expressions Ensure that you perform these operations before using the evalb command gt evalb R x lt R x 1 R x lt 1 R x gt evalb R x R x 1 lt 0 true Applying an Operation or Function to All Elements in a List Set Table Array Matrix or Vector You can use the tilde character to apply an operation or function to all of the elements in a list set table Array Matrix or Vector In the following example each element in the Matrix M is multiplied by 2 by adding a tilde character after the multiplication operator 8 3 Working with Maple Expressions 359 1 23 gt M 145 6 789 123 M 45 6 8 6 789 gt M 2 2 4 6 8 10 12 8 7 14 16 18 In the following example the function sin is applied to each element in the Matrix M gt sin M sin 1 sin 2 sin 3 sin 4 sin 5 sin 6 8 8 sin 7 sin 8 sin 9 The tilde character can also be used to apply a function to multiple data sets for example gt diff zx x WF E
223. h a box around the result click the displayed symbol and choose one of the selections from the drop down menu 4 To insert a symbol click the displayed symbol W Handwriting Figure 1 3 Handwriting Palette For more information refer to the handwritingpalette help page Snippets Palettes You can create your own custom Snippets palettes for tasks that you fin most useful Details on how to create and customize Snippets palettes can be found on the createpalette help page Symbol Names Each symbol has a name and some have aliases By entering its name or an alias in Math mode you can insert the symbol in your document All common mathematical symbols including all Greek characters m and the square root symbol J are recognized by Maple Note If you hover the mouse pointer over a palette item a tooltip displays the symbol s name To insert a symbol enter the firs few characters of a symbol name using a keyword that is familiar to you and then press the completion shortcut key Ese see Shortcut Keys by Platform page xviii Symbol completion works in the same way as command completion see Command Completion page 47 1 3 Entering Expressions 29 e Ifaunique symbol name matches the characters entered Maple inserts the corresponding symbol e If multiple symbol names match the characters entered Maple displays the completion list which lists all matches including commands To select an item click it
224. h the code interspersed or hidden there are several options available Code Edit Region The code edit region allows you to program in one contained region in a natural way Features include the ability to press Enter for line breaking and indentation preservation Figure 9 1 shows the expanded code edit region To insert a new code edit region into your worksheet e From the Insert menu select Code Edit Region Figure 9 1 Code Edit Region To execute the code within this region right click in the region and select Execute Code You can hide the code in a code edit region by minimizing the region To minimize right click in the region and select Collapse Code Edit Region When the region is minimized an icon appears with the firs line of the code written next to it It is recommended that you make the firs line a comment describing the program or programs contained in the region See Figure 9 2 Figure 9 2 Collapsed Code Edit Region To re execute the code in the region while it is collapsed click this icon For more information refer to the CodeEditRegion help page 9 5 Programming in Documents 383 Startup Code Startup code allows you to defin commands and procedures that are executed each time the document is opened and after restart is called This code is completely hidden to others reading the document For example use this region to defin procedures that will be used throughout the document code but that would
225. he firs section To change the equation label numbering scheme e From the Format menu select Equation Labels Label Display In the Format Labels dialog Figure 3 6 select one of the formats e Optionally enter a prefix gt s x dx cos x Question 1 gt z Questionl dx Format Labels Label Numbering Prefix Question Label Numbering Scheme Flat Mumeric wt Figure 3 6 Format Labels Dialog Adding a Prefi 3 10 Equation Labels 99 Features of Equation Labels Although equation labels are not descriptive names labels offer other important features e Each label is unique whereas a name may be inadvertently assigned more than once for different purposes e Maple labels the output values sequentially If you remove or insert an output Maple automatically re numbers all equation labels and updates the label references e Ifyou change the equation label format see Label Numbering Schemes page 98 Maple automatically updates all equation labels and label references For information on assigning to using and unassigning names see Names page 92 For more information on equation labels refer to the equationlabel help page The following chapters describe how to use Maple to perform tasks such as solving equations producing plots and animations and creating mathematical documents The chapters were created using Worksheet mode Except where noted all features are available in both Works
226. heet mode and Document mode 100 3 Worksheet Mode 4 Basic Computations This chapter discusses key concepts related to performing basic computations with Maple It discusses important features that are relevant to all Maple users After learning about these concepts you will learn how to use Maple to solve problems in specifi mathematical disciplines in the following chapter 4 1 In This Chapter Section Symbolic and Numeric Computation page 102 Exact Computations An overview of exact and floating poin computa Floating Point Computations tion Converting Exact Quantities to Floating Point Values Sources of Error Integer Operations page 106 How to perform Important Integer Commands integer computations Nea Basio Numbee Finite Rings and Fields Gaussian Integers Solving Equations page 111 How to solve Equations and Inequations standard mathematical equations Ordinary Differential Equations Partial Differential Equations Integer Equations Integer Equations in a Finite Field Linear Systems Recurrence Relations 101 102 4 Basic Computations Units Scientifi Constants and Units Uncertainty page 127 How to construct and compute with expressions that have units scientif ic constants or uncertainty Applying Units to an Expression Performing Computations with Units Conversions Changing the Current System of Units Extensibility Scientifi Constants Scientifi Constants Element a
227. horing Maplets page 397 Methods for authoring Maplet Builder and saving a Maplet Maplets Package Saving 10 2 Using Embedded Components Interacting Embedded components allow readers to interact with Maple code through graphical com ponents rather than commands They can be used alone as with a button that you click to execute code or together such as a drop down menu where you select an item and a change takes place in a plot component Component Descriptions Table 10 1 Embedded Component Descriptions Component Name and Description Inserted Image Button Click to perform an action that is execute code Caman GD oo Check Box Select or de select Change the caption and 7 check ox enter code to execute when the value changes 385 386 10 Embedded Components and Maplets Component Name and Description Inserted Image Combo Box Select one of the listed options from the ComboBox iw drop down menu Change the items listed and enter code to execute when the value changes Data Table Link this embedded component to a Matrix Vector or Array in your worksheet Dial Select or display an integer or floating poin value Change the display and enter code to execute when the value changes AY Label Display a label The value can be updated based Label on code in the document or another embedded component List Box Display a list of items Change the items listed and enter code to e
228. iated uncertainty To obtain the uncertainty in the value of a ScientificConstant object use the GetError command gt GetError G 1 010 gt GetError LiAtomic Weight 3 321080400 10 Performing Computations You can use constant values in any computation To use constant values with units use a Units environment as described in Performing Computations with Units page 131 For information on computing with quantities that have an uncertainty see the following section Modification and Extensibility You can change the definitio ofa scientifi constant or element or isotope property For more information refer to the ScientificConstants ModifyConstant and Scientific Constants ModifyElement help pages You can extend the set of e Constants e Elements and isotopes e Element or isotope properties For more information refer to the ScientificConstants AddConstant ScientificCon stants AddElement and ScientificConstants AddP operty help pages For more information about constants refer to the ScientificConstant help page Uncertainty Propagation Some computations involve uncertainties or errors Using the ScientificEr orAnalysis package you can propagate the uncertainty in these values through the computation to in dicate the possible error in the fina result The ScientificEr orAnalysis package does not perform interval arithmetic That is the error of an object does not represent an interval in which pos
229. iauheccusess beeen s EEEE TE R 283 Quick Paragraph Formattint 202 4 Gd bald creates a a EE 285 Character and Paragraph Styles nrsiiiecniartiecn neia a a a a eteies 287 DE CHONS maotaa a a E a N 294 Headers and Footers 6 Sesser irre uer N E E REEE 296 Showor Hide Worksheet Content ecrire d aida eae ee 297 Ind ntation and th TaD Key orrec nai a 298 Lo Commands in Documents sisena i E EAEE 299 Document Block Sosro TTEN REE O TO sa 299 IR aenn A E AE A E E E E nates 302 Contents vii AMO EXECU bibs che ancneeneon E hoe nieuerantanmnsee E E 302 Tse MA ESS betelnut a Gates les ae cae as elec se Bote abet sane Reda TTA O 304 Ceding a Table ies etre ete tite eek bee ats sata hie nate nth adios Ged catetad 304 OC COMEN omer ener een a TNE TT Sate ee eee anne 304 Navigating Table Cells tots Mati cig baniberedosl poe aa EA 305 Modifying the Structural Layout of a Table cc cece cece ccc ee ec eeeeeeenenes 305 Modifying the Physical Dimensions of a Table ccccc cece ese neeeee en eeeenes 308 Modifying the Appearance of a Table ccc ecccc ec eceeeeeeeeeeeeeseneneeaens 308 Printn OPUONS ise bot oettoul techn a sncad hauler io neice deena a a 312 Execution Order Dependency tastes iere nner enas iare EEA TAA 313 Tablesand the Classic Workshectiuistoiirecia rnae E E 313 Additonal Example Ssnan a a E thane ieee 313 ToS ADV AS e a a a e GE 316 serca Canya S ae E E E TAN 317 Diawine soneran a a N et en ee E si
230. ic Worksheet Canvas page 316 Sketch an idea in Insert a Canvas the document by inserting a canvas Daw rawing Canvas Style Inserting Images Hyperlinks page 320 and Bookmarks Inserting a Hyperlink in the Document Add hyperlinks to various sources Linking to an Email Address Dictionary Topic Help Page Maplet Application Web Page or Document Bookmarks Embedded Components page 326 In Overview of available components sert buttons sliders and more in your document Spell Checking page 328 Verify text How to Use the Spellcheck Utility with the Maple spell checking utility Example using a task template Selecting a Suggestion User Dictionary Creating Graded Assignments page 331 Creating a Question Create documents for automated testing Viewing Questions in Maple and assessment Saving Test Content Worksheet Compatibility page 332 Classic Worksheet interface does not support all Standard Compatibility Issues Worksheet interface features 7 2 Document Formatting To begin create a new Maple document From the File menu select New Document Mode For this example you can copy and paste text from any file The example text below is from a Maple help page plot but the formatting has been removed for demonstration purposes 7 2 Document Formatting 283 Copy and Paste You can cut copy and paste content within Maple documents and from other sources To copy an expre
231. ich the position from which you view a 3 D plot moves in all directions and in various angles around the plot surface based on coordinates and parameters you specify This type of animation creates the effect of flyin through around beside towards and away from a plot surface in three dimensional space The moveable position from which you view the surface is called the camera You can specify the orientation of the camera to view different sides of a surface the path along which the camera moves throughout and around a surface and the location of the camera in 3 D space in each animation frame For example you can specify coordinates to move the camera to specifi points beside a surface a pre define camera path to move the camera in a circle around the surface and the range of view to move the camera close to or away from the surface Refer to the viewpoint help page for information on the available options 6 6 Creating Animations 275 To animate the following examples click the plot object and then click the play button in the Animation context bar Example 1 Moving the Camera Around a 3 D Plot In the following example a pre define path circleleft moves the camera in a counter clockwise circle around the plot surface gt plot3d 1 3 sin y x 1 2 T y 0 2 coords spherical style patch viewpoint circleleft Example 2 Specifying a Path to Move the Camera Towards and Around a 3 D Plot In th
232. ide the section to its title 4 Similarly create a section with the title Calling Sequence containing the items under that heading 296 7 Creating Mathematical Documents Result plot create a two dimensional plot Calling Sequence plot f x plot f x x0 x1 plot w1 v2 Parameters f expression in independent variable x independent variable xO x1 le and night endpoints of horizontal range il 2 coordinates and y coordinates Note the section titles are automatically formatted as section titles but you can change the formatting through the Paragraph Style dialog Headers and Footers You can add headers and footers to your document that will appear at the top and bottom of each page when you print the document To add or edit headers and footers From the View menu select Header Footer The Header Footer dialog appears See Figure 7 8 Header and Footer I Insert Date Insert Page Insert Number of Pages Insert Picture Insert File Name Left Center Right Figure 7 8 Header and Footer Dialog Custom Header The available elements include the current date page number number of pages an image the filename or any plain text These elements can be placed in the left or right corner or the center of the page 7 2 Document Formatting 297 You can choose one of the predefine header or footer styles in the Predefine Header and Footer tab or create
233. ils refer to the restart help page From the Format menu select Outdent From the Edit menu select Execute and then Worksheet Add and edit Maple code that is executed From the Edit menu select Startup Code each time the worksheet is opened For details refer to the startupcode help page Adjusts the display size of document content Note plots spreadsheets im ages and sketches remain unchanged Opens the Maple help system For details Bp From the Help menu select Maple Help refer to The Maple Help System page 53 From the View menu select Zoom Factor and then a zoom size T E For 1 D Math and text regions the Tab icon in the toolbar allows you to set the Tab key to move between placeholders or cells in a table or to indent text Table 1 3 Tab Icon Description Tab icon off Allows you to move between placeholders using the Tab key re 10 1 Getting Started Tab icon on Allows you to indent in the worksheet using the Tab key ho ey The Tab icon is disabled when using 2 D Math Math mode and as such the Tab key allows you to move between placeholders Toolbar icons are controlled by the location of the cursor in the document For example place the cursor at an input region and the Text and Math icons are accessible while the others are dimmed See Table 1 4 for a list of the tools available in each icon Table 1 4 Toolbar Icons and their Tools Toolbar Icon Options Text tool
234. ilter Design Frequency Domain System Identification Harmonic Oscillator Image Processing and Radiator Design with CAD Systems Examples Example worksheets are executable documents covering topics that demonstrate syntax or invoke a user interface to make complex problems easy to solve and visualize You can copy and modify the examples as needed Topics include Algebra Calculus Connectivity Discrete Mathematics General Numerics and Symbolics and Integral Transforms 58 1 Getting Started e From the Help menu select Manuals Resources and more and then Applications and Examples Manuals You can access all of Maple s manuals from within Maple including the Maple Programming Guide and this manual You can execute examples copy content into other documents and search the contents using the Maple Help System e From the Help menu select Manuals Resources and more and then Manuals Task Templates Set of commands with placeholders that you can use to quickly perform a task For details see Task Templates page 40 e From the Tools menu select Tasks and then Browse Maple Tour and Quick Resources Maple Tour The Maple Tour consists of interactive sessions on several of the following topics Ten Minute Tour Numeric and Symbolic Computations Matrix Computations Differential Equations Statistics Programming and Code Generation Units and Tolerances and Edu cation Assessment with Maple T A e From the Help me
235. imensions see The plot and plot3d Options page 267 2 D Plot Options Some plots do not display as you would expect using default option values A expression with a singularity is one such example 6 3 Customizing Plots 265 In the previous plot all interesting details of the plot are lost because there is a singularity at x 1 The solution is to view a narrower range for example from y 0 to 7 Alter the y axis range 1 Right click the plot region Select Axes and then Properties 2 In the Axes Properties dialog click the Vertical tab 3 Clear the Use data extents check box and enter 0 and 7 in the Range min and Range max text regions respectively 4 Click Apply to view the changes or OK to return to the document Change the color 5 Place the mouse pointer on the curve and right click Control click Macintosh Note The curve is selected when it becomes highlighted 6 Select Color and then Green Change the line style 7 Select Style and then Point 266 6 Plots and Animations 3 D Plot Options By default Maple displays the graph as a shaded surface with a wireframe and scales the plot to fi the window To change these options use the context menu gt plotsdl 5 x 10 10 y 5 5 xX ty Maple has many preselected light source configurations Change the style 1 Right click the plot region Select Style Surface Apply a light scheme 2 Select Lighting Light 1 Change the
236. in using Maple and use Maple in the classroom Browse the many resources in the Education and Education PowerTools categories http www maplesoft com applications Student Help Center The Maple Student Help Center contains tutorials and applica tions that help students learn how to use Maple explore math ematical concepts and solve problems Available resources in clude e Study guides Complete lessons with examples for academic courses including precalculus and calculus For example the Interactive Precalculus Study Guide contains worked prob lems each solved as in a standard textbook using Maple commands and custom Maplet graphical interfaces Free course lessons for many subjects including precalculus to vector calculus high school abstract and linear algebra engineering physics differential equations cryptography and classical mechanics Applications for students written by students providing ex amples in many subject areas e Student FAQs with answers from experts http www maplesoft com academic students Student Packages and Tutors The Student package is a collection of subpackages for teaching and learning mathematics and related subjects The Student package contains packages for a variety of subjects in cluding precalculus calculus and linear algebra Instructors can e Teach concepts without being distracted by the mechanics of the computations e Create examples and quickly update
237. information on commands see Commands page 80 in Chapter 3 Worksheet Mode page 77 Important In Document mode you can execute a statement only if you enter it in Math mode To use a Maple command you must enter it in Math mode Computing with Palettes As discussed in Entering Expressions page 62 some palettes contain mathematical oper ations To perform a computation using a palette mathematical operation 1 In a palette that contains operators such as the Expression palette click an operator item 2 In the inserted item specify values in the placeholders 3 To execute the operation and display the result press Ctrl Command for Macintosh or Enter 0 e inline For example to evaluate 1 Using the Expression palette enter the partial derivative See Example 1 Enter a Partial Derivative page 63 2 Press Ctrl Command for Macintosh 68 2 Document Mode Context Menus A context menu 1s a pop up menu that lists the operations and actions you can perform on a particular expression See Figure 2 1 7 11 P Copy Special b Paste Ctrl V Evaluate and Display Inline Ctril Explore 4poply a Command Approximate b ssign to a Mame Denominator Numerator More z D Math b Figure 2 1 Context Menu To display the context menu for an expression e Right click Control click for Macintosh the expression The context menu is displayed beside the mous
238. ing function or the plot to your document 0 002762122808 x 0 04971820957 x When finished click Done 03259304755 0 8949276991 x 0 665671371 x 0 9888404085 x 1 082752470x 0 044194 Descriptions of Assistants The remaining assistants are described below Some of the assistants are interfaces to package commands For more information on package commands see Package Commands page 47 e Back Solver an interface that allows you to take a mathematical formula involving multiple parameters enter values for all but one of the parameters and solve for the re maining value You can also plot the behavior of the formula as one of the parameters change e Curve Fitting an interface to commands in the CurveFitting package Data points can be entered as independent and dependent values and interpolated with polynomials ra tional functions or splines Data Analysis an interface to the data analysis commands in the Statistics package 36 e Getting Started Equation Manipulator an interface for interactively performing a sequence of operations on an equation You can group terms apply an operation to both sides of the equation complete the square and so on Import Data an interface to read data from an external fil into Maple eBook Publisher an interface to the eBook Publisher tools Installer Builder an interface to the InstallerBuilder package in which you can create installer
239. inite 180 functional operators 342 indefinite 180 iterated 181 line 181 201 numeric 181 surface 181 with units 132 interactive commands Student 38 Interactive Linear System Solving tutor 73 Interactive Plot Builder Assistant creating animations 271 creating plots 238 customizing animations 277 customizing plots 263 interface command rtablesize option 162 verboseproc option 380 international system SI 128 InterquartileRange command 191 interval arithmetic 138 iquo command 107 iroot command 107 is command 143 isprime command 107 isqrt command 107 italic format 283 J j entering 110 Jordan form 168 K keyboard keys Command Completion xviii Context Menu xviii keystrokes 6 L Label component 386 labels 99 last name evaluation 361 lcm command 155 lcoeff command 153 Idegree command 154 least squares 170 left single quotes 95 left hand side 345 levels of evaluation 360 lexicographic order 151 Ihs command 345 Library Browser description 36 limit command 172 Limit command 173 limits 172 multidimensional 173 line break 286 line integrals 201 linear algebra 171 computations 166 efficienc 162 171 LinearAlgebra package 170 teaching 171 196 Linear System Solving tutor 74 linear systems solving 125 170 interactive 73 LinearAlgebra package description 85 LinearAlgebra package 168 commands 170 numeric computations 171 LinearSolve command 125
240. int t gt HazardRate Cauchy a b gt a l z a arctan L J b p T You can also specify that Maple compute the result numerically gt HazardRate Cauchy 10 1 7 numeric 0 003608801460 For more information refer to the Statistics DescriptiveStatistics help page Plotting You can generate statistical plots using the visualization commands in the Statistics package Available plots include e Bar chart e Frequency plot e Histogram e Pie chart e Scatter plot ees ie Ana For example create a scatter plot for a distribution of points that vary from sn gt 00 a small value determined by a normally distributed sample gt N 200 5 6 Statistics gt U Sample Normal 0 1 N gt X lt seq x x 1 N gt _ _ 27x U x __ gt FY lt seq sin N 4 X LN gt gt ScatterPlot X Y title Scatter Plot Scatter Plot G 2 40 bl BO tog 120 140 160 180 200 ee To fi a curve to the data points include the optional fi equation parameter Using the plots display command create a plot that contains e a scatter plot of the data points e a quartic polynomial fitte to the data points f x a xt bxit exr dxt e 21x e the functi i e unction sin N gt P ScatterPlot X Y fit la Y brPtertdxte xl thickness 2 193 194 5 Mathematical Problem Solving 2 mX gt 0 plot sin a x 1 N thickness 2 co
241. intosh 2 In the Insert Label dialog see Figure 3 5 enter the label value and then click OK Insert Label Identifier Figure 3 5 Insert Label Dialog Maple inserts the reference 3 10 Equation Labels 97 For example To integrate the product of 3 4 and 3 5 1 In the Expression palette click the indefinit in r gt F dx ae tegration item 4 The item is inserted and the integrand placeholder is highlighted Press CtrI L Command L for Macintosh In the Insert Label dialog enter 3 4 Click OK Insert Label Identifier 3 4 gt 64 3 5 dx Press CtrI L Command L for Macintosh i In the Insert Label dialog enter 3 4 Click OK Press To move to the variable of integration placeholder press Tab gt 3 4 G 5 dr Enter x i ea cos x To evaluate the integral press Enter Execution Groups with Multiple Outputs An equation label is associated with the last output within an execution group 98 3 Worksheet Mode gt 4 seos 35 oa 0 3265306122 Lys gt 3 7 A u Label Numbering Schemes You can number equation labels in two ways e Flat Each label is a single number for example 1 2 or 3 3 7 3 8 e Sections Each label is numbered according to the section in which it occurs For example 2 1 is the firs equation in the second section and 1 3 2 is the second equation in the third subsection of t
242. ion To start a Maple session 1 In the Startup dialog select Blank Document or Blank Worksheet A blank document displays or 1 Close the Startup dialog 2 From the File menu select New and then either Document Mode or Worksheet Mode A blank document displays Every time you open a document Maple displays a Quick Help pop up list of important shortcut keys To invoke Quick Help at any time press the F1 key Entering 2 D Math In Maple the default format for entering mathematical expressions is 2 D Math This results in mathematical expressions that are equivalent to the quality of math found in textbooks Entering 2 D Math in Maple is done using common key strokes or palette items For more information on palettes see Palettes page 21 An example of entering an expression using common key strokes is presented in the following section An example of entering an ex pression using palette items is presented in Example 3 Enter an Expression Using Palettes page 26 Common Operations oo oe xf 4 x and x y is natural in 2 D Entering mathematical expressions such as Math 6 I Getting Started To enter a fraction 1 Enter the numerator 2 Press the forward slash key 3 Enter the denominator 4 To leave the denominator press the right arrow key To enter a power 1 Enter the base 2 Press the caret key 3 Enter the exponent which displays in math as a superscript 4 To leave the
243. ipulator page 216 e Instant Solution page 218 Step by step Interactive Solution page 218 e Graphical Solution page 219 Solution through Equation Manipulator Maple provides a dialog that allows you to single step through the process of manipulating an expression This manipulator is available from the context menu 1 Enter the equation x 7 x 1 4 x 1 j x 4 in a new document block region 2 Right click this equation and select Manipu late Equation The Manipulate Equation dialog displays Group all of the terms to the left 3 In the Addition region the Group terms row allows you to group terms on a specifie side With the left side already selected click Do Expand the left side of the equation 4 In the Miscellaneous Operations region we can manipulate the equation by applying a command from the drop down menus Since we want to expand the left side of the equation only click the firs drop down menu in the second row and select expand Click Do 5 8 Clickable Math 217 Result in Document x Equation Mankputator x 7 xe i 4x C Show steps stacked vertcaky Pomer Square both sides Take aquere root of both ades Rase bath sides to power 3 Exponertiate both aces using base 2 Mscefancous Operations Mubigac ation Apply oo v to both ades Chae denominators Apply seqily to bts w with no assumptions M equation by Tree IVD ty oc Complete th
244. isabled while the Plot Builder is running Enter an expression 3 In the Specify Expressions window a Add the expression sin x x b Click OK to proceed to the Select Plot Type window Plot the expression 4 In the Select Plot Type window notice the default setting of a 2 D plot type and an x axis range 2 m 2 1 Notice also the various plot types available for this expression 5 Click Plot To see the Maple syntax used to generate this plot see Maple commands from Creating Plots Interactive Plot Builder page 249 Example 2 Display a plot of multiple expressions in 1 variable Maple can display multiple expressions in the same plot region to compare and contrast The Interactive Plot Builder accepts multiple expressions Launch the Interactive Plot Builder and enter the expressions 1 Launch the Interactive Plot Builder The Plot Builder accepts expressions in 1 D Math and performs basic calculations on expressions For example entering diff sin x 2 x in the Specify Expression window performs the calculation and displays the expression as 2 cos x 2 x in the Expression group box 2 In the Specify Expressions window e In three separate steps add the expressions sin x 2 diff sin x 2 x and int sin x 2 x Change the x axis range 3 In the Select Plot Type window a Change the x Axis range to Pi Pi b Click Options to proceed to the Plot Options window 242 6 Plots and Animations Launch the Plot
245. ith Units Standard In the Standard Units environment commands that support expressions with units return results with the correct units 132 4 Basic Computations gt area 3 ft mite area S310 Tn 78125 12 sin a x im 12sin x 27 4 15 gt int 4 15 xls 12 cos x r m 4 16 gt diff 4 16 x s 12sin x x 5 P For information on differentiation and integration see Calculus page 172 Changing the Current System of Units Ifa computation includes multiple units all units are expressed using units from the current system of units gt 132 25 mile 132 25 mi 4 17 By default Maple uses the SI system of units in which length is measured in meters and time is measured in seconds 7 4 17 3 hour 19 70701333 To view the name of the default system of units use the Units UsingSystem command gt with Units 4 5 Units Scientifi Constants and Uncertainty 133 gt UsingSystem ST To change the system of units use the Units UseSystem command gt UseSystem FPS gt 4 17 3m 1 1 ke 1 666720741 107 f 1b Extensibility You can extend the set of e Base dimensions and units e Complex dimensions e Complex units e Systems of units For more information refer to the Units AddBaseUnit Units AddDimension Units AddUnit and Units AddSystem help pages For more information about units refer to the
246. ized commands in areas such as calculus linear algebra vector calculus and code generation For a complete list of packages and commands refer to the index help pages To access the index overview help page enter index and then press Enter For information on the Maple Help System see The Maple Help System page 53 Top Level Commands To use a top level command enter its name followed by parentheses containing any parameters This is referred to as a calling sequence for the command command arguments Note In 1 D Math input include a semicolon or colon at the end of the calling sequence For example to differentiate an expression use the diff command The required parameters are the expression to differentiate which must be specifie first and the independent variable gt diff tan x sin x x 1 tan x 7 sin x tan x cos x For a complete list of functions commands that implement mathematical functions such as Bessell and AiryAi available in the library refer to the initialfunctions help page Bessell 0 1 1 AiryAi 2 2 47 5303 7086 For detailed information on the properties of a function use the FunctionAdvisor command 82 3 Worksheet Mode gt FunctionAdvisor definition Bessell A hypergeom i i 1 e 3 2 Bessell a z with no restrictions on a 1 a 2 For detailed information on how to use a function in Maple refer to its help page For example gt
247. kage the cross product operator is available as the infi oper ator amp x Otherwise it is available as the LinearAlgebra CrossProduct command For information on matrix arithmetic over finit rings and fields refer to the mod help page Point and Click Interaction Using context menus you can perform many matrix and vector operations Matrix operations available in the context menu include the following e Perform standard operations determinant inverse norm 1 Euclidean infinit or Frobenius transpose and trace e Compute eigenvalues eigenvectors and singular values e Compute the dimension or rank e Convert to the Jordan form or other forms e Perform Cholesky decomposition and other decompositions 5 3 Linear Algebra 169 For example compute the infinit norm of a matrix See Figure 5 6 18735 6985 349723 234987 9859 459 798124 14089 Copy Special Paste Evaluate and Display Inline Explore 4pooly a Command Approximate 45519gn to a Mame Browse Eigenvalues etc Map Command Onta Norm Plots Select Elements Solvers and Forms Standard Operations Conversions Curve Fitting Export 4s In Place Options Language Conversions Map Integer Functions Onto Queries 2 D Math Figure 5 6 Computing the Infinit Norm of a Matrix Ctrl Ctrl Kr Fr F F F FT Fr F FY F F F 1 Euclidean infinity Frobenius In Document mode Maple inserts a right arrow and the name of
248. kage command solves the problem using a different optimization method These are described in Table 5 9 along with the general input form for each command Table 5 9 Optimization Package Commands LPSolve Solve a linear program LP which involves computing the minimum or maximum of a linear objective function subject to linear constraints input is in equation or Matrix form LSSolve Solve a least squares LS problem which involves computing the minim um of a real valued objective function having the form gi x f x HLO i where x is a vector of problem vari ables possibly subject to constraints input is in equation or Matrix form Maximize Compute a local maximum of an objective function possibly subject to constraints Minimize Compute a local minimum of an objective function possibly subject to constraints NLPSolve Solve a non linear program NLP which involves computing the minim um or maximum of a real valued objective function possibly subject to constraints input is in equation or Matrix form QPSolve Solve a quadratic program QP which involves computing the minimum or maximum or a quadratic objective function possibly subject to linear constraints input 1s in equation or Matrix form For a complete list of commands and other Optimization package information refer to the Optimization help page 5 6 Statistics The Statistics package provides tools for mathematical statistics and data analysis
249. ksheet mode Maple inserts the calling sequence that performs the sort followed by the sorted polynomial 3 3 2 2 gt X TY FIY gt sort x 3 y 3 x 2 y 2 y x plex 3 22 3 Y Ts TZ You can use context menus to perform operations on 2 D Math content including output For more information see Context Menus page 68 for Document mode or Context Menus page 88 for Worksheet mode Collecting Terms To collect the terms of polynomial use the collect command 2 2 3y gt collec 2 axyt e x y zy tez 13by ary x 52 2 zZ lt y 2ax ex 13 b yrtaz Coefficients and Degrees Maple has several commands that return coefficien and degree values for a polynomial See Table 5 2 Table 5 2 Polynomial Coefficien and Degree Commands Coefficien of specifie degree term gt co off Le 2x 5 1 2 Leading coefficien l3 _ a a ee 77 LX 5 lcoeff 154 5 Mathematical Problem Solving Trailing coefficien coeffs Sequence of all coefficients in one to one la i gt coeffs x 2x 5 correspondence with the terms coeffs g aia Note It does not return zero coefficient 5 2 s 5 Highest degree Lowest degree term with a non zero coeffi cient Factorization To express a polynomial in fully factored form use the factor command gt factor x 1 x 1 x 1 2 1 The factor command factors the polynomial over the ring implied by the coefficients for examp
250. l 201 Live Data Plots palette 270 ODEs numeric solution 122 symbolic solution 123 optimization problem 186 playing animations 276 plots package animate command 271 contourplot command 260 432 Index display command 262 matrixplot command 258 pointplot command 257 series 179 statistics 192 viewing animations animate context bar 276 point and click 32 polynomial equations solving 115 numerically 116 polynomials algebra 148 arithmetic 148 coefficients 153 collecting terms 153 degree 153 division 148 149 efficien arithmetic 155 expanding 149 factoring 154 implied multiplication 150 numeric algebraic manipulation 155 operations 154 sorting 150 pure lexicographic 151 total degree 151 PolynomialTools package 155 IsSelfReciprocal command 155 powers entering 6 precalculus demos 195 teaching 196 precision 104 prem command 155 previously assigned 361 primality testing 107 primpart command 155 print command 380 table 312 printing embedded components 388 probability distribution 190 proc key word 378 procedures 381 and assumptions 145 calling 378 defining 378 displaying 380 inputs 379 multiple lines 378 output 379 using 378 product command 376 products entering 6 implied 6 programming 365 access to Maple s programming guides 58 programs 365 modules 381 objects 381 procedures 381 prompt input 78 properties testing 143 protected names 9
251. laced You can evaluate the function add1 with symbolic or numeric arguments gt add1 12 addI x y 13 x y l Distinction between Functional Operators and Other Expressions The expression x is different from the functional operator x gt x 1 Assign the functional operator x gt x tof gt fr x x 1 Assign the expression x to g gt g5 x i To evaluate the functional operator f at a value of x e Specify the value as an argument to f gt f 22 23 To evaluate the expression g at a value of x e You must use the eval command gt g 22 x 22 1 gt eval g x 22 23 8 2 Creating and Using Data Structures 341 For more information on the eval command and on using palettes and context menus to evaluate an expression at a point see Substituting a Value for a Subexpression page 353 Multivariate and Vector Functions To defin a multivariate or vector function e Enclose coordinates or coordinate functions in parentheses For example a multivariate function 3 xX gt e y l gt f x y ii gt f 0 0 f 2 1 1 9 0 2 008893709 A vector function gt g f sin cos TT gt g 0 e gt Using Operators To perform an operation on a functional operator specify arguments to the operator For example for the operator f specify Ax which Maple evaluates as an expression See the following examples Plotting Plot a three dimensio
252. late MATLAB code to Maple as well as call se lected MATLAB functions from a Maple session provided you have MATLAB installed on your system For more information refer to the Matlab help page Accessing Maple from External Products Microsoft Excel Add In Maple is available as an add in to Microsoft Excel This add in is supported for Excel 2010 and Excel 2007 for Windows and provides the following features e Access to Maple commands from Excel e Ability to copy and paste between Maple and Excel e Access to a subset of the Maple help pages e Maple Function Wizard to step you through the creation of a Maple function call To enable the Maple Excel Add in in Excel 2010 1 Click the File menu and select Options 2 Click Add ins 3 In the Manage box select Excel Add ins and then Go 418 11 Input Output and Interacting with Other Products 4 Navigate to the Excel subdirectory of your Maple installation and select the appropriate file For 32 bit Windows select WMIMPLEX xla that is select MAPLE Ex cel WMIMPLEX xla and click OK For 64 bit Windows select WMIMPLEX64 xla that is select MAPLE Ex cel WMIMPLEX64 xla and click OK 5 Select the Maple Excel Add in check box 6 Click OK For details on enabling the Maple Excel Add in for Excel 2007 refer to the Excel help page For information on using this add in refer to the Using Maple in Excel help fil within Excel To view this help file 1 Ena
253. layed and enter to code to execute when the value changes Volume Gauge Select or display an integer or floating point value Change the display and enter code to execute when the value changes Example 1 Using Embedded Components This example demonstrates several components working together to perform a task The user inputs an expression which is plotted when the button is clicked Plot options are controlled by text areas a combo box a math expression and radio buttons For an interactive version of this example see the mw version of this manual In Maple from the Help menu select Manuals Resources and More Manuals User Manual 388 10 Embedded Components and Maplets Then click the Plot button Plot Change the axis ranges sin x m A plot of Change the color Constrained Unconstrained Printing and Exporting a Document with Embedded Components Printing When printing a document embedded components are rendered as they appear on screen Exporting Exporting a document with embedded components to other formats produces the following results e HTML format components are exported as gif files e RTF format components are rendered as bitmap images in the rtf document e LaTeX components are exported as eps files e PDF components are rendered as static images 10 3 Creating Embedded Components Embedded Components are graphical components that you ca
254. lculus1IntApps link The Calculus1 Applications of Integration worksheet opens See Figure 5 17 4 Expand the Volume of Revolution topic 5 Examine and execute the examples Calculus 1 Applications of Integration The Student Calculus1 package contains four routines that can be used to both work with and visualize the concepts of function averages arc lengths and volumes and surfaces of revolution This worksheet demonstrates this functionality For further information about any command in the Calculus package see the corresponding help page For a general overview see Calculus Getting Started H any command in the package can be referred to using the long form for example Student Calculus1 DerivativePlot itis easier and often clearer to load the package and then use the short form command names gt restart gt with Student Calculus The following sections show how the routines work In some cases examples show to use these visualization routines in conjunction with the single stepping Calculus routines gt Function Average Volume of Revolution Arc Length Surface of Revolution Main Visualization Previous Integration Figure 5 17 Example Worksheet Check for Other Ready To Use Resources Application Center The Maple Application Center contains free user contributed applications related to math ematics education science engineering computer science statistics and data analysis
255. le integers You can specify an algebraic number fiel over which to factor the polynomial For more information refer to the factor help page The ifactor command factors an integer For more information see Integer Operations page 106 To solve for the roots of a polynomial use the solve command For information on the solve command see Solving Equations and Inequations page 111 The isolve command solves an equation for integer solutions For more information see nteger Equations page 125 Other Commands Table 5 3 lists other commands available for polynomial operations Table 5 3 Select Other Polynomial Commands 5 3 Linear Algebra 155 ga retest common divisor oF two polynomial CurveFitting PolynomialInterpolation Interpolating polynomial for list of points See also the CurveFitting Assistant Tools Assistants Curve Fitting Additional Information Table 5 4 Additional Polynomial Help General polynomial information 2 polynom help page PolynomialTools package PolynomialTools package overview help page Algebraic manipulation of numeric polynomi SNAP Symbolic Numeric Algorithms for Polyno als mials package overview help page Efficien arithmetic for sparse polynomials SDMPolynom Sparse Distributed Multivariate Polynomial data structure help page Polynomial information and commands Maple Help System Table of Contents Mathemat ics Algebra Polynomials section 5 3 Linear Alg
256. leNet Using MapleNet you can deploy Maple content on the web Powered by the Maple compu tation engine MapleNet allows you to embed dynamic formulas models and diagrams as live content in web pages The MapleNet software is not included with the Maple software For more information on MapleNet visit http www maplesoft com maplenet MapleNet Documents and Maplets After you upload your Maple document to the MapleNet server it can be accessed by anyone in the world using a Web browser Even if viewers do not have a copy of Maple installed they can view documents and Maplets manipulate 3 D plots and execute code at the click of a button Custom Java Applets and JavaServer Pages Technology MapleNet provides a programming interface to the Maple math engine so commands can be executed from a Java applet or using JavaServer Pages technology Embed MapleNet into your web application and let Maple handle the math and visualization Maple T A Overview of Maple T A Maple T A is a web based automated testing system based on the Maple engine Instructors can use pre written questions or create custom question banks and then choose from these questions to form quizzes and assignments Maple T A automatically grades responses as students complete assignments and tests For more information visit http www maplesoft com mapleta 416 11 Input Output and Interacting with Other Products Exporting Assignments to Maple T
257. lick OK Linking to an Email Address To link to an email address 1 In the Type drop down list select Email 2 In the Target field enter the email address 3 Click OK Note For information about email hyperlinks in the Classic Worksheet interface see Worksheet Compatibility page 332 Linking to a Worksheet To link to a Maple worksheet or document 1 In the Type drop down list select Worksheet 2 In the Target field enter the path and filenam of the document or click Browse to locate the file Optional In the Bookmark drop down list enter or select a bookmark Note To link within a single Maple document leave the Target fiel blank and choose the bookmark from the Bookmark drop down list Note When linking to a custom document the path is absolute When sharing documents that contain hyperlinks ensure that target documents are in the same directory 3 Click OK Linking to a Help Page To link to a help page 1 In the Type drop down list select Help Topic 2 In the Target field enter the topic of the help page Optional In the Bookmark drop down list enter or select a bookmark 3 Click OK 7 6 Hyperlinks 323 Linking to a Task To link to a task 1 In the Type drop down list select Task 2 In the Target field enter the topic name of the task template see the status bar at the bottom of the Task Browser window 3 Click OK Linking to a Dictionary Topic To link to a Dictionary topic
258. ling sequence The range can be real or complex gt fsolve equation2 z z 100 200 149 2390528 The syntax for specifying a region in the complex plane is lower left point upper right point gt fsolve equation3 vy y 2 I 0 complex 1 13846246879373 0 485062494059435 I Initial Values You can specify a value for each unknown The fsolve command uses these as initial values for the unknowns in the numerical method 118 4 Basic Computations gt fsolve equation2 z 100 z 98 98037599 4 9 For more information and examples refer to the fsolve details help page For information on verifying and using solutions returned by the fsolve command see the following section Working with Solutions Working with Solutions Verifying It is recommended that you always verify solutions that the solve and fsolve commands return using the eval command gt equation4 sin x cos x gt solve equation4 T 4 10 gt eval equation4 x 4 10 2 Jz 4 11 gt equationS cos z NIN gt fsolve equationS 2 498755763 4 12 gt eval equationS z 4 12 0 8003983544 0 8003983540 4 13 For more information see Substituting a Value for a Subexpression page 353 Assigning the Value of a Solution to a Variable To assign the value of a solution to the corresponding variable as an expression use theassign command For example consider the numeric
259. lor red s i gt plots display P Q title Scatter Plot with Fitted Quartic Polynomial Scatter Plot with Fitted Quantic Polynomial 40 For more information on statistical plots refer to the Statistics Visualization help page For an overview of plotting see Plots and Animations page 237 Additional Information For more information on the Statistics package including regression analysis estimation data manipulation and data smoothing refer to the Statistics help page The Data Analysis Assistant For more information refer to the Statistics Interact iveDataAnalysis help page 5 7 Teaching and Learning with Maple Table 5 10 lists the available resources for instructors and students For additional resources see Available Resources page 56 5 7 Teaching and Learning with Maple 195 Table 5 10 Student and Instructor Resources Resource Description Student Packages Tutors and Demonstrations Teacher Resource Center Maple Portal Mathematics and Engineering Dic tionary The Student package contains computational and visualization plotting and animation functionality and point and click inter faces for explaining and exploring concepts Tools Tutors For more information refer to the Student help page Maple s Demonstrations provide interactive visual illustrations of Precalculus concepts Tools Demonstrations Use the provided Demos or learn how these are created and using
260. lt plot create a two dimensional plot Calling Sequence plottf x plottf x x0 x1 plotiw1l 2 Parameters Bookmark parameterskyression in independent variable x ZF independent variable x0 x1 left and right endpoints of horizontal range vl w2 x coordinates and y coordinates 326 7 Creating Mathematical Documents Go to a Bookmark You can automatically move the cursor to the location of the bookmark in the active docu ment 1 From the Edit menu select Go To Bookmark The Go To Bookmark dialog opens with the current bookmarks listed 2 Select the bookmark parameters and click OK The cursor moves to the bookmark at the beginning of the Parameters section For more information refer to the bookmarks help page 7 7 Embedded Components You can embed simple graphical interface components such as a button in your document These components can then be associated with actions that are to be executed For example the value of a slider component can be assigned to a document variable or a text fiel can be used to input an equation Adding Graphical Interface Components The graphical interface components can be inserted by using the Components palette Figure 7 21 or by cutting copying and pasting existing components to another area of the document Although copied components have most of the same characteristics they are distinct By default palettes are displayed when you launch Maple
261. lt input region of each mode xvii Xvill Preface Shortcut Keys by Platform This manual will frequently refer to context menus and command completion when entering expressions The keyboard keys used to invoke these features differ based on your operating system This manual will only refer to the keyboard keys needed for a Windows operating system The shortcut keys for your operating system can be viewed from the Help menu Help Manuals Resources and more Shortcut Keys Context Menus e Right click Windows and UNIX e Control click Macintosh That is place the mouse over the input or output region and press the right button on the mouse or press and hold the Control key and click the mouse key for Macintosh For more information on Context Menus see Context Menus page 39 Command Completion e Esc Macintosh Windows and UNIX e Ctrl Space Windows e Ctrl Shift Space UNIX Begin entering a command in a Maple document Press the Ese key Alternatively use the platform specifi keys For Windows press and hold the Ctrl key and then press the Space bar For more information on Command Completion see Command Completion page 47 In This Manual This manual provides an introduction to the following Maple features e Ease of use when entering and solving problems e Point and click interaction with various interfaces to help you solve problems quickly e Maple commands and standard math notation
262. methods e Inthe Common Symbols palette click the I i or j item See Palettes page 21 e Enter i or j and then press the symbol completion key See Symbol Names page 28 Note that the output will still be displayed with I no matter what symbol was used for input You can customize Maple s settings to use a different symbol for 1 For more information on entering complex numbers including how to customize this setting refer to the HowDol help page The GIsqrt command approximates the square root in the Gaussian integers 4 4 Solving Equations 111 gt GaussInt GIsqrt 9 5j 3 For more information on Gaussian integers including a list of GaussInt package commands refer to the GaussInt help page 4 4 Solving Equations You can solve a variety of equation types including those described in Table 4 3 Table 4 3 Overview of Solution Methods for Important Equation Types LinearAlgebra LinearSolve command Note Many solve operations are available in context menus and as task templates Tools Tasks Browse Most of this section focuses on other methods Solving Equations and Inequations Using Maple you can symbolically solve equations and inequations You can also solve equations numerically To solve an equation or set of equations using context menus 1 Right click for Macintosh Control click the equations 2 From the context menu select Solve or Solve Numerically See Figure 4 2 11
263. mmediate Evaluation of the Integral 1 Enter the integral S dx in a blank 4 x document block region 2 Right click the expression and select Evaluate f and Display Inline l dx arcsin 4 230 e 5 Mathematical Problem Solving Solution by Integration Methods Tutor 1 Load the Student Calculus 1 package From Loading Student Calculus1 the Tools menu select Load Package Student Calculus 1 Ctrl drag the integrand 4 x blank document block region Right click the expression and select Tutors eggs 7 CSE ice Calculus Single Variable Integration File Edit Rule Definition Apply Rule Understood Rules Help Methods The Integration Methods Tutor Enter a function Function 1 4 x 2 1 2 Variable x from to Start displays i 1 Click on any button to 4 x d dx apply a rule Show Hints Get Hint Constant Multiple Sum Difference Parts Partial Fractions Change Revert Rewrite Exponential Natural Logarithm lt trig gt w lt hyperbolic gt v lt arctrig gt w lt archyperbolic gt v 4 Perform a change of variables by selecting i The change rule has been Change and entering x 2 sin u applied Show Hinks 5 8 Clickable Math 231 5 Apply the constant rule by clicking Constant 1 gt The revert rule has been 6 To revert back to the original variable click 4 7 dx applied 1 dz Show Hi
264. n e Use the simplify command The simplify command applies simplificatio rules to an expression Maple has simplificatio rules for various types of expressions and forms including trigonometric functions radicals logarithmic functions exponential functions powers and various special functions You can also specify custom simplificatio rules using a set of side relations 1 gt Pa 32 J 35 gt simplify sin x In 2y cos x 1 In 2 In y To limit the simplification specify the type of simplificatio to be performed 8 3 Working with Maple Expressions 349 gt simplify sin x In 2y cos x trig 1 In 2 y gt simplify sin x In 2y cos x In sin x In 2 In y cos x You can also use the simplify command with side relations See Substituting a Value for a Subexpression page 353 Factoring To factor a polynomial e Use the factor command i 5 OS 2 gt factor x x 9x9 20 12x 9 x x 2 x 3 x 2 x 1 3 2 2 3 2 2 2 2 gt factor x yr x y 3x x yt 2x 6xL 5xy y 3x 3y f y 3 x 1 x y Maple can factor polynomials over the domain specifie by the coefficients You can also factor polynomials over algebraic extensions For details refer to the factor help page For more information on polynomials see Polynomial Algebra page 148 To factor an integer e Use the ifactor command gt ifactor 196911 3 11
265. n add to your document They provide interactive access to Maple code without requiring the user to know Maple com mands and include buttons sliders math and text input areas and plot display 10 3 Creating Embedded Components 389 Inserting Components The graphical interface components can be inserted by using the Components palette Figure 10 1 or by cutting copying and pasting existing components to another area of the document Although copied components have most of the same characteristics they are distinct If the Components palette is not visible see Palettes page 21 for instructions on viewing palettes Y Components Button Combo Box Check Box Radio Button Text Area Label List Box i frix Figure 10 1 Components Palette Editing Component Properties General Process To edit properties of components embedded in the document 1 Right click Control click for Macintosh the component to display the context menu 2 If available select Component Properties otherwise select Components Com ponent Properties The related dialog opens 3 Enter values and contents in the field as necessary 4 For actions such as Action When Value Changes in the Slider component dialog click Edit A blank dialog opens allowing you to enter Maple code that is executed when the event occurs For details refer to the DocumentTools help page 390 10 Embedded Components and Maplets Removing
266. n read it into Maple 410 11 Input Output and Interacting with Other Products Reading Data from a File Import Data Assistant If you generate data outside Maple you can read it into Maple for further manipulation This data can be an image a sound file or columns of numbers in a text file You can easily import this external data into Maple using the Import Data Assistant where the supported fil formats include file of type Excel MATLAB Image Audio Matrix Market and Delimited To launch the Import Data Assistant 1 From the Tools menu select Assistants and then Import Data 2 A dialog window appears where you can navigate to your data file Select the fil that you want to import data from and then select the fil type before clicking Next 3 From the main window you can preview the selected fil and choose from the applicable options based on the format of the fil read in before importing the data into Maple See Figure 11 1Figure 11 1 for an example Data Import Assistant Additional Format Options Data Type integer 1 f8 bit ka Skip Lines 2 Source From Rectangular F Transpose Separator Space Separated wt View of File Experiment 25 i 1 i1 2 4b 2 3 9 3 4 16 4 5 a5 5 Cancel Previous Figure 11 1 Import Data Assistant ImportMatrix Command The Import Data Assistant provides a graphical interface to the ImportMatrix command For more information including options not availabl
267. nal operator as an expression using the plot3d command gt h x y gt xX cos y 342 e 8 Maple Expressions gt plot3d h x y x 2 2 y 2 7 2 T For information on plotting see Plots and Animations page 237 Integration Integrate a function using the int command gt k x gt sin cos x 7 gt m K 1 0 5 r StruveH 0 r For information on integration and other calculus operations see Calculus page 172 Strings A string is a sequence of characters enclosed in double quotes gt This is a sequence of characters 8 3 Working with Maple Expressions 343 Accessing Characters You can access characters in a string using brackets gt 11 2 sequence of characters Using Strings The StringTools package is an advanced set of tools for manipulating and using strings gt with StringTools gt Random 9 alnum Sdzrl9ema gt Stem impressive impress gt Split Create a list of strings from the words in a string Lh Create a list of strings from the words in a string 8 3 Working with Maple Expressions This section describes how to manipulate expressions using commands Topics covered include testing the expression type accessing operands of an expression and evaluating an expression Low Level Operations Expression Types A Maple type is a broad class of expressions that share common properties
268. nd Isotope Properties Value Units and Uncertainty Performing Computations Modificatio and Extensibility Uncertainty Propagation e Quantities with Uncertainty e Performing Computations with Quantities with Uncertainty Restricting the Domain page 141 How to restrict Real Number Domain the domain for computations e Assumptions on Variables 4 2 Symbolic and Numeric Computation Symbolic computation 1s the mathematical manipulation of expressions involving symbolic or abstract quantities such as variables functions and operators and exact numbers such as integers rationals z and e7 The goal of such manipulations may be to transform an expression to a simpler form or to relate the expression to other better understood formulas Numeric computation is the manipulation of expressions in the context of finite precisio arithmetic Expressions involving exact numbers for example 2 are replaced by close approximations using floating poin numbers for example 1 41421 These computations generally involve some error Understanding and controlling this error is often of as much importance as the computed result 4 2 Symbolic and Numeric Computation 103 In Maple numeric computation is normally performed if you use floating poin numbers numbers containing a decimal point or the evalf command The plot command see Plots and Animations page 237 uses numeric computation while commands such as int limit and g
269. nd denominator use the expanded option 8 3 Working with Maple Expressions 353 9 9 A F gt normal n expanded x y x y A R x 2xyt yV gt normal in l x l sin To sort the elements of an expression Sorting e Use the sort command The sort command orders a list of values or terms of a polynomial gt sort 4 3 2 1 4 43 0 4 0 2 1 3 4 43 gt sort x 42 73 14 9x 5 xX 4 9 5r e7 aH gt sort xy 6 y x 2 35x 1 6x7 2y xy 5x 1 1 For information on sorting polynomials see Sorting Terms page 150 For more information on sorting refer to the sort help page Evaluating Expressions Substituting a Value for a Subexpression To evaluate an expression at a point you must substitute a value for a variable 354 e 8 Maple Expressions To substitute a value for a variable using context menus 1 Right click Control click for Macintosh the expression Maple displays a context menu 2 From the context menu select Evaluate at a Point The Evaluate at a Point dialog is displayed See Figure 8 2 E Evaluate at a Point Evaluate the expression at the point Figure 8 2 Evaluate at a Point 3 In the drop down list select the variable to substitute 4 In the text field enter the value to substitute for the variable Click OK In Worksheet mode Maple inserts the eval command calling sequence that performs the substitution
270. nd from a plot region e Maple offers numerous plot options such as axis styles title colors shading options surface styles and axis ranges which give you complete control to customize your plots For a reference to the types of plots available in Maple see the Plotting Guide 6 1 In This Chapter Section Creating Plots page 238 Interactive and command driven methods to display 2 D and 3 D plots Customizing Plots page 263 Methods for applying plot options before and after a plot displays Analyzing Plots page 269 Plot analyzing tools Interactive Plot Builder Context Menu Dragging to a Plot Region The plot and plot3d Commands The plots Package Multiple Plots in the Same Plot Region Interactive Plot Builder Options Context Menu Options The plot and plot3d Command Options Point Probe Rotate Pan Zoom Representing Data page 270 Templates for visual e The Live Data Plots Palette representation of your data Creating Animations page 270 Interactive and e command driven methods to display animations 237 Interactive Plot Builder The plots animate Command The plot3d viewpoint Command 238 6 Plots and Animations Playing Animations page 276 Tools to run anima Animation Context Bar tions Customizing Animations page 277 Methods for Interactive Plot Builder Animation Op applying plot options before and after an animation tions displays e Context Menu
271. nding command help page 9 4 Procedures A Maple procedure is a program consisting of Maple statements Using procedures you can quickly execute the contained sequence of statements Defining and Running Simple Procedures To defin a procedure enclose a sequence of statements between proc and end proc statements In general you assign a procedure definitio to a name The following procedure returns the square root of 2 gt p proc sqrt 2 end proc p proc sqrt 2 end proc Note Maple returns the procedure definition To improve readability of procedures it is recommended that you defin a procedure using multiple lines and indent the lines using space characters To begin a new line without evaluating the incomplete procedure definition press Shift Enter When you have finishe entering the procedure press Enter to create the procedure 9 4 Procedures 379 For example gt p proc sqrt 2 end proc To run the procedure p enter its name followed by parentheses gt p J7 Procedures with Inputs You can defin a procedure that accepts user input In the parentheses of the proc statement specify the parameter names For multiple parameters separate the names with commas gt geometric_mean proc x y sqrt x y end proc When the user runs the procedure the parameter names are replaced by the argument values gt geometric_mean 13 17 J 221 gt geometric_mean 13 5 17
272. ne that 1s text input and output in one line as presented in business and education documents In document mode content is displayed inline by default 7 3 Commands in Documents 301 To display content inline 1 Place the cursor in the document block 2 From the View menu select Inline Document Output View Document Code To view the contents that is all code and expanded execution groups within a document block you must expand the document block 1 Place the cursor in the document block region 2 From the View menu select Expand Document Block i Plot the expression sin x and its integral gt sin x dx gt print l input placeholder ouiput redirected cos x Ay in the same plot 3 To hide code again select View and then Collapse Document Block Expand an Execution Group within a Document Block An execution group is a grouping of Maple input with its corresponding Maple output It is distinguished by a large square bracket at the left called a group boundary As document blocks can contain many execution groups you can select to expand an exe cution group within a document block 1 Place the cursor near the end of the document block region 2 From the View menu select Expand Execution Group Plot the expression sin x and its integral kald dx cos x A i in the same plot 3 To hide the group select View and then Collapse Execution Group Switch betwe
273. ne word per line e It is case sensitive This means that integer and Integer require individual entries in the dictionary file e It does not require manual maintenance You build your dictionary fil by using the Add functionality of the Spellcheck However you can manually edit the file To specify a custom dictionary to be used with the Maple Spellcheck utility 1 Create a txt fil in a directory folder of your choice 2 In Maple open the Options dialog Tools Options and select the General tab 3 Inthe User Dictionary field enter the path and name of the txt fil you created or click Browse to select the location and filename 4 To ignore Maple words that are command and function names clear the Use Maple words in spellchecker check box 5 Click Apply to Session or Apply Globally to save the settings or Cancel to discard Adding a Word to Your Dictionary When running the spellcheck if the word in the Not Found text box is correct you can add the word to your dictionary 1 Click the Add button If this is the firs time you are adding a word the Select User Dictionary dialog opens 2 Enter or select the custom dictionary txt file you created See User Dictionary page 330 7 9 Creating Graded Assignments 331 3 Click Select The word is automatically added to your custom dictionary file Note Specification in the Options dialog determine whether this word is recognized in your next Maple session If you s
274. nfa log 2 log a sin a cos a tan a a f a flab f5a y X xa gt ca e Figure 3 1 Expression Palette f a b f x You can use palettes to enter input h 7 dx For example evaluate a definit integral using the definit integration item a in the Expression palette In 2 D Math clicking the definit integration item inserts b gt fax 1 Enter values in the placeholders To move to the next placeholder press Tab Note If pressing the Tab key inserts a tab click the Tab icon in the toolbar 2 evaluate the integral press Enter gt tanh x dx 0 In 2 Inle e In 1 D Math clicking the definit integration item inserts the corresponding command calling sequence 88 3 Worksheet Mode gt int f f x a b Specify the problem values using the Tab to move to the next placeholder and then press Enter gt int tanh x x 0 1 In 2 Ine e Note Some palette items cannot be inserted into 1 D Math because they are not define in the Maple language When the cursor is in 1 D Math input unavailable palette items are dimmed For more information on viewing and using palettes see Palettes page 21 in Chapter 1 3 5 Context Menus A context menu 1s a pop up menu that lists the operations and actions you can perform on a particular expression See Figure 3 2 gt 946929 946929 Copy Special b Numeric Formatting Explore Apply a Command
275. ng the cursor in the firs task command and then pressing Enter repeatedly to execute each command 1 4 Point and Click Interaction 43 e Selecting all the template commands and then clicking the execute toolbar icon f 3 If the template contains a button that computes the result click it For more information on task templates refer to the tasks help page Exploration Assistant The Exploration Assistant allows you to interactively make parameter changes to expressions and view the result The assistant can be used with almost any Maple expression or command that has at least one variable or parameter To launch the Exploration Assistant 1 Enter an expression or command 2 Right click Control click Macintosh the expression or command From the context menu select Explore 3 The Explore parameter selection dialog appears where you can select the parameters to explore and the range for each parameter If you enter integer ranges only integer values are allowed for parameters To allow floating point values enter floating poin ranges Select skip for any of the parameters to leave that parameter as a variable 4 Click Explore to continue to the Exploration Assistant The assistant opens in a new document You can use the slider or sliders to vary the parameters and see your changes as the expression output is updated 5 Once you are finishe interacting with the assistant you can copy and paste the results into
276. normal form 352 factorial command 107 FAIL 366 372 false 366 372 Faraday constant 134 Favorites palette 21 file image formats 319 reading from 411 writing to 407 fil option 163 finit fields 109 solving equations 125 finit rings 109 floating poin computation 103 accuracy 105 hardware 105 significan digits 104 numbers 102 rational approximation 89 Flux command 183 font color 283 foot pound second FPS system 72 128 footers 296 for from loops 369 for in loops 371 formal power series solutions 124 format labels 49 Format menu bookmarks 324 quick formatting 283 frac command 144 fractions approximating 69 entering 6 frequency plot 192 Frobenius form matrix 170 from clause 369 excluding 369 fsolve command 116 full evaluation 360 362 FunctionAdvisor command 81 functional operators 339 differentiating 175 plotting 341 versus expressions 340 functions converting between 351 definin as functional operators 339 G Gaussian elimination 170 Gaussian integers 110 GaussInt package 110 gcd command 155 gcdex command 155 Global Optimization Toolbox 184 global variables 379 glossiness of 3 D plots 267 go to bookmark 326 gradient 199 Gradient Tutor 198 Graphing Calculator xvii greatest common divisor 107 155 H Handwriting palette 27 has command 345 hastype command 344 HazardRate command 191 headers 296 Help Navigator Using 55 help page
277. nowledge of plot command syntax 1 Enter and evaluate an expression for example gt x Ty 2 Right click Control click for Macintosh the expression 3 From the context menu select Plots 3 D Plot x y hw xy Ty io Copy Special Numeric Formatting Explore 4oply a Command 455i9gn to a Mame Collect Combine Denominator Differentiate Evaluate at a Point Expand Factor Integrate Limit Mormal Numerator Plots Series Simplify Solve Complete Square Complex Maps Constructions Conversions Integer Functions Integral Transforms Optimization Sequence Sorts Tutors Units xy 2 xX ty Pa rr F F FT Fr F0 i F0 F0 F F F F 3 D Flot b 2 D Implicit Plot 3 D Implicit Plot Plot Builder 6 2 Creating Plots 247 6 1 ay Y YX Is 248 6 Plots and Animations For information on customizing plots using the context menu see Context Menu Options page 264 Dragging to a Plot Region To use the drag and drop method use the plot region created by one of the other methods or insert an empty plot region into the document Empty plot regions can be two dimensional or three dimensional Advantages of the drag and drop method include the ease of adding and removing plots and the independence from plotting command syntax Example 1 From the Insert menu select Plot 2 D 2 Enter the expression sin x in an input region 3 When dragging an e
278. nt session or Apply Globally to set for all Maple sessions To convert 2 D Math input to 1 D Math input 1 Select the 2 D Math input 2 From the Format menu select Convert To and then 1 D Math Input Important In Document mode you can execute a statement only if you enter it in Math mode Input Separators In 1 D and 2 D Math input you can use a semicolon or colon to separate multiple inputs in the same input line gt J 4 4 tan 3 2 2 097617696 0 05847385446 If you do not specify a semicolon or colon Maple interprets it as a single input This can either give unexpected results as below or an error gt J 4 4 tan 3 2 Q0 1226557919 3 3 Commands Maple contains a large set of commands and a powerful programming language Most Maple commands are written using the Maple programming language You can enter commands using 1 D or 2 D Math You must use 1 D Math input when programming in Maple Basic Programming page 365 provides an introduction to Maple programming To learn how to use Maple commands see the appropriate help page or use task templates For more information see The Maple Help System page 53 and Task Templates page 90 3 3 Commands 81 The Maple Library Maple s commands are contained in the Maple library There are two types of commands top level commands and package commands e The top level commands are the most frequently used Maple commands e Packages contain related special
279. nts Get Hint ni l aT arcsin gt x Constant Multiple Fi Revert 7 Now that the integral has been evaluated click Close to close the tutor and return the evalu ated integral to the document integration methods tutor inmid Solution by First Principles 1 Ctrl drag the integrand to a blank 4 x document block region and press Enter Perform trig substitution evaluate at point 2 Right click the output and select Evaluate at a point In the dialog that displays enter 2 sin u 4 4 sin u Right click the output and select Simplify simplify symbolic Symbolic l 2 cos u 232 e 5 Mathematical Problem Solving 9 sin Calculate a x 2sin u dv x 2sin u 4 Ina blank document block enter the substitu PO implicit differentiation tion equation x 2sin u and press Enter E Right click the output and select Differentiate Implicitly In the dialog that displays change the Independent Variable to u 2 cos i Calculate the integral in terms of u 5 9 5 10 6 Referencing the results by their equation labels multiply the original simplifie expression by this derivative 7 Integrate the resulting expression 65 10 du Revert the substitution x 2sin 5 12 8 Place the equation x 2 sin w in a blank doc x 2sin u ument block Delete w and insert the equation label for the previous result the value of the
280. nu select Take a Tour of Maple Quick Help and Quick References The Quick Help dialog is a list of key commands and concepts e From the Help menu select Quick Help Alternatively press F1 For additional inform ation click an item in the Quick Help The Quick Reference is a table of commands and information for new users that opens in a new window It contains hyperlinks to help pages for more information e From the Help menu select Quick Reference Alternatively press Ctrl F2 Command F2 for Macintosh Web Site Resources Welcome Center A Maple web site offering all of Maplesoft s key user resources in one central location In the Welcome Center you can view sample applications participate in user forums access 1 7 Available Resources 59 exclusive premium content and listen to podcasts You can also access our support services view training videos download user manuals and more http www maplesoft com welcome Student Help Center The Student Help Center offers a Maple student forum online math Oracles training videos and a math homework resource guide http www maplesoft com studentcenter Teacher Resource Center The Teacher Resource Center is designed to ensure you get the most out of your Maple teaching experience It provides sample applications course material training videos white papers e books podcasts and tips http www maplesoft com teachercenter Application Center Maple w
281. o Other Programming Languages 6 00 416 Accessing External Products from Maple cccccceccecececeeseeeseeneeaens 416 Accessing Maple from External Products ccccccceceecec eae eeseseeeeeenens 417 Sharing and Storing Maple Worksheet Content cccccecececeeeeeceeenes 419 x Contents List of Figures Figure L ne Maple Envir Oniment s cccstioeasasnrwladeaar AT a 3 Figure 1 2 Text and Math Buttons on the Toolbar ccc cece ececec ec ec ee eeeeenenees 19 Fieu to Hindwrimno Palette e es A alate AAT E 28 Feme 1 4 Optimization ASSISA raa aE E T A aalata dates 32 Figure 1 5 Accessing the Assistants from the Tools Menu ccccseeeeeeeeeeeees 33 Figure 1 6 Accessing Tutors from the Tools Menu cccecececececec sees eeenenenes 37 Figure 1 7 Calculus Single Variable Differentiation Methods Tutor 38 Figure 1 8 Right click the expression to see a menu of applicable operations 40 Figure 1 9 Right click the plot to see a menu of plot Options ssesoessosseeseessessee 40 Fiere 110 Browse Tasks Dialogissa a a 41 Pacure tA Egunon Labela e a E NA ET 48 Figure 1 12 Inserting an Bquation Label ereis aveinsaladieins E E E 49 Figure 1 13 Format Labels Dialog Adding a Prefi nnonnsonnsonnsonnssrnsssressressn 50 Peme el ea Dew Re ihe Ces 5440 a a E E tua annenasaaessenaccou 50 Figure 1 15 Document Block M
282. o an equation use the isolve For more information refer to the isolve help page gt isolve h y 13 x Zl y _ZI 13 Integer Equations in a Finite Field To solve an equation modulo an integer use the msolve For more information refer to the msolve help page gt msolve 7 1 13 x 1 x 12 Solving Linear Systems To solve a linear system use the LinearAlgebra LinearSolve For more information refer to the LinearAlgebra LinearSolve help page 126 4 Basic Computations For example construct an augmented matrix using the Matrix palette see Creating Matrices and Vectors page 156 in which the firs four columns contain the entries of A and the fina column contains the entries of B gt linearsystem 59 44 17 1 1 10 25 2 100 2 0 7 oe TEE 23 9 12 gt gt LinearAlgebra LinearSolve linearsystem For more information on using Maple to solve linear algebra problems see Linear Algebra page 155 31753441047 41858667400 16991806239 8371733480 1489266217 1674346696 262603866 209293337 Solving Recurrence Relations To solve a recurrence relation use the rsolve For more information refer to the rsolve help page gt rsolve fn fin 1 fin 2 A 1 A DAY fn sov5 3 205 3 GovS a 2 ij 2 4 5 Units Scientifi Constants and Uncertainty 127 4 5 Units Scientific Constants and Uncertainty In addition to manipulating exact symboli
283. o evaluate the product For more information on entering complex numbers refer to the HowDol help page Toolbar Icons In the introduction section you learned about the toolbar icons and context toolbars available in Maple see Toolbar Options page 9 The toolbar can be used to format your document alter plots and animations draw in a canvas write in both Math and Text modes in one line and much more The last of these is demonstrated in the next example Example 6 Enter Text and 2 D Math in the Same Line Using Toolbar Icons Enter the following sentence 2 3 Sepsis i LM Evaluate 3 x box 3 x dx and write in simplest terms l Result in Document To enter this sentence Say 1 Select the Text icon and enter Evaluate 2 Select the Math icon 3 From the Expression palette select the amp a5 math h a P as Evaluate 7 dx a FAR definit integration template a expression is displayed with the firs placeholder highlighted With the firs placeholder highlighted enter 1 then press Tab Enter 5 and press Tab to highlight the in tegrand region Enter 3x 2 and press the right arrow to leave the superscript position Enter 2 Press the Space bar for implicit multiplic ation Enter sqrt and press Esc to show the command completion options Maple displays a pop up list of exact matches Select the square root symbol Jx Maple inserts the symbol with the x
284. often by right clicking Control click Macintosh the palette template you want to add and selecting Add To Favorites Palette from the context menu 22 1 Getting Started Table 1 7 Palette Categories Palette Category Palette Description Expression Palettes MapleCloud view worksheets shared by other users and share your worksheets OW Matrix Variables manage all of your assigned variables in your current Maple Rone session Columns h Choose o Type Custom values Expression construct expressions such as integrals a Shape A oil Matrix enter the number of rows and columns required designate Data type Any type such as zero filled and designate shape such as diagonal Hi Insert Matrix J Layout add math content that has specifi layout such as expressions h with one or more superscripts and subscripts Components embed graphical interface components such as a button into your document or worksheet Components can be programmed to perform an action when selected such as executing a command when a button is clicked Handwriting an easy way to fin a desired symbol Units SI insert a unit from the International System of Units SI or any general unit L 2 Units FPS insert a unit from the Foot Pound Second System FPS or any general unit 7 Accents insert decorated names such as an x with an arrow over it to denote a vector 4 Fa
285. ollowing calling sequence returns false gt has x y 2 x z false To return all subexpressions of a particular type use the indets command For more inform ation see Indeterminates page 347 Accessing Expression Components Left and Right Hand Side To extract the left hand side of an equation inequality or range e Use the Ihs command To extract the right hand side of an equation inequality or range e Use the rhs command 346 8 Maple Expressions For example gt y xt I y x 1 8 1 gt lhs C8 1 y 8 2 gt rhs C8 1 x 1 8 3 For the following equation the left endpoint of the range is the left hand side of the right hand side of the equation gt x 3 5 x 3 5 8 4 gt lhs rhs 8 4 3 8 5 Numerator and Denominator To extract the numerator of an expression e Use the numer command To extract the denominator of an expression e Use the denom command l y sin x x gt am m y Ee If the expression is not in normal form Maple normalizes the expression before selecting the numerator or denominator For more information on normal form refer to the normal help page 8 3 Working with Maple Expressions 347 gt numer e 3 x sin x x y gt denom e 9 x s 1 x gt denom denom e l The expression can be any algebraic expression For information on the behavior for non rational expressions refer to the numer help page
286. ombine d2 errors The value of the result 1s gt evalf result 43 74124725 The uncertainty of the result 1s gt GetError result 14 42690612 Additional Information For information on topics including e Creating new rounding rules e Setting the default rounding rule and e Creating a new interface to quantities with uncertainty refer to the ScientificEr orAnalysis help page 4 6 Restricting the Domain By default Maple computes in the complex number system Most computations are per formed without any restrictions or assumptions on the variables Maple often returns results that are extraneous or unsimplifie when computing in the fiel of complex numbers Using restrictions you can more easily and efficientl perform computations in a smaller domain Maple has facilities for performing computations in the real number system and for applying assumptions to variables Real Number Domain To force Maple to perform computations in the fiel of real numbers use the RealDomain package The RealDomain package contains a small subset of Maple commands related to basic precalculus and calculus mathematics for example arccos limit and log and the symbolic manipulation of expressions and formulae for example expand eval and solve For a complete list of commands refer to the RealDomain help page 142 4 Basic Computations After you load the RealDomain package Maple assumes that all variables are real Com mand
287. on labels and equation label references see Equation Labels page 95 For more information on context menus see Context Menus page 68 in Chapter 2 90 3 Worksheet Mode 3 6 Assistants and Tutors Assistants and tutors provide point and click interfaces with buttons text input regions and sliders See Figure 3 3 WE ODE Analyzer Assistant Differential Equations Conditions Parameters i Solve Numerically Solve Symbolically Classify Figure 3 3 ODE Analyzer Assistant Launching an Assistant or Tutor To launch an assistant or tutor 1 Open the Tools menu 2 Select Assistants or Tutors 3 Navigate to and select one of the assistants or tutors For more information on assistants and tutors see Assistants page 32 in Chapter 1 3 Task Templates Maple can solve a diverse set of problems The task template facility helps you quickly fin and use the commands required to perform common tasks After inserting a task template specify the parameters of your problem in the placeholders and then execute the commands or click a button The Task Browser Figure 3 4 organizes task templates by subject To launch the Task Browser e From the Tools menu select Tasks and then Browse 3 7 Task Templates 91 You can also browse the task templates in the Table of Contents of the Maple Help System 2 Browse Tasks File view 7 Overview 4 5 Algebra H Calculus Differential 5 1 Calculus
288. onent 386 dictionary 57 195 dictionary topic adding hyperlink to 323 diff command 121 175 differential equations ordinary 120 partial 124 differentiation 174 with uncertainty 140 with units 132 Differentiation Methods Tutor 197 Digits environment variable 104 dimension 127 168 base 127 Directional Derivative Tutor 176 discrim command 155 display bookmark 324 distribution probability 190 divide command 149 divisors 107 document blocks 50 299 Document mode 61 documents running 9 DocumentTools 394 double colon operator 142 dsolve command 124 E e notation 104 eBook Publisher Assistant 36 Edit menu in help system 56 eigenvalues 168 eigenvectors 168 element wise operators 358 elementary charge 134 elements 133 definition 135 isotopes 135 definition 135 properties 135 list 135 properties list 135 uncertainty 138 units 137 using 134 value 136 value and units 137 elif clauses 367 order 368 else clause 367 email adding hyperlink to 322 embedded components 326 385 inserting 388 properties 389 end do keywords 369 371 372 end if keywords 366 end proc keywords 378 engineers portal for 57 environment variables Digits 104 Order 179 equation solving step by step 216 equation labels 99 displaying 96 features 99 formatting 50 inserting 49 numbering schemes 98 overview 48 references to 96 versus names 99 with multiple outputs
289. ons To add a new distribution specify a probability distribution in a call to the Distribution command gt U Distribution PDF t gt t lt 0 t lt 3 v 0 otherwise To construct a piecewise continuous function in 1 D Math use the piecewise command for example t gt piecewise t lt 0 0 t lt 3 1 3 0 Defin a new random variable with this distribution 5 6 Statistics 191 gt Z RandomVariable U PDF Z t 0 t lt 0 L 3 3 0 otherwise Calculate the mean value of the random variable gt Mean Z N be Statistical Computations In addition to basic functions like mean median standard deviation and percentile the Statistics package contains commands that compute for example the interquartile range and hazard rate Example 1 Interquartile Range Compute the average absolute range from the interquartile of the Rayleigh distribution with scale parameter 3 gt InterquartileRange Rayleigh 3 J36 Vin 18 In To compute the result numerically e Specify the numeric option gt InterquartileRange Rayleigh 3 numeric 2 719744818 Example 2 Hazard Rate Compute the hazard rate of the Cauchy distribution with location and scale parameters a and b at an arbitrary point t 192 e 5 Mathematical Problem Solving gt HazardRate Cauchy a b t l 1 ae arctan trb 1 b 2 T You can specify a value for the po
290. or Differential Equations Conditions y select y from the drop down yl Ay E 13 y t cos 2 t CEN menu In the text fields enter 0 and 1 y 0 1 Click Add Click Done to close this dialog and return to the main dialog Notice that the initial conditions are in the Conditions section 6 Click Solve Numerically A new dia log appears Parmeatar ie Burg iui hban 42th onder i Cashiip Eh onder i heer k TE ade Oh Geer singe step extrapolation 0 Rossnbnect shit J th onder Absolute 100000007 dit Relative LOOO detsk na Batum Pint 3 7 Click Solve to solve the initial value Output problem Show Function values at t 8 Click Plot to plot the solution of the desatitlet DE Plot Options 5 8 Clickable Math 235 9 Click the Plot Options button to solve DE interactively y t 4y t 13 y t cos 2 1 ___ gt modify the default graph if desired 10 Click Quit to close the ODE Analyzer and return a plot of the solution to the document 236 e e 5 Mathematical Problem Solving 6 Plots and Animations Maple can generate many forms of plots allowing you to visualize a problem and further understand concepts e Maple accepts explicit implicit and parametric forms to display 2 D and 3 D plots and animations e Maple recognizes many coordinate systems e All plot regions in Maple are active therefore you can drag expressions to a
291. orizontal distancefromaxis 0 amp showvolume true showsum false showregqion true method midpoint partition v Maple Command Figure 5 15 Volume of Revolution Tutor After you Close the tutor the plot is inserted into your worksheet Check for Existing Tools Task Template 1 From the Tools menu select Tasks and then Browse The Browse Tasks dialog opens displaying a list of tasks in the left pane The tasks are sorted by subject to help you quickly fin the desired task 2 Expand the Calculus Integral Applications Solids of Revolution folder 3 From the displayed list select Volume The Volume of Revolution task is displayed in the right pane of the Browse Tasks dialog 4 Select the Insert into New Worksheet check box 5 Click Insert Default Content Before inserting a task Maple checks whether the task variables have assigned values in your worksheet If any task variable is assigned the Task Variables dialog opens allowing you to modify the names Maple uses the edited 5 7 Teaching and Learning with Maple 207 variable names for all variable instances in the inserted task The content is inserted into your document See Figure 5 16 Volume of Revolution Calculate the volume of revolution for a solid of revolution when a function is rotated about the horizontal or vertical azis Enter the function as an expression and specify the range sinfx cos x 1 0 a sin x cos x
292. orksheet e Help Topic e Task e Dictionary Topic e Maplet 7 6 Hyperlinks 321 Hyperlink Properties Link Text Type Help Topic ve Target Figure 7 18 Hyperlink Properties Dialog Inserting a Hyperlink ina Document To create a hyperlink from existing text in the document 1 Highlight the text that you want to make a hyperlink 2 From the Format menu select Convert To and then Hyperlink 3 In the Hyperlink Properties dialog box the Link Text fiel is grayed out since the text region you highlighted is used as the link text This is demonstrated in Figure 7 18 The highlighted text region Diff is grayed out 4 Specify the hyperlink Type and Target as described in the appropriate following section To insert a text or image hyperlink into the document 1 From the Insert menu select Hyperlink 2 In the Hyperlink Properties dialog box enter the Link Text Optionally use an image as the link Select the Image check box and click Choose Image for the file In mw files the image appears as the link You can resize the image as necessary Click and drag from the corners of the image to resize 3 Specify the hyperlink Type and Target as described in the appropriate following section 322 7 Creating Mathematical Documents Linking to a Web Page To link to a Web page 1 In the Type drop down list select URL 2 In the Target field enter the full URL for example http www maplesoft com 3 C
293. orksheet Migration Assistant 36 Index 437 Worksheet mode 61 77 worksheets running 9 write to files 407 X xor operator 366 Z zero recognition 352 zip command 377 438 Index
294. ort form makes all of the commands in the package available using the with command with package If you are using a number of commands in a package loading the entire package is recommended When you execute the with command a list of all commands in the package displays To suppress the display of all command names end the with package command with a colon Alternatively you can load packages through the Tools menu by selecting Load Package and then the package name with Optimization ImportMPS Interactive LPSolve LSSolve Maximize Minimize NLPSolve OPSolve After loading a package you can use the short form names that is the command names without the package name ESSolve x 2 x 6 x 9 12 3333333333333322 x 5 66666666666666696 For a list of the top packages in Maple see Top Packages page 85 Command Completion To help with syntax and reduce the amount of typing when entering Maple commands you can use command completion Command completion displays a list of all Maple packages commands and functions that match the entered text If there are multiple ways to call a command then the command completion list contains each one with appropriate placehold ers 48 1 Getting Started To use command completion 1 Begin entering a command or package name 2 Select Tools Complete Command or use the shortcut key Ese see Shortcut Keys by Platform page xviii If there is a unique
295. ot Calling Sequence plot f x plot f x x0 x1 plot v1l v2 Parameters f expression in independent variable amp independent variable 0 xl left and right endpoints of horizontal range y v2 x coordinates and y coordinates Bookmarks Use a bookmark to designate a location in an active document This bookmark can then be accessed from other regions in your document or by using hyperlinks in other documents To display bookmark formatting icons activate the Marker feature e From the View menu select Markers o gt Section 1 1 ee Bookmark Indicator Section 1 2 Figure 7 19 Bookmark Indicator Note You can display bookmark properties by holding the pointer over a bookmark indic ator See Figure 7 19 Inserting Renaming and Deleting a Bookmark To insert a bookmark 1 Place the cursor at the location at which to place the bookmark For example place the cursor in the Parameters section title 2 From the Format menu select Bookmarks The Bookmark dialog opens listing existing bookmarks in the document 7 6 Hyperlinks 325 3 Click New The Create Bookmark dialog opens See Figure 7 20 Enter a bookmark name parameters and click Create F ee Ed Create Bookmark Figure 7 20 Create Bookmark Dialog 4 The new bookmark appears in the Bookmark dialog list Click OK Note You can also rename and delete bookmarks using the Bookmark dialog Resu
296. ot by selecting from the numerous plot types and applying plot options without any knowledge of plotting command syntax 4 Apply the discont true option for a discontinuous graph The output from the Interactive Plot Builder is a plot of the expression or the command used to generate the plot in the document To launch the Interactive Plot Builder e From the Tools menu select Assistants and then Plot Builder Note The Tools menu also offers tutors to easily generate plots in several academic subjects For more inform ation see Teaching and Learning with Maple page 194 Table 6 1 Windows of the Interactive Plot Builder 1 Specify Expressions window 2 Select Plot Type window MI Interactive Plot Builder Specify Expressions Ml Interactive Plot Builder Select Plot Type File Select Plot Type and Functions Plot Edit Functions Select Plot 3 D contour plot 2 D contour plot 2 D density plot 2 D gradient vector field plot 2 D implicit plot Expressions sin x y yiix2 y 1 Select Variable Purposes Ranges and Plot Options Variables x r x Axis xim 2 pi to 2 Pi ly y Axis yi 2i tori On Plot return plot command 1 Specify Expressions window Add edit or remove expressions and variables Once finished you can advance to the Select Plot Type window 2 Select Plot Type window Select the plot type and corresponding plot and edit the ranges Once finish
297. ou want to copy Press and hold the Ctrl key while you drag the input to the new region using the mouse The steps are the same for Macintosh with the exception of pressing the Command key Example 2 Solve and Plot an Equation Using Context Menus and Copy amp Drag Review the following example I r In this example we will enter the equation and then solve and plot the equation using context menus and Maple s copy amp drag feature This example will only refer to the keystrokes needed on a Windows operating system to invoke the context menus and the copy amp drag feature For your operating system refer to section Shortcut Keys by Platform page xviii for the equivalent keystrokes 1 2 Introduction to Maple To solve the equation 1 Enter the equation 2 Right click the equation and select Move to Left Input Ssx 7 3x4 2 Result 5x 7 3x 2 Copy Special b Paste Ctrl V Evaluate and Display Inline Ctrlt Explore 4poply a Command Differentiate b Evaluate at a Point Integrate b Left hand Side Manipulate Equation Map Command Onta Move to Left Move to Right K Negate Relation Plots b Right hand Side Simplify b Solve Test Relation Conversions b Integral Transforms d Sequence b 2 D Math F move to lefi 2x 9 0 13 A brief description move to left is displayed above the arrow that connects the input and output 14 1 Getting Started 3 Right click the output from
298. pace 170 binary numbers 108 Bohr radius 134 bold format 283 bookmarks using 324 boolean expressions 357 366 372 brackets angle 156 159 break statement 374 browser Matrix 160 338 Task 90 bullets format 286 button embedding 326 Button component 385 by clause 369 excluding 369 negative 370 C CAD Link Assistant 36 calculus 183 clickable problem solving 235 multivariate 182 Student package 183 of variations 183 packages 182 study guides 196 teaching 183 196 vector 182 Student package 183 calling sequence 81 canvas inserting 317 canvas style sketch pad 318 caret entering 110 central tendency 138 character styles creating 289 description 287 Check Box component 385 Cholesky decomposition 168 Classic Worksheet tables 313 Classic Worksheet Interface xvii clickable math 235 Code Edit Region 382 CodeGeneration package description 85 coeff command 153 coefficient polynomials 153 coeffs command 154 collect command 153 colon 79 80 color of plots 267 combine command 350 errors option 141 Combo Box component 386 command completion 7 47 Command line Interface xvii commands 85 and task templates 91 displaying procedures 380 entering 45 help 53 hiding 382 383 iterative 377 mapping over set or list 377 package 83 top 83 top level 81 Index 423 compatibility worksheet 332 complex expressions 357 complex numbers 29 compoly command 15
299. ple select the firs row of the table and apply a light blue color This sets the header off from the content below sin wx el 92 cos ax a sin wx p Jx sin x sini x cos x Controlling the Visibility of Cell Content The Table Properties dialog includes two options to control the visibility of cell content These options allow control over the visibility of Maple input and execution group bound aries Thus these elements can be hidden in a table even 1f they are set to visible for the document in the View Show Hide Contents dialog Printing Options The Table Properties dialog contains options to control the placement of page breaks when printing You can fi a table on a single page allow page breaks between rows or allow page breaks within a row 7 4 Tables 313 Execution Order Dependency The order in which cells are executed is set in the Table Properties dialog The following tables illustrate the effect of execution order Row wise execution order Tables and the Classic Worksheet Tables are flattene on export to the Classic Worksheet interface For example the following table in the Standard Worksheet appears as one column in the Classic Worksheet interface Additional Examples For more practice creating and manipulating tables try creating the following tables at the end of your document 314 7 Creating Mathematical Documents Table of Values This example illustrates how to
300. plet For more information on the Maplets package refer to the MapletsPackage help page For more examples of designing Maplets using the Maplets package see the Maplets Roadmap help page 404 10 Embedded Components and Maplets Example 4 Design a Maplet Using the Maplets Package To introduce the structure of designing Maplets using the Maplets package this example illustrates the equivalent syntax for the Example 3 Design a Maplet Using the Maplet Builder page 399 Load the Maplets Elements package gt with Maplets Elements Defin the Maplet application To suppress the display of the data structure associated with the Maplet application end the definitio with a colon gt PlottingMaplet Maplet BoxLayout BoxColumn First Box Row BoxRow Define a Plot region Plotter reference Plotterl1 End of first Box Row Second Box Row BoxRow Define a Label Label Enter a function of x Define a Text Field TextField reference TextFieldl Define a Button Button caption Plot Evaluate value plot TextField1 x 10 10 target Plotterl End of second Box Row End of BoxColumn End of BoxLayout End of Maplet l Launch the Maplet gt Maplets Display PlottingMaplet 10 5 Authoring Maplets 405 For further examples using both the MapletBuilder and Maplets package commands see the Maplets example worksheets For a listing ref
301. plete list of conversions refer to the convert help page Convert a measurement in radians to degrees gt convert n degrees 180 degrees To convert measurements that use units use the Unit Converter or the convert units com mand gt convert 450 2 kg units Ib 992 5211043 b For information on the Unit Converter and using units see Units page 127 Convert a list to a set gt convert a b c d set 123 c d 4 5 6 Array 1 2 2 5 1 2 1 2 1 3 4 9 1 4 6 3 1 5 789 7 1 2 2 9 2 2 3 5 5 2 4 2 4 2 5 1 7 datatype anything storage rectangular order Fortran_order Maple has extensive support for converting mathematical expressions to a new function or function class 352 e 8 Maple Expressions gt convert cos x exp Ix 7 e Find an expression equivalent to the inverse hyperbolic cotangent function in terms of Le gendre functions gt convert arccoth z Legendre LegendreQ 0 T gt e For more information on converting to a class of functions refer to the convert to_spe cial_ function help page Normalizing To normalize an expression e Use the normal command The normal command converts expressions into factored normal form 2 2 x y gt normal oe x y x y 2 x y You can also use the normal command for zero recognition gt normal x 1 x 1 3x 1 x Q To expand the numerator a
302. point and click interfaces You can combine text and math in the same line add tables to organize the content of your work or insert images sketch regions and spreadsheets You can visualize and animate problems in two and three dimensions format text for academic papers or books and insert hyperlinks to other Maple files web sites or email addresses You can embed and program graphical user interface components as well as devise custom solutions using the Maple programming language 1 2 Introduction to Maple 3 Maple alee File Edit view Insert Format Table Drawing Plot Spreadsheet Tools Window Help D2ad S XBR oe TP EE es MI Oo amp BR ow Favorites Text Math Drawing Plot Animation 4 C 2D Math w TimesNewRoman 12 B U 4 2x 63 OO E T Rome x 7 ml 10 2 2 s na sal 4 944444444 5 h 5 va e Inla x 8x 25x 200 cost 520 sin x 0 5 x 0 0 log log a Siol gl E ord COME eee t m 8 x 3 20 72 4 He BHD sin a cos a tan a 3 Fla 22 W Recall that a gt y i x f a b gt z x x lt 0 x 0 The graph of y x consists of the right half of the line on the line y x with the left half of the line y x as shown 1 0 Ll a 4 SS w m s gt Memory 0 37M Time 0 03s Math Mode Figure 1 1 The Maple Environment Starting the Standard Document Interface To star
303. priate numbering prefix 50 1 Getting Started lt a sin x dx Ey cos x Answerl pS ka Answerl dx a sin x Answer Format Labels Label Numbering Prefix Answer Label Numbering Scheme Flat Numeric Figure 1 13 Format Labels Dialog Adding a Prefi The Label Reference menu item allows you to switch between the label name and its ref erence content Place the cursor on the referenced equation label and select Format Equation Labels Label Reference re q sin x dx Is El c0s x 1 z cos x dx siti x 2 Figure 1 14 Label Reference The label is associated with the last output within an execution group You cannot apply equation labels to the following e Error warning and information messages e Tables images plots sketches or spreadsheets Document Blocks In Document mode content is created as a series of document blocks Document blocks allow you to hide the syntax used to perform calculations which in turn lets you focus on the concept presented instead of the command used to manipulate or solve the problem You can also create document blocks in Worksheet mode to perform the same function 1 5 Commands 51 Document blocks are typically collapsed to hide the Maple code but these regions can also be expanded to reveal this code To create a document block From the Format menu select Create Document Block If text or m
304. r Specifi Unknowns By default the solve command returns solutions for all unknowns You can specify the unknowns for which to solve gt solvel q rs A 5 a 2 gt 2 To solve for multiple unknowns specify them as a list 4 4 Solving Equations 115 q r q 7 gt lve Ee o s if 5 s 2 solve 4 re z 5 rs Marl 5 1 5s _ 1 3 2 p stl et s 9 Transcendental Equations In general the solve command returns one solution to tran scendental equations gt equation sin x cos x gt solve equation kam 4 To produce all solutions use the allsolutions option gt solve equation allsolutions true A tr n Zi Maple uses variables of the form _ZN where N is a positive integer to represent arbitrary integers The tilde indicates that it is a quantity with an assumption For information about names with assumptions see Assumptions on Variables page 142 RootOf Structure The solve command may return solutions for example to higher order polynomial equations in an implicit form using RootOf structures gt solve x 2 32 2 1 Root0f _ 7 Z 2 Z 2 Z 2 index 1 Rootof 27 2 2 242 Z 2 index 2 RootOf _ Z 2 742 Z 2 4 7 index 3 RootOf Z F 2 F 2 Z 2 index 4 These RootOf structures are placeholders for the roots of the equation 9 2 7 27 2z 2 The index parameter numbers and orders the four solutions
305. rating Components into a Document ccc ccc ccc e cece cence e ene eneenens 390 Example 2 Creating Embedded Components ccc cceceeceeeseeeeeenees 392 WOA STi NAS Cor Scie sleuth a etc dae Coe Darel udelen a ala neha 396 Mape T Ee ee a acetate ecu set eaten acai eae cca Grete 396 Maple IDOCUIMEIIE toin5 sch adniahiatt cues e aeaaaee seen eeu e aae 397 IUS Author MaplelS scactscceuces set orien eseeeeree si wea ceter eats sale pie lnaa aie sia sete telusntetes 397 Siiiplic Maple Carera a tee clatter el Diet a 398 Contents 1x Maple 1 eA C0 otera aer a a nats 398 Maplets Package misc ite mee eT EREE TEATRET S 403 E A NOA E E E ENA OS E E E 405 11 Input Output and Interacting with Other Products c cece cece ese ee eee eeeeees 407 BE Lola Tits Chapter riranna a a a a bah 407 TEZ WAOS WO PS raa E TE TT AT 407 Savine Darai to a AN inne ei al Sects reelected Corl cesta nha 407 Savin Expressions to a File carinei a E a 408 IES IR CACHING Momi BAGS 5 50 seo at saescs ve ateals rc eepeticn 409 Reading Data from a Pile ainccse case eetec essen se leat enamel sea te ead 410 Reading Expressions trom a File saksritiisra tice mikica ad ahh even alana ade 411 11 4 Exporting to Other Formats sesiis nenna a a a a 412 Exporting Documents tsarraren a r neal teubaseabantes 412 Maple Norii a EEEE TE E TEES 415 Maple T Ar Fates ae ech ere AE N AE 415 MESC ONNECUVII Y anie eee ees 416 Translating Maple Code T
306. rating system Refer to Shortcut Keys by Platform page xviii for the keys needed for your operating system Example 1 Graph a Function and its Derivatives On the interval l T T graph f f and f for f x x cos x We solve this problem using the following methods Solution by Context Menus page 211 Solution by Tutor page 213 5 8 Clickable Math 211 e Access the Tutor from a Task Template page 215 Solution by Context Menus Make a copy of the expression and calculate differentiate w r t x ee xcos x cos x xsin x the derivative 2 Insert anew document block region by select ing from the Format menu Create Docu ment Block Highlight the original expression Ctrl drag the expression to the new document block Right click the expression and select Differ entiate With Respect To x Make a copy of the derivative and calculate the second derivative dines cos x xsin x _ 2 sin x xcos x 5 Insert anew document block and Ctrl drag the derivative to the document block 6 Right click the derivative and select Differ entiate With Respect To x Plot the original expression x cos x 7 Insert anew document block and Ctrl drag the original expression to the new block Right click the expression and select Plots Plot Builder In the Interactive Plot Builder Select Plot Type dialog change the x
307. rbolic gt ae Figure 1 7 Calculus Single Variable Differentiation Methods Tutor Math Apps Maple provides Math Apps that offer interactive entertaining ways to explore precalculus concepts The demonstrations are accessible in the Tools menu by selecting Math Apps For more information on the tutors demonstrations and related resources for mathematics education see Teaching and Learning with Maple page 194 1 4 Point and Click Interaction 39 Context Menus A context menu is a dynamically generated menu of actions that are applicable for the region upon which it is invoked Context menus allow you to perform calculations and manipulations on expressions without using Maple syntax To display a context menu right click an object expression or region Context menus are available for many input regions including expressions to perform calculations manipulations or plotting plot regions to apply plot options and manipulate the plot tables to modify the table properties palette regions to add or remove palettes and palette regions text regions to add annotations and format text spreadsheets to manipulate the spreadsheet When performing calculations or manipulations on an expression a self documenting arrow or equal sign connects the input and output indicating the action that took place See Figures 1 8 and 1 9 for two examples of context menus 40
308. region 2 Right click the expression and select Solve x 7 x 1 _ 4 x 1 ti 4 Obtain Solutions for X DTS ee solutions for x 1 3 Step by step Interactive Solution This equation can also be solved interactively in the document by applying context menu operations or commands one step at a time 1 Ctrl drag the equation f x 7 x 1 4 x 1 x 4 to a blank document block region 5 8 Clickable Math 219 Group all terms on the right x 7 x 1 a 4 x _ 1 x 4 2 Right click this equation and from the context menu select Move to Right move to right 7 0 3 x 1 4 x 4 x 7 Expand the expression on the right hand side 2 expand 0 3 x 1 4 x 4 x 7 3 Right click on the result and from the context y 6 24 4 18 menu select Expand Use Maple s factor command on the resulting 0 62 24x 18 right hand side right hand side factor 6x 24x 18 6 x 1 x 3 4 Right click on the result and select Right hand Side 5 Right click on the result and select Factor Solve for x 6 x 1 x 3 solutions for x 1 3 6 Right click on the result and select Solve Obtain Solutions for x Graphical Solution Now that we have seen several methods to solve this problem we can check the answer by plotting the expression 1 Ctrl drag the equation x 7 x 1 4 x
309. rmation refer to the interface help page Creating Matrices and Vectors with Specific Properties By default matrices and vectors can store any values To increase the efficienc of linear algebra computations create matrices and vectors with properties You must specify the properties for example the matrix shape or data type when definin the object The Matrix palette Figure 5 2 supports several properties To specify the matrix type e Use the Shape and Type drop down lists To specify the data type e Use the Data type drop down list For example defin a diagonal matrix with small integer coefficients In the Matrix palette 1 Specify the size of the matrix for example 3 x 3 In the Shapes drop down list select Diagonal In the Data type drop down list select integer 1 Click the Insert Matrix button aA A Ww N Enter the values in the diagonal entries 23 0 0 0 17 OF 0 0 32 V You cannot specify properties when definin vectors using the angle bracket notation You must use the Vector constructor To defin a column vector using the Vector constructor specify e The number of elements If you explicitly specify all element values this argument is not required e A list of expressions that defin the element values 5 3 Linear Algebra 163 e Parameters such as shape datatype and fil that set properties of the vector The following two calling sequences are equivalent gt Vector
310. rmation on optional arguments to the selection commands refer to the select help page Mapping a Command over a Set or List The map command applies a name procedure or command to each element in a set or list See Table 9 6 Table 9 6 The map Command map name_proc_cmd expression gt map f a b c f a f b fe gt map u gt int cos x x 0 u Pi 4 Pi 7 Pi 3 0 5 l J2 cos rr r 0 8660254038 For information on mapping over the operands of other expressions optional arguments to the map command and other mapping commands refer to the map help page Mapping a Binary Command over Two Lists or Vectors The zip command applies a name or binary procedure or command component wise to two lists or vectors By default the length of the returned object is that of the shorter list or vector If you specify a value as the optional fourth argument it is used as the value of the missing elements of the shorter list or vector In this case the length of the return value is that of the longer list or vector See Table 9 7 378 9 Basic Programming Table 9 7 The zip Command zip proc_cmd a b gt zip f i j k 1 zip proc_cmd a b fil fC k f 1 gt zip AiryAi 1 2 0 1 pis TS a 1 2 2 2 For more information on the zip command refer to the zip help page Additional Information For more information on looping commands refer to the correspo
311. s 181 90 gt e In t de assuming a gt 0 0 yt In a a To compute iterated integrals line integrals and surface integrals use the task templates Tools Tasks Browse in the Multivariate and Vector Calculus folders The int Command b f dx and f dxuse the int command To use the int command directly specify the follow a ing arguments e Expression to integrate e Variable of integration gt xsin a x x sin ax 5 4 gt int CS 4 x sin ax xcos ax a 5 5 d a For a definit integration set the variable of integration equal to the interval of integration 1 gt in 5 4 x 0 a T gt 5 6 a Numeric Integration To perform numeric integration e Use the evalf Int arguments calling sequence Important Use the inert Int command not the int For more information refer to the int help page 182 5 Mathematical Problem Solving In addition to the arguments accepted by the int command you can include optional argu ments such as method which specifie the numeric integration method gt evalf Int x 0 2 method Dewp T x 1 626378399 Note To enter an underscore character _ in 2 D Math enter _ For information on the evalf command see Numerical Approximation page 356 For information on numeric integration including iterated integration and controlling the algorithm refer to the evalf Int help page Differential Equations
312. s Animations allow you to emphasize certain graphical behavior such as the deformation of a bouncing ball more clearly than in a static plot A Maple animation is a number of plot frames displayed in sequence similar to the action of movie frames To create an animation use the Interactive Plot Builder or commands 6 6 Creating Animations 271 Interactive Plot Builder Creating Animations Using the Interactive Plot Builder Launch the Interactive Plot Builder and enter the expression 1 Add the expression sin i sqrt x 2 y 2 10 For information on interacting with the Interactive Plot Builder see Example 1 Display a plot of a single variable expression page 240 In the Select Plot Type window 2 From the Select Plot Type drop down menu select Animation 3 The default x Axis range is 2 Pi 2 Pi Change the x Axis range to 6 6 4 The default yAxis range is 2 Pi 2 Pi Change the y Axis range to 6 6 5 Change the Animation Parameter i range to 1 30 In the Plot Options window 6 From the Style group box select surface 7 From the Color group box in the Light Model drop down menu select red turquoise 8 From the Color group box in the Shading drop down menu select z grayscale 9 In the View group box select the Constrained Scaling check box Plot the expression 10 Click Plot gt plots interactive For information on playing the animation see Playing Animations page 276
313. s Drawing Plot Animation i C Text 7 Times Hew Roman Z alaa Math tools Text lat Drawing Plot Animation CC 2inpt timesNewRoman 42 B Z Drawing tools Text Math n Plot Animation P7T OG09 GREENS 2 D Plot tools Text Math Drawing fil Animation r a Ajy AOs LA HH 3 D Plot tools Math Drawing fid Animation Animation tools Text Math Drawing Plot le ta gt Current Frame 1 1 2 Introduction to Maple 11 Table 1 5 Toolbar Icon Availability The Text and Math icons allow you to enter text and math in the same line by choosing the appropriate input style at each stage when entering the sentence The derivative of sin x is cos x For an example see Example 6 Enter Text and 2 D Math in the Same Line Using Toolbar Icons page 30 Using the tools available in these icons you can customize the input style of the text and 2 D Math For the Text and Math icons the icon that is selected remains in that state until prompted otherwise therefore if the Text icon is selected and you press the Enter key the new input region remains a Text region The Text and Math icons differ while at a Maple input prompt The Math icon displays input as 2 D Math whereas the Text icon displays Maple input For details refer to Math Mode vs Text Mode page 19 gt 2 he gt x2 2 To access the tools available in the Plot and Drawing icons click a plot region These tools allow you to manipulate th
314. s To draw a line through the points use the style line option For further analysis of data points use the Curve Fitting Assistant Tools Assist ants CurveFitting which fit and plots a curve through the points For more information refer to the CurveFitting Interactive help page 258 6 Plots and Animations gt pointplot 0 1 1 1 3 0 4 3 2 0 4 1 3 2 4 1 axes BOXED symbolsize 25 svmboF circle The matrixplot Command The matrixplot command plots the values of a plot object of type Matrix The matrixplot command accepts options such as heights and gap to control the appearance of the plot For more information on Matrices see Linear Algebra page 155 gt with LinearAlgebra 6 2 Creating Plots 259 gt A HilbertMatrix 6 iid i 2 34 5 6 E E SR E S S 5 2 3 4 5 6 7 iall Ll L 3 4 5 6 7 8 A te es O E 3 4 5 6 7 8 9 Fees L 5 6 7 8 9 10 L1 1 1 1 1 1 gt B ToeplitzMatrix 1 2 3 4 5 6 symmetric 1123456 212345 32721234 432123 543212 654321 gt matrixplot A B heights histogram axes normal gap 0 25 style patch 260 6 Plots and Animations The contourplot Command The contourplot command generates a topographical map for an expression or function To create a smoother and more precise plot increase the number of points using the num points option 6 2 Creating Plots 261 gt contourplot cos xy x
315. s constant is known Special Functions an interface to the properties of over 200 special functions including the Hypergeometric Bessel Mathieu Heun and Legendre families of functions Units Calculator an interface to convert between 500 units of measurement Worksheet Migration an interface to convert worksheets from Classic Maple mws files to Standard Maple mw files CAD Link an interface to explore the properties of models from supported CAD applic ations available on Microsoft Windows only 1 4 Point and Click Interaction 37 Tutors Maple provides over 40 interactive tutors to aid in the learning of e Precalculus e Calculus e Multivariate Calculus e Vector Calculus e Differential Equations e Linear Algebra e Complex Variables These tutors are easily accessible in the Tools menu by selecting Tutors See Figure 1 6 Tools Window Help Assistants ae eel eer ie PB Tutors b Calculus Multivariate Tasks b Calculus Single Variable i Complex Yariabl em gt i Demonstrations ampie Varlaples mH Ch aa Differential Equations Load Package b 3 Linear Algebra b Eigenvector Plot Unload Package b Numerical Analysis b Eigenvalues spellcheck F7 Precalculus Eigenvectors Complete Command Vector Calculus I Gauss Jordan Elimination Help Database 3 Gaussian Elimination Linear System Plot Options Linear Transform Plot Matrix Builder Matrix In
316. s page 374 Specialized Creating a sequence eee aave commande Adding and Multiplying Expressions Selecting Expression Operands Mapping a Command over a Set or List Mapping a Binary Command over Two Lists or Vectors Procedures page 378 Maple programs Definin and Running Simple Procedures Procedures with Inputs Procedure Return Values Displaying Procedure Definition Displaying Maple Library Procedure Definition Modules Programming in Documents page 382 Dis Code Edit Region play methods for Maple code Startup Code Document Blocks 365 366 9 Basic Programming 9 2 Flow Control Two basic programming constructs in Maple are the if statement which controls the condi tional execution of statement sequences and the for statement which controls the repeated execution of a statement sequence Conditional Execution if Statement You can specify that Maple perform an action only ifa condition holds You can also perform an action from a set of many depending on which conditions hold Using theif statement you can execute one statement from a series of statements based on a boolean true false or FAIL condition Maple tests each condition in order When a condition is satisfied Maple executes the corresponding statement and then exits the if statement Syntax The if statement has the following syntax if conditional expressioni then statement sequencel elif conditional expressions then sta
317. s 1 4 e Math and Text icons in the 7 toolbar required for products of numbers 7 i 7 use the right arrow key to leave a denominator superscript or subscript region gt for more information see Command Completion page 47 For a complete list of shortcut keys refer to the 2 D Math Shortcut Keys and Hints help page To access this help page in the Maple software in Math mode enter MathShortcuts and then press Enter For information on the Maple Help System see The Maple Help System page 53 Example 1 Enter and Evaluate an Expression Using Keystrokes Review the following example 1 E x y 2 In this example you will enter a and evaluate the expression 8 1 Getting Started To enter the expression 1 Enter x 2 Press Shift 6 the or caret key The cursor moves to the super script position a 4 Press the right arrow key The cursor moves right and out of the superscript position a e l 7 Press Shift 6 to move to the superscript position e er Enter y 8 Enter 2 and press the right arrow key 9 With the mouse select the expression that will be the numerator of g e the fraction os 10 Enter the symbol The cursor moves to the denominator with the 2 k entire expression in the numerator r 4 12 Press the right arrow key to move right and out of the denominator position To evaluate the expression and display the result inline 13 Press Ctrl
318. s for your Maple toolboxes For information on toolboxes go to http www maplesoft com developers index aspx Library Browser an interface to manipulate the libraries in a specifie directory Maplet Builder an interface to the Maplets package The Maplets package contains commands for creating and displaying Maplet applications point and click interfaces Using the Maplet Builder you can defin the layout of a Maplet drag and drop elements visual and functional components of Maplets set actions associated with elements and directly run a Maplet application The Maplet Builder is available in the Standard interface only ODE Analyzer an interface to obtain numeric or symbolic solutions to a single ordinary differential equation ODE or a system of ODEs and plot a solution of the result Optimization an interface to the solver commands in the Optimization package The Optimization package is a collection of commands for numerically solving optimization problems which involves findin the minimum or maximum of an objective function possibly subject to constraints Plot Builder an interface for creating two and three dimensional plots animations and interactive plots Scientifi Constants an interface to over 20 000 values of physical constants and properties of chemical elements All of these constants come with the corresponding unit and if applicable with the uncertainty or error that is how precisely the value of thi
319. s name or symbol Example 4 Square Root To fin the square root of 603729 2 Press the symbol completion shortcut key o nry Esc Maple displays a pop up list of exact matches 3 In the completion list select EEN ple inserts in symbol with the x placeholder selected 4 Enter 603729 603729 5 Press Ctrl Command Macin q 603729 777 Example 5 Complex Numbers When you simply type the letter 7 in Math mode it is in italics This letter is just a variable and is not the same as the imaginary unit y 1 denoted by I or i in Maple Multiply two complex numbers 0 123 0 7451 and 4 2 1 1 Ina new document block enter 0 123 0 745 if 0 123 0 7453 2 Press the symbol completion shortcut 0 123 0 745 i key Esc Maple displays a pop up list of partial and exact matches includ ing symbols and commands lconfent p icontent icosahedron location ploftools icosahedron Ji x p 21 icosahedron location scale plotfools icosahedron Ji x p 21n lt A 30 1 Getting Started 3 Select the imaginary unit 0 123 0 745 j i imaginary 4 Close the parentheses enter a space 0 123 0 745 i 4 2 i for implicit multiplication and type the second expression in parentheses using symbol completion for the second imaginary number 5 Press Ctrl Command 0 123 0 745i 4 2 i 0 2284 3 25201 Macintosh t
320. s relative you can access the end of the array by entering 1 gt a 1 2 gt b 1 1 1 2 The Array constructor supports other syntaxes It also supports many options For more information on the Array constructor and the Array data structure refer to the Array help page For more information on indexing methods refer to the rtable_indexing help page Large Arrays Only one and two dimensional Arrays with at most 10 indices in each dimension display in the document Larger Arrays display as a placeholder gt Array 0 100 0 100 Array Data Type anything Storage rectangular Order Fortran order 338 8 Maple Expressions To view large Arrays e Double click the placeholder The Matrix Browser displays the Array For more information see Viewing Large Matrices and Vectors page 160 Tables Tables are conceptually an extension of the Array data structure but the table data structure is implemented using hash tables Tables can be indexed by any values not only integers Defining Tables and Accessing Entries gt Greek table a a b B c y gt Greek b B You can also assign anything for example a list to each element gt Translation table one un uno two deux dos three trois tres gt Translation two deux dos For more information on tables refer to the table help page Matrices and Vectors Matrices and Vectors are specialized data structures
321. s return simplifie results appropriate to the fiel of real numbers gt with RealDomain gt simplify 2 gt In e x Some commands that generally return NULL instead return a numeric result when you use the RealDomain package gt ant i Complex return values are excluded or replaced by undefine gt solve x 1 gt arcsin e undefined Assumptions on Variables To simplify problem solving it is recommended that you always apply any known assump tions to variables You can impose assumptions using the assume command To apply as sumptions for a single computation use the assuming command Note The assume and assuming commands are not supported by the RealDomain package The assume Command You can use the assume command to set variable properties for example x real and re lationships between variables for example x lt 0 or x lt y For information on valid proper ties refer to the assume help page For information on the double colon operator refer to the type help page The assume command allows improved simplificatio of symbolic expressions especially multiple valued functions for example computing the square root 4 6 Restricting the Domain 143 To assume that x is a positive real number use the following calling sequence Then compute the square root of va 2 gt assume O lt x y xX x The trailing tilde on the name x indicates that it carries assumptions
322. s to None 6 Optional Change Table Size Mode size option to Scale with zoom factor Using the Table menu 7 Set Alignment of columns 3 and 4 to Center 2 D Math and Plots The following example illustrates the use of tables to display 2 D Math and plots side by side m gt E r r Plotofe and its rational approximation Approximating exp x as a rational polynomial using a 3 order Pad approximation 1412 13 10 1207 l l 1 E a Y 2 10 120 x A X Insert a table with 1 row and 2 columns Enter the information in text and executable 2 D Math to create the calculation and plot as shown 316 7 Creating Mathematical Documents Table Settings In the Properties dialog Table Properties menu 1 Set Exterior and Interior Borders to None 2 Hide Maple input and execution group boundaries Clear the Show input and Show execution group boundaries check boxes Using the Table menu 3 Change row Alignment to Center 7 5 Canvas Using the drawing tools you can sketch an idea in a canvas draw on plots and draw on images See Figure 7 15 For details about the drawing feature refer to the DrawingTools help page Text Math Plot Animation hl4 70 GG00 DCSE E Plant Constant Gain Feedback Figure 7 15 Drawing Tools and Canvas 7 5 Canvas 317 Insert a Canvas To insert a canvas 1 Place the cursor where the canvas is to be inserted
323. s uriinis a eae 263 Context Menu ODINS ic hol Sich toned ceed non boanelalt a e 264 The plotand plot3d Options sririrsiiirieri isre riaa ca veg s ERER 267 GA Amaby 210 PloS eriin E N E E NE 269 Point Probe Rotate Pan and Zoom Tools ssssssssssssssssesssssesesesseseeeeee 269 03 Repe sentin Dataran e a E EE 270 6 6 Creating AMMA ONS soora EKE ETa spatiale EET TE Reisen wien ATRA 270 Interachive PIO RS Ut Me eseese a bach caitelat Gta iad k N ered OH i The plotslanmnate Command nccicestesncerauriciacaeacine Suede eee a E 271 The plot3d viewpoint Command i533 555 beccadnii cick Gud cada nichaeebncmabel cach ieabers 274 627 Play ine Amin allOns eraai na RT ERA Senne tinea sarees 276 Anman COMEX bale 1 1 Senne neee NaN e oem se May emma eae 276 6 8 Customizing Am Mallon ssccccctei ceeds ee tec a a a se mlaaesatents 211 Interactive Plot Builder Animation Options ccccececeseeeeceeeeeesenenes 2T Context Men OPUS amiroo ea TTNET E E T i mene 217 Theanimate Command OptotSoraerserikan e stat cab dea EEEE 278 O RE PONID asa a a noe PMENE Tart a oper ne tree 280 6 10 Code for Golor Plates atraire Sick tonbe tbat eel a a ten aea 280 7 Creating Mathematical Documents sie cve1craresaretecascawiatnenanete Ge veaqtaeaarnerereaeaciek 281 Pk TAI APU adie atte ei echo ese eee ee Deli ee Coe aah ea Ce laut elon 281 42 Document Formalno 2233122645h ho ath a a aA 282 COPY and Pase enaa a aaaea 283 Quick Character FOrmmattin ccc seaq
324. sed to solve this expression is hidden TA ke erae n Ea E TrA yy ey x 42h x55 When starting Standard Maple the default mode is Document mode Worksheet Mode Worksheet mode uses a Maple prompt as the default input region The Maple input prompt is a red angle bracket gt When using context menus on input in Worksheet mode all commands are displayed ee gran gt sofve x 24 7 x4 10 0 fx Z2 x 4 To work in Worksheet mode select File New Worksheet Mode 1 2 Introduction to Maple 5 Document and Worksheet Modes Regardless of which mode you are working in you have the opportunity to show or hide your calculations You can hide commands in Worksheet Mode by adding a document block from the Format menu Format Create Document Block see Document Blocks page 50 or you can show commands in Document mode by adding a Maple prompt from the Insert menu Insert Execution Group Before After Cursor see Input Prompt page 78 This chapter discusses features common to both modes Specifi aspects of Document mode are explained in Document Mode page 61 and aspects of Worksheet mode are explained in Worksheet Mode page 77 The Startup dialog also contains links to items such as various document options help re sources including updates and other introductory help pages and application resources on the Maplesoft web site Subsequent sessions display Tip of the Day informat
325. set the visibility options for cell contents to display a table of values gt l 2 gt J t 5 Create a table with 2 rows and 7 columns Enter the values as below and then select all table cells In the Table Alignment menu select Columns and then Center eS ee eee Table settings In the Properties dialog Table Properties menu 1 Set Table Size Mode to Scale with zoom factor 2 Hide Maple input and execution group boundaries Clear the Show input and Show execution group boundaries check boxes Formatting Table Headers The following table uses cell merging for formatting row and column headers and row and column grouping to control the visibility of cell boundaries By default invisible cell boundaries are visible on mouse pointer roll over You can hide the visibility of lines on mouse pointer roll over by using the View Show Hide Contents dialog and clearing the Hidden Table Borders check box Parameter 2 Low High Parameter Low 13 24 High 18 29 7 4 Tables 315 Table settings 1 Insert a table with 4 rows and 4 columns and enter the information shown above Using the Table menu 2 Merge the following sets of Row Column cells R1 C1 to R2 C2 R1 C3 to R1 C4 and R3 C1 to R4 C1 3 Group columns 1 and 2 and columns 3 and 4 4 Group rows and 2 and rows 3 and 4 In the Properties dialog Table Properties menu 5 Set Exterior Border
326. sharing documents Important commands can be executed as soon as the user opens your document The user is not required to execute all commands For more information refer to the restart help page Setting the Auto Execute Feature 1 Select the region to be automatically executed when the document opens 2 From the Format menu select Autoexecute and then Set 7 3 Commands in Documents 303 Regions set to Autoexecute are denoted by exclamation mark symbols in the Markers region View Markers A For example to display a plot in your document without saving the plot making your doc ument use less memory you can set a plot command to autoexecute 1 After the plot instruction enter a Maple prompt Insert Execution Group After Cursor 2 Enter the plot command plot sin x sin x d and press Enter to execute 3 Select the plot then select Edit Remove Output From Selection 4 Place the cursor in the plot command then select Format Autoexecute Set 5 Save and close the document on reopening the command is re executed Result plot create a two dimensional plot Calling Sequence plottf x plottf x x0 x1 plotiw1 v2 Parameters f expression in independent variable x F independent variable x0 1 left and right endpoints of horizontal range vi V2 z coordinates and y coordinates Plot the expression sin x and its derivative ea sin x cos
327. sia a iaetia tema a a 398 Figure 10 7 Maplet Builder Interface oi scal cscs nce vacdabat sich Mant a Neuds 399 Picure 10 8 Image of the MAIC wire cen taeus ri ea n te niceatunis a AE 400 Figure 10 9 Body Elements Used to Defin This Maplet ccccecececeeee ee ee es 400 Figure 11 1 Import Data Assistant tists cocuasscntias urease E 410 xiv List of Figures List of Tables Table 1 1 Table 1 2 Table 1 3 Table 1 4 Table 1 5 Table 1 6 Table 1 7 Table 1 8 Table 1 9 Table 3 1 Table 3 2 Table 4 1 Table 4 2 Table 4 3 Table 4 4 Table 4 5 Table 5 1 Table 5 2 Table 5 3 Table 5 4 Table 5 5 Table 5 6 Table 5 7 Table 5 8 Common Keystrokes for Entering Symbols and Formats 00068 6 Maple Toolbar Opon 5 42c caesnn eect ncaa a lundman cha aatecnans E 9 Tap COMMIESCHPUOM aerate nail decen len nia cata t Ae ape ae A T AE ES 9 Toolbar cons and their Toli ssrin eE ae sae ak ees 10 Toolbar loom Av alla Dility serti ana reae heraaese ted A EE TA 11 Matn Mode ys Text VIOUS enais a aa 20 Palete C ate 210 6 ai ra arer Oey om ee TAEA EAE A AEN 22 Manasina Pale lS oense E E E EE E ok neeuee sens 24 Hep Page ICONS eaae E E E TERTNES 55 TOD C OMAN e EA nea TEEE PN Ane ree On SRE RITES 82 MOP PICKA TE Spa seas natncas dees we S E EA deen eee E TAE 85 Select Mecer Command Ir rin aren e aE E e 107 Modular Arithmetic Operators 3 0 c2sccccesantcasadeantendsaeatere dadeteeseets eens 109
328. sible values must be contained 4 5 Units Scientifi Constants and Uncertainty 139 To perform interval arithmetic use the Tolerances The quantities represent unknown values with a central tendency For more information on central tendency refer to any text on error analysis for the physical sciences or engineering For more information refer to the Tolerances help page Quantities with Uncertainty Creating To construct quantities with uncertainty use the Quantity command You must specify the value and uncertainty The uncertainty can be define absolutely relatively or in units of the last digit For more information on uncertainty specification refer to the ScientificEr orAnalysis Quantity help page The output displays the value and uncertainty of the quantity gt with ScientificConstants with ScientificErrorAnalysis gt Quantity 105 1 2 Quantity 105 1 2 gt Quantity 105 0 03 relative Quantity 105 3 15 4 18 To specify the error in units of the last digit the value must be of floating poin type gt Quantity 105 0 12 uld Quantity 105 0 1 2 To access the value and uncertainty of a quantity with uncertainty use the evalf and Scien tificEr orAnalysis GetError commands gt evalf C4 18 105 gt GetError 4 18 3 15 Rounding To round the error of a quantity with uncertainty use the ApplyRule command For a description of the predefine rounding rules refer to the Scientific
329. sing Palettes Review the following example 10 gt 77 5i 2420 i 1 3 Entering Expressions 27 10 In this example we will enter gt 7 77 5 i and evaluate the expression i 0 1 Place the cursor in a new document block In the Ex F Sy af pression palette click the summation template Maple inserts the summation symbol with the range variable placeholder highlighted Enter i and then press Tab The left endpoint place holder is selected Notice that the color of the range placeholder has changed to black Each placeholder must have an assigned value before you execute the expression The Tab key advances you through the placeholders of an inserted palette item Enter 1 and then press Tab The right endpoint placeholder is selected Enter 10 and then press Tab The expression place holder is selected Enter 7 5 i For instructions on entering this type of expression see Example 1 Enter and Evaluate an Expression Using Keystrokes page 7 Press Ctrl Command for Macintosh to evaluate the summation Handwriting Palette The Handwriting palette provides another way to fin and insert desired symbols easily 1 Draw the symbol with your mouse in the space provided T 2 Click the recognize button malt available in the system See Figure 1 3 Maple matches your input against symbols 28 1 Getting Started 3 To view more symbols where indicated wit
330. sion groups and a form for requesting technical support http www maplesoft com support For a complete list of resources refer to the MapleResources help page 2 Document Mode Using the Maple software you can create powerful interactive documents You can visualize and animate problems in two and three dimensions You can solve complex problems with simple point and click interfaces or easy to modify interactive documents You can also devise custom solutions using the Maple programming language While you work you can document your process providing text descriptions 2 1 In This Chapter Introduction page 61 e Comparison of Document and Worksheet Modes Entering Expressions page 62 Overview of Palettes tools for creating complex mathematical expres e Symbol Names sions e Mathematical Functions Evaluating Expressions page 65 How to eval Displaying the Value Inline nan eres Ome Displaying the Value on the Following Line Editing Expressions and Updating Updating a Single Computation Output page 66 How to update expressions Updating a Group of Computations and regenerate results Updating All Computations in a Document Performing Computations page 67 Overview Computing with Palettes of tools for performing computations and solving problems Context Menus Assistants and Tutors 2 2 Introduction Maple has two modes Document mode and Worksheet mode Document mode is designed for qui
331. sk Templates page 40 You can also create your own task templates for performing common tasks For details refer to the creatingtasks help page 92 e 3 Worksheet Mode 3 8 Text Regions To add descriptive text in Worksheet mode use a text region To insert a text region e In the toolbar click the Text region icon T The default mode in a text region is Text mode In a text region you can e Enter text with inline mathematical content by switching between Text and Math modes To toggle between Text mode and Math mode press F5 or click the Math and Text toolbar icons Math Note The mathematical content in a text region is not evaluated To enter mathematical content that is evaluated enter it at an Input Prompt page 78 e Insert any palette item Palette items are inserted in Math mode 2 D Math Note After you insert a palette item you must press F5 or click the toolbar icon to return to Text mode You can format text in a text region Features include e Character styles e Paragraph styles e Sections and subsections e Tables For more information on formatting documents see Creating Mathematical Documents page 281 3 9 Names Instead of re entering an expression every time you need it you can assign it to a name or add an equation label to it Then you can quickly refer to the expression using the name or an equation label reference For information on labels see the following section Equation Labels
332. ssion or part of an expression to another location on the document 1 Select the expression or part of the expression to copy 2 From the Edit menu select Copy 3 Place the cursor at the insertion point 4 From the Edit menu select Paste Result plot create a two dimensional plot Calling Sequence plott x ploti z z0 xz1 plotil v2 Parameters f expression in independent variable z x independent variable X0 z1 left and right endpoints of horizontal range wl v2 x coordinates and y coordinates If you paste into a math input region Maple interprets all the pasted content as input If you paste into a text region Maple interprets all the pasted content as text However note that 2 D Math retains its format in both input and text regions When you copy and paste to another application in general Maple retains the original Structure Quick Character Formatting The Format Character menu provides access to the following quick formatting features Bold Italic Underline Superscript Subscript Font Color and Highlight Color To modify text 1 In the document select the text to modify 2 From the Format menu select Character and then the appropriate feature 284 7 Creating Mathematical Documents For example in the pasted text select Calling Sequences and apply Bold character formatting Alternatively use the context bar icons For example to apply a color to the parameters
333. t 2x output 2 x twice 1342 2684 twice y z 2y 2z Note To insert the right arrow symbol you can also enter the characters gt in Math mode In this case symbol completion is automatic Important The expression 2 x is different from the function x gt 2 x For more information on functions see Functional Operators page 339 2 4 Evaluating Expressions To evaluate a mathematical expression place the cursor in the expression and press Ctrl Command for Macintosh That is press and hold the Ctrl or Command key and then press the equal sign key To the right of the expression Maple inserts an equal sign and then the value of the expres sion 7 85 99 w b You can replace the inserted equal sign with text or mathematical content To replace the equal sign 1 Select the equal sign Press Delete 2 Enter the replacement text or mathematical content For example you can replace the equal sign with the text is equal to 2 T 85 9 TL is equal to 09 In mathematical content pressing Enter evaluates the expression and displays it centered on the following line The cursor moves to a new line below the output 66 2 Document Mode 2 7 lt 4 9 Il 85 99 2 1 By default Maple labels output that is generated by pressing Enter For information on equation labels see Equation Labels page 95 In this manual labels are generally not displayed In t
334. t Maple on From the Start menu select All Programs Maple 16 Maple 16 Alternatively Double click the Maple 16 desktop icon 4 e Getting Started Macintosh 1 From the Finder select Applications and Maple 16 2 Double click Maple 16 Enter the full path for example usr local maple bin xmaple Alternatively 1 Add the Maple directory for example usr local maple bin to your command search path 2 Enter xmaple The firs Maple session opens with a Startup dialog explaining the difference between Document Mode and Worksheet Mode Using either mode you can create high quality in teractive mathematical documents Each mode offers the same features and functionality the only difference is the default input region of each mode Document Mode Document mode uses Document Blocks as the default input region to hide Maple syntax A Document Block region is indicated by two triangles located in the vertical Markers column along the left pane of the Maple Document 2S 1 If the Markers column is not visible open the View menu and select Markers This allows you to focus on the problem instead of the commands used to solve the problem For example when using context menus on Maple input in Document mode invoked by right clicking or Control clicking for Macintosh input and output are connected using an arrow or equal sign with self document ing text indicating the calculation that had taken place The command u
335. t click the equation and select Left hand Side Input 2x 9 0 Result 2x 9 0 7 Right click the expression and select Plots 2 D Plot Copy Special Paste Evaluate and Display Inline Ctri Explore 4poly a Command Differentiate Evaluate at a Point Integrate Left hand Side Manipulate Equation Map Command Onta Move to Right Negate Relation Plots Right hand Side Simplify Solve Test Relation Conversions Integral Transforms Sequence 2 D Math left hand side 2x 9 Input 2x Copy Special Paste Evaluate and Display Inline Ctrl Explore 4poply a Command 455i9gn to a Mame Coefficients Collect Differentiate Evaluate at a Point Factor Integrate Lirnit Plots Series Simplify Solve Complex Maps Constructions Conversions Integer Functions Integral Transforms Language Conversions Optimization Sequence Sorts Units 2 D Math rr F F Fr Fr F0 i F0 F0 F F F r 2 D Plot 3 D Plot b 2 D Implicit Plot 3 D Implicit Plot Plot Builder 1 2 Introduction to Maple 17 18 1 Getting Started Result 2x 9 Saving a Maple Document To save these examples you created from the File menu select Save Maple documents are saved as mw files 1 3 Entering Expressions Execution Groups An execution group is a grouping of Maple input with its corresponding Maple output It is distinguished by a large square bracket called a group bo
336. t of the window Wem Insert Format Next Tab Previous Tab w Toolbar w Context Bar w Status Bar Markers Task Elements Slideshow Palettes zoom Factor Typesetting Rules Show sHide Contents Header Footer Expand All Sections TP Animation Z ala E Arrange Palettes Show Palette Show All Palettes Show Default Palettes Expand All Palettes Colapse All Palettes Expand Docks Collapse Docks 1 3 Entering Expressions 25 To add a palette 1 Right click the palette dock Maple dis Show Palette plays a context menu near the palette Show All Palettes Show Default Palettes Remove Palette 2 From the context menu select Show Palette and then select the palette Expand all Palettes Collapse All Palettes Expand Docks Collapse Docks Arrange Palettes In a Accents a cos a Roman Extended Upper Case Roman Extended Lower Case fla b 2 Diacritical Marks Cyrillic Fenced Constants and Symbols Punctuation 26 1 Getting Started To expand or collapse a palette in the palette dock e Click the triangle at the left of the palette title To move a palette in the palette dock e Move the palette by clicking the title and dragging the palette to the new location To expand or collapse the palette docks e Select the appropriate triangle at the top right or top left side of the palette region Example 3 Enter an Expression U
337. t the Plot toolbar is open However the Drawing toolbar is also available Click on Drawing to see the toolbar Select the Text icon T and click on the plot Enter the expression f x in one text area and its derivative in another as shown You can move the text areas around on the plot so that they indicate the correct lines For details on the rest of the drawing features refer to the DrawingTools help page Canvas Style You can alter the Canvas in the following ways e Add a grid of horizontal and or vertical lines By default the canvas opens with a grid of horizontal and vertical lines e Change the grid line color e Change the spacing between grid lines e Change the background color These options can be changed in the Drawing Properties Canvas Icon See Figure 7 17 7 5 Canvas 319 Horizontal Vertical Canvas Figure 7 17 Drawing Properties Canvas Icon Change the Gridline Color Inserting Images You can insert images in these fil formats into your document Graphics Interchange Format gif Joint Photographic Experts Group jpe jpeg jpg Portable Network Graphics png Bitmap Graphics bmp Tagged Image File Format tif tiff jf Portable aNyMap pnm Kodak FlashPix fpx To insert an image into the document at the cursor location 1 From the Insert menu select Image The Load Image dialog opens 2 Specify a path or folder name 3 Select a filename 4 Click Open
338. t tool 1s Maple 1 1 In This Chapter Introduction to Maple page 2 The main Starting the Standard Document Interface features of Maple s Standard Interface Entering commands and mathematical expres sions Toolbars Context menus Copy and drag keys Saving Maple documents Entering Expressions page 18 Methods of Execution groups entering expressions in 1 D and 2 D Math Math Mode and Text Mode Palettes Symbol names Toolbar icons Point and Click Interaction page 32 Anintro Assistants duction to the point and click features in Maple T utors Context menus Task templates Exploration Assistant Commands page 45 An introduction to the Using commands from the Maple library commands of the Maple language Entering commands Document blocks 2 1 Getting Started The Maple Help System page 53 Accessing How to access help for Maple features help on commands packages point and click Interacting with help pages features and more Viewing and interacting with examples Available Resources page 56 Both online and New user resources including the Maple Tour from within Maple and the Maple Portal Examples Online help Maple web site resources 1 2 Introduction to Maple Working in Maple With Maple you can create powerful interactive documents The Maple environment lets you start solving problems right away by entering expressions in 2 D Math and solving these expressions using
339. tement sequences elif conditional expressions then statement sequences else statement sequencen end if The conditional expressions conditional _expressionl conditional _expression2 can be any boolean expression You can construct boolean expressions using e Relational operators lt lt gt gt lt gt e Logical operators and or xor implies not e Logical names true false FAIL The statement sequences statement _sequencel statement _sequence2 statement _ sequen ceN can be any sequence of Maple statements including if statements The elif clauses are optional You can specify any number of elif clauses The else clause is optional 9 2 Flow Control 367 Simple if Statements The simplest if statement has only one conditional expression if conditional expression then statement sequence end if If the conditional expression evaluates to true the sequence of statements is executed Otherwise Maple immediately exits the if statement For example gt x 1173 gt if not isprime x then ifactor x end if 3 17 23 else Clause In a simple if statement with an else clause if the evaluation of the conditional expressions returns false or FAIL Maple executes the statement sequence in the else clause For example gt if false then if statement else else statement end if else statement elif Clauses In an if statement with elif
340. teractive x y y x y lt 6 x 0 5 y 0 5 134 491 161539748162 x 4 53559292539129189 y 1 46440707460870746 e When the Optimization Assistant opens select Maximize then Solve After findin a solution you can plot it To plot a solution e Inthe Optimization Assistant window click the Plot button The Optimization Plotter window is displayed See Figure 5 9 Note When you close the Optimization Assistant you can choose to return the solution problem command used plot or nothing using the drop down in the bottom right corner of the assistant window 5 5 Optimization 187 ie Optimization Plotter extrema at 4 53559 extrema at 1 46441 Range of ion 0 r Range of y 4 O sis Range of objective values default n default extrema of 134 491 Plot Using Problem Domain Plot Constraints as Surfaces Figure 5 9 Optimization Assistant Plotter Window For information on the algorithms used to solve optimization problems refer to the Optim ization Methods help page Large Optimization Problems The Optimization Assistant accepts input in an algebraic form You can specify input in other forms described in the Optimization InputForms help page in command calling sequences 188 5 Mathematical Problem Solving The Matrix form described in the Optimization MatrixForm help page is more complex but offers greater flexibilit and efficienc For example solve the linear program
341. the Graphics check box ensures that a plot an image or the Canvas inserted in the document by using the Insert menu option is also hidden Command Output Versus Inserted Content Output is considered an element that results from executing a command Inserted components are not considered output Consider the following examples The plot resulting from executing the plot sin command is considered output e To show a plot from the plot sin command select both the Output and Graphics check boxes in the Show Contents dialog If you insert a plot by using the Insert menu option that plot is not considered output Therefore if you clear the Output check box in the Show Contents dialog that plot will be visible in the document e To hide an inserted plot clear the Graphics check box in the Show Contents dialog Inserted images and the Canvas are not considered output As such they are not hidden if you clear the Output check box e To hide an inserted image or canvas clear the Graphics check box in the Show Contents dialog Indentation and the Tab Key The Tab icon allows you to set the Tab key either to move between placeholders or to indent For example with the Tab icon off click the exponent button in the Expression palette The expression is inserted with the firs placeholder highlighted To move to the next placeholder use the Tab key Tab icon off Allows you to move between placeholders using the Tab key i The Tab
342. the Maplet code To display the Maplet application you must use the Maplets Display command Note The Maplet code may be quite large if the Maplet ap plication is complex In this case execute the document to ensure user define procedures that are referenced in the Maplet application are also defined Typical procedure 1 If present evaluate user define procedures Myproc proc 2 Load the Maplets Elements package with Maplets Elements 3 Evaluate the Maplet definition Maplet name Maplet Maplet definition 4 Display the Maplet application Maplets Display Maplet_name j Important When a Maplet application is running you cannot interact with the Maple document 10 5 Authoring Maplets To author Maplets you can use the Maplet Builder GUI based or the Maplets package syntax based The Maplet Builder allows you to drag and drop buttons sliders text re gions and other elements to defin the Maplet application and set the element properties to perform an action upon selection or update of the element The Maplet Builder is designed 398 10 Embedded Components and Maplets to create simple Maplets The Maplets package offers more capabilities control and options when designing complicated Maplet applications Designing a Maplet application is similar to constructing a house When building a house you firs construct the skeletal structure that 1s foundation floors and walls and then proceed to a
343. the computation performed followed by the norm Le755 6965 S49 725 254987 9659 459 f98l24 14069 infirity norr 3 0798359990 10 Vector operations available in the context menu include the following e Compute the dimension e Compute the norm 1 Euclidean and infinity 170 5 Mathematical Problem Solving e Compute the transpose e Select an element For more information on context menus see Context Menus page 68 for Document mode or Context Menus page 88 for Worksheet mode LinearAlgebra Package Commands The LinearAlgebra package contains commands that construct and manipulate matrices and vectors compute standard operations perform queries and solve linear algebra problems Table 5 7 lists some LinearAlgebra package commands For a complete list refer to the LinearAlgebra Details help page Table 5 7 Select LinearAlgebra Package Commands Basis Retumabasisfora vectorspace Dimension Determine the dimension ofa matrix ora vecior MatrixInverse Compute the inverse of a square matrix or pseudo inverse of a non square matrix QRDecomposition Compute the QR factorization of a matrix RandomMatrix Construct a random matrix Sylvester Matrix Construct the Sylvester matrix of two polynomials For information on arithmetic operations see Matrix Arithmetic page 166 For information on selecting entries subvectors and submatrices see Accessing Entries in Matrices and Vectors page 164
344. the style from the Styles drop down menu in the toolbar select Parameter a Equation Label C Header and Footer C Hyperlink C Maple Input C Maple Input Placehe Page Number E Parameter C Text Result 7 2 Document Formatting 291 plot create a two dimensional plot Calling Sequence plottf x plot f x x0 x1 plot v1l v2 Parameters f expression in independent variable z E independent variable 0 zl left and night endpoints of horizontal range i v72 x coordinates and y coordinates Applying Paragraph Styles By using the drop down list in the document context bar you can apply e Existing Maple paragraph styles e New styles that you have created through the Style Management Figure 7 4 and De finin a Paragraph Style Figure 7 6 dialogs To apply a Maple paragraph style to text in your document 1 Select the text to modify 2 In the styles drop down list in the context bar of your document select an appropriate paragraph style All Maple paragraph styles are preceded by the letter P The selected text now reflect the attributes of the paragraph style you have chosen P Annotation Title Bh P Author P Bullet Item P Dash Item P Diagnostic P Error P Fixed width F Heading 1 For example to format the title of the pasted text as a title firs select the line plot create a two dimensional plot In the Styles drop down select Title Result 292
345. the text has been entered First Section The introductory sentence gt cose dx subsection f sine dx Using the Insert Menu to Add Sections 1 Place the cursor in the paragraph or execution group above the location at which you want to insert a new section e Ifthe cursor is inside a section Maple inserts the new section after the current section 7 2 Document Formatting 295 e Ifthe cursor is in an execution group Maple inserts the new section after the execution group 2 From the Insert menu select Section An arrow marks the start of the section 3 Enter the section heading 4 Press the Enter key 5 Enter the body of the section Tips for Adding Subsections The insert location of subsections is the same as for sections with a few exceptions e Subsections are inserted at the current cursor location when in a subsection e To insert a subsection immediately after the current subsection collapse the subsection and place the cursor in the subsection title Using the Indent and Outdent Toolbar Icons You can shift sections to create or remove subsections Enclose the selection in a section or subsection Outdent the selection to the next section level if possible For example to create two sections containing the two categories of information in the pasted text 1 Select Parameters and all of the items under it 2 Click the Indent toolbar item 3 Cut and paste Parameters from ins
346. them during a lesson to demonstrate different cases or show the effect of the variation of a parameter e Create plots and animations to visually explain concepts for example the geometric re lationship between a mathematical function and its derivatives Tools Tutors Calculus Single Variable Derivatives See Figure 5 10 5 7 Teaching and Learning with Maple 197 FJ Calculus 1 Derivative File Help Plot Window Enter a Function and an interval a b fixi costs a 0 Derivalives l Pixi costs ex sinks Display Fid in the plot aaa sin x cosx Display F s in the plot Display Flot Options Maple Command S DerivativePlot x cos x E a i i B ok ar ene Pele ae 6 26 4 24 7 24 1 Figure 5 10 Calculus 1 Derivatives Tutor Students can e Perform step by step computations for example compute a derivative by applying dif ferentiation rules using commands or a tutor Tools Tutors Calculus Single Vari able Differentiation Methods See Figure 5 11 e Perform computations e Visually explore concepts 198 5 Mathematical Problem Solving Kj Calculus 1 Differentiation Methods File Edit Rule Definition Apply Rule Understood Rules Help Enter a Function Function sins 3 Variable x d f sin x o The power rule has heen applied Show Hints Get Hint hyperbolic gt ae ee
347. tive x H x y 1 2 2 1 0 Series To generate the Taylor series expansion of a function about a point use the taylor command gt taylor sin 4x cos x x70 _ 38 34 421 5 3 30 4x x o x Note If a Taylor series does not exist use the series command to fin a general series ex pansion For example the cosine integral function For more information refer to the Ci help page gt taylor Ci x x 0 Error does not have a taylor expansion try series To generate a truncated series expansion of a function about a point use the series command gt series Ci x x 0 l 2 4 6 v In x x x Ob y ln x 4 96 x By default Maple performs series calculations up to order 6 To use a different order specify a non negative integer third argument 5 4 Calculus 179 gt expansion series Ci t t 0 4 expansion Y In t 7 P o 7 To set the order for all computations use the Order environment variable For information about the Order variable and the ol term refer to the Order help page The expansion is of type series Some commands for example plot do not accept arguments of type series To use the expansion you must convert it to a polynomial using the con vert polynom command l gt plor Ci t convert expansion polynom t 2 For information on Maple types and type conversions see Maple Expressions page 333 For information
348. ts and Maplets Parameters a and bd Plot Window Use the Dials to set parameters Piotof 7 fet 8 10 4 Using Maplets A Maplet is a pop up graphical user interface that provides interactive access to the Maple engine through buttons text regions slider bars and other visual interfaces You can create your own Maplets and you can take advantage of the built in Maplets that cover numerous academic and specialized topics Built in Maplets include some assistants and tutors such as the ODE Analyzer For more information on this assistant see Ordinary Differential Equations ODEs page 120 Maplet applications are launched by executing Maplet code Maplet code can be saved in a Maplet maplet fil or Maple document mw Maplet File To launch a Maplet application saved as a Maplet file e In Windows double click the fil from a Windows fil browser 10 5 Authoring Maplets 397 e In UNIX and on Macintosh use the command line interface At the command line enter maple q lt maplet_filenam gt To view and edit the Maplet code contained within the maplet file 1 Start Maple From the File menu select Open Maple displays the Open dialog In the Files of Type drop down list select maplet Navigate to the location of the maplet fil and select the file Click Open Mn A Ww N Maple Document To launch a Maplet application for which the Maple code is contained in a Maple document you need to execute
349. tyles colors shadings axis styles and titles where applic able Plot options are applied using the Interactive Plot Builder the context menus or as options in the command syntax Interactive Plot Builder Options The Interactive Plot Builder offers most of the plot options available in Maple in an easy to use interface 264 6 Plots and Animations Example Launch the Interactive Plot Builder and enter the expression 1 Add the expression 2 x 5 10 x 3 6 x 1 For information on interacting with the Interactive Plot Builder see Example 1 Display a plot of a single variable expression page 240 Set the x axis range 2 In the Select Plot Type window change the x axis range to 2 2 In the Plot Options window 3 From the Line group box select dot from the left drop down menu 4 From the Color group box select Blue 5 From the Axes group box select frame 6 From the Title group box enter My Plot in the text field Plot the expression 7 Click Plot Context Menu Options Using the context menu you can alter a plot by right clicking Control click for Macintosh the plot output You can also access a large subset of plot options using the Plot toolbar and Plot menu options These menus display when a plot region is selected Regardless of the method used to insert a plot into Maple you can use the context menu to apply different plot options For a list of options available when plotting in two and three d
350. undary at the left An execution group may also contain any or all of the following a plot a spreadsheet text embedded components and a drawing canvas Execution groups are the fundamental computation and documentation elements in the document If you place the cursor in an input command and press the Enter or Return key Maple executes all of the input commands in the current execution group 1 3 Entering Expressions 19 Math Mode vs Text Mode The default mode of entry in Document or Worksheet mode is Math Mode which displays input in 2 D Math In earlier releases of Maple commands and expressions were entered using Maple Input or 1 D Math Important With Maple input you must terminate commands with a semicolon or colon gt cos alpha 2 sin alpha 2 cos a sin a gt a int exp sqrt 2 x x gt a JZ gt limit f x x infinity dim f x gt sum a k x k k 0 m product b j x j jJj 0 n in M gt a x pi b x k 0 j 0 In Document Mode to enter input using Maple Input mode insert a Maple prompt by clicking in the toolbar and then click the Text button in the toolbar In Worksheet Mode simply click the Text button See Figure 1 2 Drawing Piot Animation C20 Math Times Mew koman 7 Ek Figure 1 2 Text and Math Buttons on the Toolbar 20 1 Getting Started Table 1 6 Math Mode vs Text Mode Math Mode Text Mode Maple s default setting
351. undary value problems symbolically and numerically ODE Analyzer Assistant The ODE Analyzer Assistant is a point and click interface to the Maple ODE solving routines To open the ODE Analyzer e From the Tools menu select Assistants and then ODE Analyzer Maple inserts the dsolve interactive calling sequence in the document The ODE Analyzer Assistant Figure 4 3 is displayed W ODE Analyzer Assistant Differential Equations Conditions Parameters Solve Numerically Solve Symbolically Classify Figure 4 3 ODE Analyzer Assistant 4 4 Solving Equations 121 In the main ODE Analyzer Assistant window you can defin ODEs initial or boundary value conditions and parameters To defin derivatives use the diff command For example adiff x t t corresponds to oe and diff x t t t corresponds to LAUN For more information on the diff command see The diff Command page 175 dt After definin an ODE you can solve it numerically or symbolically To solve a system numerically using the ODE Analyzer Assistant 1 Ensure that the conditions guarantee uniqueness of the solution 2 Ensure that all parameters have fixe values 3 Click the Solve Numerically button 4 In the Solve Numerically window Figure 4 4 you can specify the numeric method and relevant parameters and error tolerances to use for solving the problem 5 To compute solution values at a point click the Solve button 122 4 Basic
352. ure 7 17 Drawing Properties Canvas Icon Change the Gridline Color 319 Figure 7 18 Hyperlink Properties DidlOO ici ii dente statoednioninceutl aemGalinthutiuedd 321 igure 719 Bookmark Indicator ceaitiidatashemawaa riianededtenaunanpeiacdtal Oemedsaacedebauncats 324 Figure 720 Greate Bookmark Diao es basilica ionbareaholenmebolkneuthaiiboentebaaabeent 325 Fig re 7 21xComponents Paletleri iTi E Sak igen Reds Santen meaTeRaE 327 Figure 7 22 Interactive Application Task Template ccccccecececeeeeeeeeenenenens 328 Figure 7 23 Spe lleheck Diallo ax cisitchte po widne a a iaaneiamess 329 Figure 8 1 Function Definitio Palette Items isatsndicciadocs iertielisieltalendiclicindidd 339 Figures 2 Evyaliate at a PONE enaar ET EEEE 354 Figure 9 1 Code Gil RET ON si et N 382 Figure 9 2 Collapsed Code Edit Region onsonssessnessesseossessessressesserssressesseeso 382 Feme g o Starup Code Editol ieaie e E 383 Fig re 10 l7 Components Palette ssrfi sn soeatutin sa narcae ses T E TEE T 389 Fioure 10 2 Label Properties Dialog cicd ces cet ladi headin a iedielnaed 391 List of Figures xiii Fiure 10 3 Slider Properties Dialog 2 xiakic tlic beboreeiaihnehuonberaclatd coaheobareneusens 391 Figure 10 4 The Inserted Component c 0cccccccececenssececesescscsesseseneceeesceeess 393 Figure 10 5 DialComponent Action Dialog ccccecececec eee ene eeeeeneeeeeeeeneaenens 395 Fore IOC A Simple VIA DIC ri
353. used in linear algebra and vector calculus computations 12 33 83 12 y lt 2 14 gt i For information on definin Matrices and Vectors see Creating Matrices and Vectors page 156 8 2 Creating and Using Data Structures 339 gt Mv 486 334 gt v M 1186 234 gt M l 4A Il 865 865 83 4 2595 865 For more information on these data structures including how to access entries and perform linear algebra computations see Linear Algebra page 155 Functional Operators A functional operator is a mapping f x y x The value of f x is the result of evaluating y x Using functional operators you can defin mathematical functions Defining a Function To defin a function of one or two variables 1 In the Expression palette click one of the function definitio items See Figure 8 1 Maple inserts the function definition 2 Replace the placeholders using Tab to move to the next placeholder Note If pressing the Tab key indents the text click the Tab icon in the toolbar This allows you to move between placeholders 3 Press Enter e PE tan os Figure 8 1 Function Definitio Palette Items 340 e 8 Maple Expressions For example defin a function that adds 1 to its input gt addi x gt x 1 Note To insert the right arrow you can enter the characters gt In 2 D Math Maple replaces gt with the right arrow symbol In 1 D Math the characters are not rep
354. variable unassign its name gt unassign x y For more information see Unassigning Names page 94 For more information on the assume command refer to the assume help page The assuming Command To perform a single evaluation under assumptions on the names in an expression use the assuming command The syntax of the assuming command is lt expression gt assuming lt property or relation gt Properties and relations are introduced in The assume Command page 142 The frac command returns the fractional part of an expression gt frac x assuming x integer 0 Using the assuming command is equivalent to imposing assumptions with the assume command evaluating the expression and then removing the assumptions gt about x X nothing known about this object If you do not specify the names to which to apply a property it is applied to all names 4 6 Restricting the Domain 145 2 a y l me gt ty assuming positive a b Assumptions placed on names using the assume command are ignored by the assuming command unless you include the additionally option gt assume x lt 1 gt is l1 x gt 0 assuming x gt 1 false l 2 oe gt is l x gt 0 assuming additionally x gt irue The assuming command does not affect variables inside procedures For information on procedures see Procedures page 378 You must use the assume command gt f proc x sqrt a 2 x end proc f
355. ve command To fin global solutions generally purchase the Global Optimization Toolbox For more information visit http www maplesoft com products toolboxes Point and Click Interface The primary method for solving optimization problems is the Optimization Assistant To launch the Optimization Assistant e From the Tools menu select Assistants and then Optimization Maple launches the Optimization Assistant See Figure 5 8 5 5 Optimization 185 IM Optimization Assistant X Solver Probie Local Dofouk Objacthe Function Edt 3 3 x y C Nonlinear ix o 5 Options ye 0 5 xt 6 C Minimize Maximize Feasiity Tolerance def suk Salution Objective value 1394 491161539748162 Optimality Tolerance def anh x 4 595592925399129 7 1 46440707460871 iteration Limi def uit Infinte Bound def auit On Qu Return Salution x Figure 5 8 Optimization Assistant To solve a problem 1 Enter the objective function constraints and bounds 2 Select the Minimize or Maximize radio button 3 Click the Solve button The solution is displayed in the Solution text box You can also enter the problem objective function constraints and bounds in the calling sequence of the Optimization Interactive command 186 5 Mathematical Problem Solving For example fin the maximum value of xy _ y subject to the constraints x y lt 6 x E 0 5 y 0 5 gt Optimization In
356. verse Linear System Solving Figure 1 6 Accessing Tutors from the Tools Menu Some of the tutors can also be accessed through the Student package The Differential Equations tutor DE Plots is accessible through the DEtools package For a definitio of the term package see Package Commands page 47 The Student package is a collection of subpackages designed to assist with the teaching and learning of standard undergraduate mathematics The subpackages contain many com mands for displaying functions computations and theorems in various ways and include support for stepping through important computations 38 1 Getting Started The interactive commands help you explore concepts and solve problems using a point and click interface These commands launch tutors that provide a graphical interface to some of the visualization and computation commands described above See for an example of one of the tutors Fd Calculus 1 Differentiation Methods File Edit Rule Definition Apply Rule Understood Rules Help Enter a Function Function 2 y costscyfsingx Variable x cos x any df cos x dx simi x cas x sire x Show Hints ay ea t e on d e sire X dx Feel sinl x cos x sin a dx d dx 24 3 et SiR K d Constant Multiple sin x cas x sial x al na i e p lt trig gt lw hyperbolic et ht lt arctrig gt it lt archype
357. vorites add templates that you use most often from other palettes Live Data Plots templates for visual representation of your data eBook Metadata markup tags 1 3 Entering Expressions 23 Palette Category Palette Description Mathematical Palettes Palettes for constructing expressions Common Symbols Relational Relational Round i Y common Symbols Operators Large Operators i i Negated Fenced Arrows gt Si u H Rk Kee Constants and Symbols lt D Soe Ap Oe TY be Gal Punctuation insert punctuation symbols such as inserting the re gistered trademark and copyright symbols into text regions Miscellaneous insert miscellaneous math and other symbols outside the above categories Alphabetical Palettes Greek Script A Fraktur J Open Face C Cyrillic aK Diacritical Marks Roman Extended Upper Case W Greek w gs e g Se oe tO eH gt n Roman Extended Lower Case DE ow OF EG mo A om Da 7 tS 5 fo d amp om T qa a X uw R Viewing and Arranging Palettes By default palettes display in palette docks at the right and left sides of the Maple window To view and manage palettes and palette docks see Table 1 8 24 1 Getting Started Table 1 8 Managing Palettes To view palette docks e From the View menu select Palettes and then Expand Docks There are docks on the far right and lef
358. w ace he Macie indo U Cutanae he Mage Sten variables optional name of set nawe y unknowns fer which to solve Correctnty gt O Mathews complex optional iteral nawe search for complex solotons U Atre J Dm Mhen p O Cands Basic Information Cats of Vinstons A ee Y Description O erda touara L Offerentat sigetr e Cquatone The fwolve command wamerically computes the zerees of ene of more equations expressions or precedares O Offerwnatcometry Cencrete Matt wena oO m Y Output O ivatan O atorren and Sorg Cquatere The solutions to a ngle eguamea ae returned as an expression sequence new gt S aoe pous The solutions te a set oc list of equations are returned as sets of equation seqornces rv soiste For a dagie polynomial equation of one variable with real coeficieees by default the solve command computes al real non complex U temre reots it may net return all roots for exceptionally M conditioned polynomials D Uoer as Fot a dangle polynomial eqaatica of one variable with some non real complex coeficients the fsolve command computes al real and Sua complex roots It may net return all roots for exceptionally ill condoned polynomials reg ive 8 froo For a gencral eqeahon of system of equations the fsolve command computes a single real root L Momor area p 5 _ Y Examples i noce O Nemca Stra 5 tore Y A Polynomial Equation in One Variable fete oa Fee a urivanate real polynomial
359. x in the same plot dx W gt zef sin x Sia dx Removing the Auto Execute Setting To remove the setting in a region 1 Select the region 2 From the Format menu select Autoexecute and then Clear To remove all autoexecuted regions from a document From the Format menu select Autoexecute and then Clear All 304 7 Creating Mathematical Documents Repeating Auto Execution To execute all marked groups e From the Edit menu select Execute and then Repeat Autoexecution Security Levels By default Maple prompts the user before automatically executing the document To set security levels for the autoexecute feature use the Security tab in the Options dialog For details refer to the OptionsDialogSecurity help page 7 4 Tables Tables allow you to organize content in a document Creating a Table To create a table 1 From the Insert menu select Table 2 Specify the number of rows and columns in the table creation dialog 3 Click OK The default properties for the table include visible borders and auto adjustment to 100 of the document width These options as well as the table dimensions can be modifie after table creation Create a table with 4 rows and 2 columns at the end of your document In document mode the input mode is set to Math by default in worksheet mode the default is Text mode Cell Contents Any content that can be placed into a document can also be placed into a
360. x 2 gt eval x 3 th 8 3 Working with Maple Expressions 361 For more details on levels of evaluation refer to the lastnameevaluation assigned and evaln help pages Delaying Evaluation To prevent Maple from immediately evaluating an expression e Enclose the expression in right single quotes Because right single quotes delay evaluation they are referred to as unevaluation quotes gt Fh Using an Assigned Name as a Variable or Keyword If you use an assigned name as a variable Maple evaluates the name to its value and passes the value to the command In this example that causes Maple to return an error message n 2 D i Error in sum summation variable previously assigned second argument evaluates to 4 1 n Note In general it is recommended that you unassign a name to use it as a variable See Unassigning a Name Using Unevaluation Quotes page 362 To use an assigned name as a variable e Enclose the name in unevaluation quotes Maple passes the name to the command iT gt gt 4 i 3 2 1 1 17 gt n n 1 n 1 guts bo 1 3 Important It is recommended that you enclose keywords in unevaluation quotes 362 e 8 Maple Expressions For example if you enclose the keyword left in unevaluation quotes Maple uses the name not its assigned value gt left 3 x gt limit x 0 teft Full Evaluation of an Expression in Quotes Full ev
361. x I LS Lee Prl Figure 2 5 SI Units Palette To insert an expression with a unit 1 Enter the expression 2 In a unit palette click a unit symbol Note To include a reciprocal unit divide by the unit 2 6 Performing Computations 73 To evaluate an expression that contains units 1 Enter the expression using the units palettes to insert units 2 Right click Control click for Macintosh the expression 3 From the context menu select Units and then Simplify For example compute the electric current passing through a wire that conducts 590 coulombs in 2 9 seconds 590 C simplify units es 2 9 s For more information on using units see Units page 127 203 4482759 A Assistants and Tutors Assistants and tutors provide point and click interfaces with buttons text input regions and sliders For details on assistants and tutors see Point and Click Interaction page 32 Assistants and tutors can be launched from the Tools menu or the context menu for an ex pression For example you can use the Linear System Solving tutor to solve a linear system specifie by a matrix or a set of equations 74 2 Document Mode Example 3 Using a Context Menu to Open the Linear System Solving Tutor Use the Linear System Solving tutor to solve the following system of linear equations I 3 0 2 l l l 4 2 1 5 7 written in matrix form 0 3 5 4 7 I 13 6 5 1 Ina new document block create the m
362. xecute when an item is selected Math Expression Enter or display a mathematical expres sion The value can be updated based on code in the docu ment or another embedded component Meter Select or display an integer or floating poin value Change the display and enter code to execute when the value changes Plot Display a 2 D or 3 D plot or animation This plot or animation can be interacted with in the same way as other plots see Plots and Animations page 237 The value can be updated based on code in the document or another em bedded component You can also enter code to be executed when the execute code pointer is used to click or drag in the plot region Radio Button Use with other radio buttons to select one RadioButton in a group Enter code to execute when the value changes 10 2 Using Embedded Components 387 Component Name and Description Inserted Image Rotary Gauge Select or display an integer or floating point value Change the display and enter code to execute when the value changes Slider Select or display an integer or floating poin value Change the display and enter code to execute when the value changes Text Area Enter or display plain text The value can be updated based on code in the document or another embed ded component and you can enter code to execute when the value changes Toggle Button Select or display one of two options Change the images disp
363. xpression to a plot region you can either make a copy of the expression from the input region or you can cut the expression thereby removing it from the input region To make a copy of the expression select the full expression in the input region and press Ctrl Command Macintosh while you drag the expression to the plot region To cut the expression and paste it in the plot region highlight the expression and drag it to the plot region 4 Repeat steps 2 and 3 using the following expressions sin 2 x sin x 2 and sin x 5 To remove an expression from the plot region drag and drop the expression plot from the plot region to a Maple input region 6 2 Creating Plots 249 The plot and plot3d Commands The fina method for creating plots is entering plotting commands The main advantages of using plotting commands are the availability of all Maple plot structures and the greater control over the plot output Plot options are discussed in Customizing Plots page 263 Table 6 2 The plot and plot3d Commands plot plotexpression x a b plot3d plotexpression x a b y a b e plotexpression expression to be plotted e x a b name and horizontal range e y a b name and vertical range Maple commands from Creating Plots Interactive Plot Builder The following examples show the plotting commands returned by the examples in nteractive Plot Builder page 238 250 6 Plots and Animations Example 1
364. yle file are set for printing the tex fil using the dvips printer driver You can change this behavior by specifying an option to the usepackage LaTeX command in the preamble of your tex file For more in formation refer to the exporttoLaTeX help page 11 4 Exporting to Other Formats 413 Maple Input You can export a Maple document as Maple input so that it can be loaded using the Maple Command line version Important When exporting a document as Maple input for use in Command line Maple your document must contain explicit semicolons in 1 D Math input If not the exported mpl fil does not contain semicolons and Command line Maple generates errors Maplet Application The Export as Maplet facility saves a Maple document as a maplet file so that you can run it using the command line interface or the MapletViewer The MapletViewer is an executable program that can launch saved Maplet applications It displays and runs Maplet applications independently of the Maple Worksheet interface Important When exporting a document as a Maplet Application for use in Command line Maple or the MapletViewer your document must contain explicit semicolons If not the exported maplet fil does not contain semicolons and Command line Maple and the MapletViewer generates errors Maple Text Maple text is marked text that retains the distinction between text Maple input and Maple output Thus you can export a document as Maple text send the t
365. yntax and related Maple command syntax reduces the possibility of introducing typing er rors WwW Expression h i W Expression jf dx int f x a If you prefer 1 D Math input you can change the default math input notation To change math input notation for a session or globally across all documents 1 From the Tools menu select Options The Options Dialog opens 2 Click the Display tab 3 In the Input Display drop down list select Maple Notation 1 3 Entering Expressions 21 4 Click the Apply to Session or Apply Globally button Important The new input display becomes the default setting after pressing the Enter key Palettes Palettes are collections of related items that you can insert into a document by clicking or drag and dropping The Maple environment provides access to over 20 palettes containing b items such as symbols layouts 4 mathematical operations f a and much a More By default palettes are displayed in the left pane of the Maple environment when you launch Maple If the palettes are not displayed 1 From the View menu select Palettes 2 Select Expand Docks 3 Right click Control click Macintosh the palette dock From the context menu select Show All Palettes Alternatively from the main menu select View Palettes Arrange Palettes to display specifi palettes You can create a Favorites palette of the expressions and entities you use
366. you access to thousands of free Maple resources and MaplePrimes which is an active web community for sharing techniques and experiences with Maple and related products To sign up for a free Maplesoft com membership account visit http www maplesoft com members sign_up_form aspx The MapleCloud is integ rated with several of these online features so it is strongly recommended that you use a Maplesoft com membership account 420 11 Input Output and Interacting with Other Products Index Symbols toolbar icon 66 toolbar icon 66 342 175 H 168 T 168 amp gt 78 amp lt amp gt 156 159 amp x 168 94 361 379 amp gt 94 167 1 D Math 79 switching to 2 D 79 2 D Math 78 converting to 1 D 80 entering 5 shortcuts 7 switching to 1 D 79 79 80 1 142 93 79 80 9 help topic 54 165 334 335 6 110 entering 110 _ 95 entering 95 _ZN 115 95 334 159 115 143 element wise operations 358 A about command 143 abs command 107 absolute value 107 add word to your dictionary 330 add command 375 additionally command 143 algebra 153 linear 171 polynomial 148 algsubs command 355 alignment format 286 American spelling spellcheck 328 and operator 366 angle brackets 156 159 203 angles 351 animations creating 275 customizing 279 Application Center 59 applications sample documents 57 apply character styles 2
367. your document or save the interactive document for later use 44 e 1 Getting Started Example 8 Use the Exploration Assistant to Explore a Plot sin ax b cos x x In this example we will explore how the plot of changes as we vary the parameters a and b Action Result in Document 1 Enter the plot command shown sin ax b cos x plot x 1 10 2 Right click Control click for ree pS Macintosh the expression and plot Sales Post select Explore 5 x 1 10 fa Copy Special b Paste Crh Evaluate and Display Inline Ctrl Explore 4oply a Command Assign to 4 Mame Conversions Language Conversions Help on Command 2 D Math 3 In the Explore parameter selec tion dialog set the ranges a 0 10 0 and b 5 0 5 0 Select ico floating poin computation a 5 0 floating point computation 1 5 Commands 45 4 Click Explore The Explora aaae tion Assistant opens ina new Maplesoft document Move the sliders to see the plot as the parameters change 1 5 Commands Even though Maple comes with many features to solve problems and manipulate results without entering any commands you may fin that you prefer greater control and flexibilit by using the set of commands and programming language that Maple offers The Maple Library Commands are contained in the Maple library which is divided into two groups the main library and packages The main li

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