Getting started with Maple 10
Contents
1. Figure 6 Items in the Manuals Dictionary and more entry for Maple 10 s Help menu New User Roadmap Out of the items shown in Figure 6 for the Manuals Dictionary and more entry the first one is the New User Roadmap This document is a diagram of suggested resources for using Maple 10 relevant to the user s objective The New User Roadmap is shown next Getting Started with Maple 10 Page 5 Learn principles and review major features Read the Getting Started Guide Fromthe Help menu select Manuals Dictionary and more Select Manuals and then Getting Started Guide Solve a problem immediatel Check for point and click tools Assistants Tutors Task Templates For analyzing For topics in Show you the ODEs and ODE precalculus steps required Systems calculus to solve a creating plots multivariate problem Each supporting cume calculus task is a collection fitting performing vector of Maple worksheet unit conversion calculus content such as and more and linear 2 D math embedded algebra components Fromthe Tools commands and menu select Fromthe Tools plots thatyou can Assistants meny select insert into your Tutors worksheet Fromthe Tools menu select Tasks and then Browse in the Browse dialog exoand the Task folder to view a list of topics Check for instructions Help Pages An online help sy stem that you can use to find information about a specific top2. degrees asterisk for products dot product e regular product the del or nabla operator for vector analysis V factorial aleph X Planck s constant for quantum mechanics 7 etc These symbols can be very useful for editing equations for inclusion in texts or as input for Maple operations As an example of equation editing using Maple here are a couple of examples from vector analysis built using the del or nabla operator and the partial derivative symbol from the Expression palette Ff Of Of VE oy aa Iv az TA OF n OF n OF Ox dy Oz Union and intersection of sets can be calculated using Maple as follows 1 3 5 7 9 U 5 7 9 11 1 3 5 7 9 11 1 1 3 5 7 9 M 5 7 9 11 57 9 2 Getting Started with Maple 10 Page 27 The Common Symbols palette is useful when inserting the base of the natural logarithms e which is a different symbol than the letter e This difference is illustrated by the use of the Approximate gt 5 operation in the context menus of the following two entries P45 3 e745 e2 5 12 389 In the first entry we typed the letter e therefore the Approximate gt 5 operation does not produce a floating point result e is assumed to be an unassigned variable In the second entry the symbol e was inserted from the Common Symbols palette producing the correct result when Approximate gt 5 was used The Greek palette contains the letters of t
3. a Point probe determines coordinates of cursor location on graph b Scale zooms in and out c Pan moves graph about the plot frame 6 Grid button shows grid on plot area when active Click on the different menus or buttons and select different properties of the graph For example by selecting options 2 a 3 a and activating the 1 1 scale button the graph of Figure 28 is now as shown in Figure 30 Figure 31 shows the same graph with a grid hi O M 0 5 10 15 20 Figure 30 Same as Figure 28 but using boxed axes and 1 1 scaling 0 5 10 15 ZU Figure 31 Same as Figure 30 but activating the grid Getting Started with Maple 10 Page 35 Two dimensional animation with context menus A Maple animation can be produced on a function of the form y x a where the graph to be animated is y f x and the animation parameter is a For example to produce an animation of the equation y a sin ax we need just type the expression a sin ax and do a right click on the expression to activate a context menu Then we select the item Plots gt Plot Builder from the context menu and select the Animation option in the box entitled Select Plot Type We keep the selection 2 D plot in the box entitled Select Plot as well as the ranges 0 to 10 for the x Axis and 0 to 10 for Animation Parameter a in the box entitled Select Variable Purpose and Ranges Then we press Plot Asa result we obtain a plot that shows no curves on
4. 43 ma NAA me Damped sine sine plus Cosine Sine times Cosine Figure 40 Multiple curve graph generated with a context menu for a damped sine expression and modified by drag and drop operations for sine cosine addition and multiplication Plot context menu was used to edit and add legends to the plot Plots with logarithmic scales using context menus Consider the expression ex ale ex Using context menu we can generate a 2 D plot showing the variation of the function y e e The vertical scale in the default range 10 lt x lt 10 reaches from 1 to about 5x105 Using a logarithmic scale for y would be use to better understand the variation of the function with x In order to replace the natural scale for a logarithmic one in a graph we first generate the graph following a procedure similar to that leading to the plot of Figure 28 namely Type the expression e e in Math input format Click on the expression and generate a context menu right click Select option Plots gt 2 D plot Getting Started with Maple 10 Page 44 The resulting plot will be shown in you Maple worksheet In order to replace the y scale with a logarithmic one proceed as follows Click on the plot to select it Generate the context menu by doing a right click Select the option Axes gt Mode This will produce a dialog box Modify it so it looks as in Figure 41 below then press Apply OK or simply OK to produce a logarithmic scale
5. Figure 32 and press the Play button in the toolbar item 3 in Figure 32 to see the animation of the surface produced Getting Started with Maple 10 Page 48 Animation of a contour plot using context menus Consider once more the expression sin a x cos ay Enter this expression in as a Math input in a Maple worksheet Click on the expression and generate the corresponding context menu right click Then select the options Plots gt Plot Builder In the resulting dialog box select Animation in the Select Plot Type box and select 2 D Contour plot in the Select Plot box Make sure that x y and a are selected as the First Second and Animation parameters in the dialog box with ranges of 5 to 5 for both x and y and of 0 to 2 for a Press Plot Click on the resulting plot to open the animation toolbar see Figure 32 and press the Play button in the toolbar item 3 in Figure 32 to see the animation of the contour plot produced Animation of a density plot using context menus Repeat the exercise from the previous section but selecting 2 D Density Plot in the Select Plot box in the Plot Builder dialog box Make sure that the parameters and ranges are the same as in the contour curve animation exercise and press Plot Run the animation from the animation toolbar after clicking on the plot Example of a well documented worksheet Maple includes some examples of well documented worksheets that address specific problems in
6. These are the commands available right away as soon as Maple is started Commands in packages need to be called by referring to the package name or by loading the package first with the command with For example to produce an implicit plot of an equation in two dimensions we can write plots implicitplot x 2 y 2 25 0 x 10 10 y 10 10 or alternatively with plots implicitplot x 2 y 2 25 0 x 10 10 y 10 10 Manuals This item contains two entries Getting Started Guide e User s Manual Select one of these items to open the corresponding manual These are the official Maple 10 manuals in worksheet format These manuals are provided in printed form with each copy of Maple 10 On the Web These entries require an Internet connection and provide additional Maple 10 resources on line Check the different entries for details Getting Started with Maple 10 Page 10 Maple Tour The Maple Tour is a good way to get initiated with Maple 10 To activate the tour use Help gt Take a Tour of Maple The resulting worksheet has links to worksheets illustrating the following issues in Maple 1 Ten Minute Tour A quick tour of Maple 2 Numeric and Symbolic Computations Basic calculations in Maple 3 Matrix Computations Matrix and linear algebra 4 Differential Equations Ordinary and partial differential equations 5 Special Functions E g Bessel Airy etc 6 Optimization Finding maxima a
7. a semi colon or a colon When you end a command with a colon the command is executed but no output is shown e g Getting Started with Maple 10 Page 51 gt int x x 0 2 In Maple 10 if you are using Maple Input to enter commands and you forget to end it with a semi colon or colon Maple will complete the command anyway but issue a warning that an incomplete command was entered Here s an example gt int x 2 x 0 2 Warning inserted missing semicolon at end of statement 4 To correct this oversight one needs only click back on the offending command type the semi colon or colon and press Enter again Maple will recalculate the command and remove the warning message Inserting execution groups An execution group can be inserted below the current location of the cursor by using Cntl j or above the current location of the cursor by using Cntl k Alternatively you just can use the options nsert gt Execution Group gt Before Cursor or Insert gt Execution Group gt After Cursor Another possibility is to click the nset Maple Input button item 12 in Figure 10 available in the toolbar As an exercise click on any of the execution groups currently available in your worksheet and insert execution groups before and after Deleting execution groups To delete an execution group click in front of the prompt and use Cnt Delete You can also use Cnt Delete to delete individual objects such as Ma
8. at a point and multiple valued functions Getting Started with Maple 10 Page 15 W Expression fra fra Sy j k T d a IF qa aa lim a fa wa ct e hia loggie logta anig costa tanta 2 He fla b panes FS el ee a FK rcg p xai 7 ee I Figure 12 Components of the Expression palette Typing mathematical expressions in Math entry mode The Expression palette can be used to build mathematical expressions For example click under the last expression in your worksheet and use the summation symbol in the Expression palette to create the following summation OO 5 2 r 1r Here are the step by step instructions to build this expression Getting Started with Maple 10 Page 16 Click on the summation symbol in the Expression palette the 7 in the lower side of the symbol will be highlighted Type r Press the tab key in your keyboard moves cursor from one entry point to the next Type 1 Press tab Click on the infinity symbol cc from the Common Symbols palette the f will be highlighted now Type l r 2 At this point the expression is complete We can do a couple of things with it 1 highlight it and use Edit gt Copy or Cntl C to copy it to the clipboard and then paste it into say a Word file in this case we would have used Maple as an equation editor or 2 press Enter to calculate the expression Press Enter to calculate the expression The result should be
9. characters in Maple Input format are shown below gt Tsum 1 Pi k k 1 infinity o pas TT l l 1 gt falpha I betaj alpha 2 1I betaj evalf expand cat IP ta 21iB a 1IlaB 2 p 2 Summary In summary we can create worksheets in Document mode or in Worksheet mode Document mode which is the new preferred mode for Maple 10 allows for free location of entry points and allows to enter commands in Math input format The F5 key in Document mode toggles input from Math input form to Text On the other hand in Worksheet mode we use execution groups which can take commands in Math input form or in Maple Input form Use F5 to toggle between these two input forms in an execution group Maple Input form is the old fashioned but still useful particularly for programming way to enter Maple commands So which mode is better The Document mode is definitely the best and it is today s preferred mode for Maple worksheets There is however an enormous quantity of old fashioned Maple worksheets that have been developed in the last 10 years for that we can use the Maple 10 Classical Worksheet application to operate upon those worksheets This approach is presented in the next section The Maple 10 Classical Worksheet application This application can be used to read old fashioned worksheets created in earlier versions of Maple For an individual Maple 10 server you will find the Classic Works
10. e 7 Paste Ctrl io Style Lighting bov WYT Axes Scaling Constrained z Hue Projection z Grayscale Transparency Default Coloring Manipulator b Mo Coloring Export b Black Blue Cyan Gald aray areen Orange Red Yellow Figure 36 Context menu for a three dimensional surface plot Color sub menu highlighted Two dimensional implicit plots with context menus A function of the form f x y 0 or of the form g x y c can be used to generate an implicit plot in the x y plane through context menus Consider the equation x 9 N al Type this equation in a Maple worksheet in Math entry mode Click on the equation and generate a context menu for the same right click then select the item Plots gt 2 D Implicit Plot The result is a plot that looks like a circle In order to see the true shape of the implicit plot we need to use a 1 1 scaling which we can get by simply clicking on the plot area and using the 1 1 button in the toolbar The resulting graph is an ellipse with semi axes 3 in x and 4 in y as shown next Getting Started with Maple 10 Page 40 Figure 37 An ellipse generated as a two dimensional implicit plot Implicit plots can also be generated out of an expression of the form f x y In such case Maple will assume that the corresponding equation to be plotted is f x y 0 For example using the expression x sin x y cos y which generated the surface plot of Figure
11. first curve being labeled Ellipse while that for the second curve the legend shows the label Curve 2 Legend Labels fx Legend Labels CUVE Legend for Curve 1 wv q Label Ellipse Label Hyperbola Figure 38 Dialog boxes for editing curve legends in a plot To edit the legend for the second curve once more open the context menu for the plot and select the option Legend gt Edit Legend Select Legend for Curve 2 in the Curve field and type Hyperbola for the Label field in the dialog box Then press Done The result from these operations will be the plot as shown in Figure 39 Getting Started with Maple 10 Page 42 Ellipse Hyperbola Figure 39 Ellipse of Figure 37 with hyperbola added by a drag and drop operation Plot includes legend edited through context menus Exercise Using the expression 253 6 0 017 Sin t to generate a 2 D plot in the range 70 lt t lt 10 similar procedure to that leading to Figure 28 except that default range for x is not modified in the present exercise Use drag and drop to add the graphics corresponding to the expressions sin t cos t and sin t cos t Use the plot s context menu to edit the legends so that the legends for the three expressions read Damped Sine Sine plus Cosine and Sine times Cosine respectively The resulting graph should look like that in Figure 40 Getting Started with Maple 10 Page
12. in y The resulting graph is shown in Figure 42 below Axis Mode Axis Defaut All Axis Mode CO Detaul Linear Logarithmic Figure 40 Dialog box for axes modes generated using a 2 D plot context menu and selecting Axes gt Mode Using the Axes gt Mode option in a 2 D plot context menu thus allows us to select logarithmic scales for the x axis only semilogarithmic plot in x for the y axis only semilogarithmic plot in y or for both axes double logarithmic or log log plot Exercise Using the context menu for the plot of Figure 41 try the following Change the horizontal scale from 1 to 10000 Produce a semilogarithmic plot in x x scale logarithmic y scale natural Produce a semilogarithmic plot in y x scale natural y scale logarithmic Produce a double logarithmic plot both scales logarithmic Add the plots for the functions xe and e to the existing plot by a drag and drop procedure Edit the legends of the resulting plot to read Exp Sum X time Exp and Exp Produce the plots indicated in steps 2 and 3 above JI Ae GO N Re N O Getting Started with Maple 10 Page 45 Figure 41 Two dimensional plot with y logarithmic scale semilogarithmic plot in y Contour plots and density plots using context menus An expression of the form f x y can be plotted in a two dimensional format as a contour plot or as a density plot In a contour plot curves cor
13. it this is so because the valuea 0 produces no plot In order to see the animation we need to click on the plot and check out the new animation toolbar 1 24 3 4 5 6 Aid m gt pl current Frame o 9 T m g LU 11 DE lt BE es J amp r b K Figure 32 Maple 10 s animation toolbar Figure 32 shows the Maple 10 s animation toolbar split in two parts to fit in the page The items numbered in Figure 32 are described next Moves animation backward by one frame Stops animation Plays animation Moves animation forward by one frame Shows framed currently being shown in the graph area Slider that shows the progress of the animation Menu to select animation direction backward oscillating and forward default Menu to select animation type single realization or continuous repeated animation Shows the number of frames per second FPS 10 Slider to adjust the FPS value 11 Plot manipulator menu same as discussed in Figure 29 O OND UB WN The reader is invited to run the animation using the different buttons and menus shown Getting Started with Maple 10 Page 36 Three dimensional surface plotting with context menus A function of the form z f x y can be plotted as a surface in space Consider the expression x sin x y cos y Type this expression in a Maple worksheet click on the expression and do a right click to generate a context menu Select the item Plots gt 3 D Pl
14. space from which the surface plot is being observed Many of the options available through the toolbar are also available through the context menu for the graph Figure 35 shows some of the options available in particularly the lightning scheme Some of the options shown in Figure 35 are described next Style same as item 3 in Figure 34 Color changes the color s of the surface see Figure 36 for a list of options Lighting changes illumination patterns on surface see Figure 35 for a list Axes Same as item 4 in Figure 34 Scaling same as button 5 in Figure 34 Projection scale plot manipulator same as option 5 b in Figure 29 Transparency slider to select surface transparency 0 opaque to 1 transparent Manipulator same as item 6 in Figure 34 or item 5 in Figure 29 Export options for saving a Maple plot as a variety of graphics format files The reader is invited to manipulate the different options available for three dimensional surface plots in the context menu or in the toolbar Getting Started with Maple 10 Page 38 a Cr Copy Ctrl C Paste trl Style b Color ABs b User Lighting 7 Scaling Constrained Light Scheme 1 Projection Light Scheme 2 Transparency Light Scheme 3 Manipulator b Light Scheme 4 Export Figure 35 Context menu for a three dimensional surface plot Lighting sub menu highlighted Getting Started with Maple 10 Page 39 Cut Ctrl x Copy Chrl
15. ssign to a Mame 10 Complex Maps e Integer Functions ro Plats b 100 Units a Help on Command Operator Row Rational Fence Delimiter Square Root 2 D Math r F F F F F Figure 14 Context menu for an arithmetic operation For the case under consideration using 10 digits for example will produce the result al gt 1590412451 545 3 l 7 Lil 1 Notice that the use of the context menu produced an arrow indicating an operation was performed followed by the floating point result Thus context menu items do not document their operation very well in a Maple worksheet Added comments by the user can help interpret the results for any potential reader of their worksheets if context menus are used The use of text to document Maple 10 s worksheets is shown later Next we ll try using the Approximate context menu item but selecting the output of the square root operation rather than the input Getting Started with Maple 10 Page 18 Going back to your worksheet click on the output for the square root operation namely on the term l ee i Then use the context menu right click to calculate an approximation with 20 digits 34 _ gt 1590412451 5 2 4 73 15 Apply a Command Approximate 5 2 Assign to a Mame 10 Complex Maps b EET Integer Functions to Plots 100 Units d Figure 15 Using context menu to approximate a symbolic result using the output of a Maple ope
16. the Components palette in the Maple 10 s palette collection see Figure 11 The building of Maplets is an advanced application in Maple therefore it will not be covered in this document However information on Maplets is available in the Help facility For example try Help gt Manuals Dictionary and more gt Manuals gt User Manual to open the User Manual worksheet Click on item 9 Maplets to learn the basics of Maplets Typically you ll need some programming to activate a Maplet Maple programming has not yet covered another reason to postpone working with Maplets for the time being Worksheet mode By default e g when using Cntl n Maple worksheets follow a Document mode Thus so far we have used File gt New gt Document mode to generate new Maple worksheets In this exercise we ll open a new Maple worksheet in Worksheet mode by using File gt New gt Worksheet mode This will generate a new worksheet showing what is called a execution group prompt at the upper left corner of the worksheet Such a prompt is shown in the following figure gt Figure 44 Execution group prompt available in Worksheet mode Getting Started with Maple 10 Page 50 When you type in front of the execution group prompt the input shows up by default in Math input format For example at the prompt type int x 0 2 and press return This command calculates the definite integral of x within the limits 0 and 2 The result given in
17. the Remove Section button button 14 in Figure 10 Multiple lines in a single execution group To enter more than one command into a single execution group type Shift Return after each line For example type F5 xty 2 Shift Return x y 2 Shift Return Return to produce the following results gt x y 2 x y 2 6 Ziy x y 7 zy y t aty 6 Using palette commands in Maple Input format If we have selected the Maple Input format in an execution group inserting expressions from the Expression palette will produce the original Maple command corresponding to the desired expression Table 2 in the following page shows a listing of some of the calculus commands from the Expression palette and their equivalent Maple Input commands Table 3 on the other hand shows a similar listing for a number of algebraic operations The operation a is straightforward i e a b So it s the case with the trigonometric functions i e sin a cos a tan a Table 4 shows operations related to the definition of functions These operations are also available at the Expression palette Table 4 shows palette expressions from the Expression palette and their equivalent Maple Input commands for function evaluation and definitions The six items shown are the following Evaluation of univariate functions Evaluation of bivariate functions Definition of univariate functions using the standard mapping notatio
18. to specific instructions on using Maple s Help facilities Click the various links to learn more about searching the Help facilities etc The following are some of the links available in this worksheet Finding Information To learn about different ways of finding help topics click the following links Context Help Display a Known Help Topic Display Tool Tips Help Navigator Perform a Search Search Topic Index Review Help History Table of Contents Help Menus and Toolbars For descriptions of the menus menu items and toolbar buttons displayed when viewing Meee help pages click the following links Overview of Help Menu Overview of Help System Menu Bar Help Toolbar Status Bar Tasks This entry describes Maple tasks Typically these are worksheets that perform a specific set of operations and to which one can attach a Help facility entry Getting Started with Maple 10 Page 7 Applications and Examples This item opens a worksheet with links to examples of Maple applications Shortcut keys This item produces a list of most commonly used shortcut keys Here is the listing of the shortcuts for the Windows version of Maple 10 Shortcut Keys Function Ctrl Space Complete Command Home Cursor to Start of Line End Cursor to End of Line Ctrl Home Cursor to Top of Worksheet Ctrl End Cursor to Bottom of Worksheet Ctrl Down Arrow Move to Bottom of Execution Group Ctrl Up Arrow Move to Top of Execution Gro
19. 33 try to generate a two dimensional implicit plot using a context menu Select the option Plots gt 2 D Implicit plot gt x y Drag and drop plotting Once you have produced a plot e g the ellipse of Figure 37 you can drag an expression or equation from a Maple output and drop it on top of the plot Maple will automatically generate a new plot atop the existing one corresponding to the expression or equation dropped on the existing plot For example repeat the exercise leading to Figure 37 Then type the equation 2 ie as 4 9 and press Enter Getting Started with Maple 10 Page 41 The corresponding Maple worksheet with the output highlighted will look as follows 2 L 4 9 1 Next click on the highlighted output and drag it on top of the plot area for the ellipse of Figure 37 in your Maple worksheet As a result Maple will add the implicit plot for the equation you just dropped on the plot area Legends in graphics As an additional exercise click on the plot and do a right click to generate the corresponding context menu Then select the option Legend gt Edit Legend to generate a dialog box corresponding to the legends description of each of the plots shown in the plot area For Legend for Curve 1 type Ellipse in the Label field of the dialog box see Figure 39 below then press Done As a result legends will be shown at the bottom of the plot in your Maple worksheet with the legend for the
20. As an example of application of the Maple Input commands and characters of Tables 2 through 4 consider the following Maple command and its result gt int alphatbeta xit tau xi 0 alpha l 3 3 i Co te a By a 5 One disadvantage of using Maple Input format is that the mathematical expression thus typed is not shown in full mathematical format before it is calculated One possible solution if using this type of input is to enclose the expression in quotes and add a symbol referred to as the ditto operator to the command line e g gt tTint alphat beta 2 xi tau xi 0 alpha l zi 2 a B E cde 0 a B oP 2 va The ditto operator The ditto operator represented by the percentage symbol is a reference to the most recent result in Maple Two ditto operators represent the second to most recent result and so on As shown above the ditto operator is very useful when using Maple Input notation but has not much use in the Document mode of Maple 10 s worksheets The ditto and double ditto operators were used in an earlier example see equation 6 in page 53 Additional characters in Maple Input representation The Common Symbols palette includes some characters of interest for which we present its Maple Input representation in Table 6 Table 6 Additional characters and their references in Maple Input form Getting Started with Maple 10 Page 56 Examples using these
21. Axis Grid Mode Range Gridline Properties Figure 26 Context menu for a two dimensional plot Getting Started with Maple 10 Page 32 Axes Ranges k Detautt to Figure 27 Axes Ranges dialog box to adjust ranges in a two dimensional plot Getting Started with Maple 10 Page 33 Figure 28 Final version of the two dimensional plot after adjusting axes ranges Two dimensional plot manipulation Having generated a two dimensional plot through a context menu we will now show how to manipulate such plot using the corresponding toolbar in the main Maple 10 window First one needs to click on the plot This will produce a new row in the toolbar as shown next 1 16 2 435 6 5 ai 1 y 7 m mo om p Figure 29 Graphics toolbar for a two dimensional plot Getting Started with Maple 10 Page 34 In order to describe the different components of the graphics toolbar we assign numbers to the different fields and menus and letters to the items in the drop down menus The description of the numbered components is as follows 1 Coordinates of cursor on graph 2 Plot style a Line b Symbols points c Patch and grid applies mainly to three dimensional surfaces d Patch but no grid applies mainly to three dimensional surfaces 3 Axes style a Boxed b Framed c Normal axes d No axes 4 Constrained scale button 1 1 scale when active 5 Plot manipulator
22. Getting started with Maple 10 by Gilberto E Urroz July 2005 Maple 10 is the latest version of the mathematical symbolic software Maple Information about Maple can be found at http www maplesoft com Launching Maple 10 The location of the Maple 10 icon varies from computer to computer particularly if using the computer labs on campus For an individual Maple 10 server you will find the Maple 10 icon at Start gt All Programs gt Maple 10 gt Maple 10 This will launch the preferred Maple 10 interface as shown below 7 Maple 10 1 Server 1 Me Ce Yew eet Forms tat Widin Hep DSa JS DA O TE RE M 0 o RAS amp Teg faam E30 atts set Tenses mew koman wae B u g Eja E FOS ars 1 Shei eas Ja A Symi Recognition Lins a LEU FPR J ae b malri er prumer Componenti amp i Tp J Elari Did you know Sian with Template Arrows fie a FI The linalg package has been superseded by the Fenced Help Resources LinearAlgebra and VectorCalculus packages For more feat Wanie Toa information see LinearAlgebra and VectorCalculus i enticed aad tien ng Prem F b piile an sies MICE FROner rice cag E Lang Cpa a i Operators Open Face Frade geria ie Shaw this aog on stertup nar af we b fiy biano HA Tre 119s biin Roce Figure 1 Maple 10 interface when first launched The Quick Help window You will notice an informat
23. a new worksheet Cntl n and type the title Examples of ordinary differential equations and press enter To insert the table use Jnsert gt Table to produce the following dialog Insert Table Rows J cancel Figure 20 Dialog box for Insert gt Table Select the default values namely 3 rows 2 columns and press OK As a result you will get a blank table with 3 rows and 2 columns In the first row and first column cell type the following text Example 1 First order linear homogeneous In the first row second column enter the differential equation x xD 0 Click on the equation and generate a context menu right shift click and select the item Solve DE gt x t to obtain a symbolic solution for the equation In the second row first column type the text Example 2 Second order linear homogeneous In the second row second column enter the differential equation y y O yv0 0 Note the double prime in this equation y t is typed as two apostrophes and not as a double quote Click on the equation and use the context menu right shift click to solve this second equation Finally in the third row and first column type the text Example 3 Second order linear non homogeneous In the third row second column type the equation s x s x sin x which you will solve using the context menu When done the spreadsheet should look somewhat like Figure 21 Getting Started with Ma
24. as follows mo 3 r 1 2 m Figure 13 Example of algebraic operation in Math entry mode in Maple 10 Notice that as in the case of the arithmetic expression used earlier we have an input left hand side and output center and an automatic label right hand side Context menus Context menus are menus that are available to operate on Maple inputs and or outputs The items in the context menus are selected automatically by Maple and contain only operations that are relevant to the expression selected These menus are activated by clicking on the input or output expression sometimes the whole expression must be highlighted and then doing a right click with the computer mouse As an example go back to the input algebraic expression used earlier the one with the square root and click somewhere inside it Then do a right click with the mouse The context menu that you get will look like the following figure Among the operations available we could try for example the option Approximate This operation produces a floating point result for the symbolic operation under the square root Clicking on the Approximate item produces a sub menu with the options 5 10 20 50 100 These numbers indicate the number of digits in the approximate floating point result Getting Started with Maple 10 Page 17 see Paste Ctrl Evaluate Evaluate and Display Inline Ctril 4oply a Command Approximate 5
25. e left 33 Center characters 34 Align to the right 35 Bulleted list 36 Numbered list All of the button operations are available under the different menus e g buttons 9 and 10 undo redo are also available in the Edit menu So the tool bar facilitate performing a good number of operations by a single click tool bar to use Maple more efficiently Getting Started with Become familiar with all the buttons in the Maple 10 Page 14 Maple palettes Maple offers a number of palettes listed on the left hand side of the interface as shown in the figure below b Expression b Common Symbols b Components P Greek l b Arrows Fenced l Relational l Relational Round l b Negated Large Operators l b Operators l b Fraktur b Script b Miscellaneous Figure 11 Collection of Maple 10 s palettes Each palette is opened by clicking on the arrow attached to its name For example the Expression palette shows a collection of mathematical operations including integrals summations products derivatives partial derivatives limits powers sub indices square root n th root factorials absolute value exponential function natural logarithm base 10 logarithm base b logarithm trigonometric functions combinations binomial coefficient function references for one or two variables mapping definition of a function of one or two variables evaluation of a function
26. electrical engineering Let s look to one of them the Harmonic Oscillator worksheet as an example of the type of worksheets you want to develop for the solution of your own assignments To access the Harmonic Oscillator worksheet select the option Help gt Take a Tour of Maple This will open the tour worksheet On the right hand side of this worksheet there is a column labeled Sample Documents The Harmonic Oscillator worksheet can be opened by clicking on the first link in the Sample Documents column Open the worksheet and explore it using the scroll bar on the right hand side of the document Alternatively use Help gt Manuals Dictionary and more gt Applications and Examples This will open the Applications and Examples worksheet The Harmonic Oscillator worksheet can be accessed by clicking in the proper link under the section Applications The Harmonic Oscillator worksheet contains a title a figure which was produced in a sketching software and pasted into the worksheet two sections Initialization System Analysis and tables with text equations and graphics Use the options View gt Collapse All Sections to close down the sections in the worksheet Then use View gt Expand All Sections to open them up If you have collapsed all sections at once View gt Collapse All Sections you can open one at a time by clicking on the arrow attached to the section title You can also selectively close one section at a time by cl
27. esourcesAl Z22220 O l mathematical expressions In Worksheet mode Table of Contents toggling between Math and Text modes swatches e between 2 D and 1 D Math commands Ey default Reference en Maple uses Math mode Applications and Example Worksheets 9 Getting Started Use the FS key to switch between Math and Text New User Roadmap modes Math mode is characterized by a slanted italic Applications prompt whereas the Text mode is characterized by a it Configure Maple regular prompt f Document Mode and Worksheet Mode Example Worksheets Graphing Calculator In Document Mode rai ead Examples Examples Steps Maple Tour p P o E Math Dictionary x is a function of x z a F5 is a function of Menus FS x Style Guide A simple problem 1 3 FS A simple problem FS _ Tasks 1 3 CtrH Tip of the Day Command for Toolbars Macintosh i E Using Help Web Resources z z I Manuals T must he eotered in lath marde b gt O E E ote In Document mode any statement to evaluate Figure 3 Maple 10 Help window with Quick Help Detailed Information document highlighted Using the Math Dictionary The Math Dictionary is an alphabetical listing of quick references on mathematical concepts The Math Dictionary and other references are available by selecting Help gt Manuals Dictionary and more gt Dictionary in the main Maple 10 interface As an exercise find informati
28. he Greek alphabet which are commonly used in mathematical expressions The Greek alphabet is listed in the following table Table I The Greek Alphabet Lower Upper Letter English Lower Upper Letter English case case name equivalent case case name equivalent a A Alpha a V N Nu n B Beta b 4 E Xi X y I Gamma g O O Omicron O A Delta d 1 IT Pi p E E Epsilon e p P Rho r 4 Z Zeta Z o 2 Sigma S n H Eta h T T Tau t 0 O Theta th U Y Upsilon u l I lota i H D Phi ph K K Kappa k X X Chi ch A A Lambda I y Y Psi ps u M Mu m w Q Omega O The Expression Common Symbols and Greek palettes can be used to produce mathematical expressions for equation editing or as Maple entries such as ar 2 Caio amp w nt 1 pal 1 a aE 3 Getting Started with Maple 10 Page 28 Using sub indices To type sub indices in mathematical expressions in Maple simply use Shift _ before typing the sub index It is necessary to press the right arrow key to return to the main entry level in an expression Sub indices are used in both the numerator and denominator of the following expression T A sie art 4 ar w wm A sinimi m 4 dio 200 07 200 05 Symbol recognition The Symbol Recognition palette presents a sophisticated symbol recognition device that allows the user to sketch a mathematical symbol or a letter and provides the closest Maple characters that resemble the user s input The user then can select t
29. he intended character to use in Maple When you click on the Symbol Recognition you get the following form Y Symbol Recognition Ho results Figure 23 Maple 10 s Symbol Recognition form The numbers shown in Figure 23 do not appear in the Symbol Recognition form and were added to identify the following components 1 Sketch area this is where the user sketches the intended symbol 2 Erase button clears the sketch area 3 Apply button press this button to allow Maple to recognize the symbol sketched 4 Output area the area where Maple shows the possible symbols based on the sketch Getting Started with Maple 10 Page 29 If the symbol intended by the user is shown in the output area the user can just click on the symbol to copy it into the Maple entry area If the intended symbol is not included in the output area then the user can repeat the recognition attempt by pressing the erase button and sketching the symbol in the sketch area once more For example the approximate symbol can be sketched as follows Y Symbol Recognition Figure 24 An exercise in symbol recognition Notice however that Maple suggested the symbols qt O and as the first three choices in the symbol recognition operation To obtain the approximate symbol it was necessary to look under the More list as shown above Clicking in the symbol copies it to the Maple entry location Other examples of symbol recognition are shown in the foll
30. heet Maple 10 icon at Start gt All Programs gt Maple 10 gt Classic Worksheet Maple 10 Use it to open old fashioned Maple worksheets created with previous versions of the software You can find many of those worksheets in my web site http www engineering usu edu cee faculty gurro Find the Software and then the Maple links The following is a picture of a classic worksheet opened and operated upon in Classic Worksheet Maple 10 Getting Started with Maple 10 Page 57 F Maple 10 FluidsV mws Server 1 Sele File Edit View Insert Format window Help The velocity components are gt u evdle Re subs z x 1 y w miri y Z x p tAr y u gt vizevale Im subs z x I y wi 2x f p tAr p The denominator in the fractions included in u and y can be simplified by using gt factorfexpandis y 2 grx ety E E Available 565M Figure 45 Classic worksheet interface in Maple 10 The preferred Maple 10 interface shown in the previous 50 pages does not support many elements that were used in the classic worksheets Thus care must be exercised if opening an old fashioned worksheet in Maple 10 Ifin doubt use the Classic Worksheet Maple 10 application and try to copy and paste components from the old fashioned worksheets into new versions using the new Maple 10 interface Getting Started with Maple 10 Page 58
31. hose default ranges press Plot to produce the contour plot The resulting contour plot is shown in Figure 43 Click on the plot and open the corresponding context menu to see the options available The contour plot being a two dimensional plot will show a context menu like that of the 2 D plot of Figure 26 Exercise To produce a density plot click on the expression of interest and open the corresponding context menu right click then select Plots gt Plot Builder but this time select 2 D density plot in the Select Plot box Modify the scales for the two parameters if you so desire and press Plot to produce the density plot equivalent to the contour plot of Figure 43 Getting Started with Maple 10 Page 47 Figure 43 Contour plot for the expression x sin x y cos y produced using a context menu and the option Plots gt Plot Builder Animation of a surface using context menus Consider the expression sin ax cos a y Enter this expression in as a Math input in a Maple worksheet Click on the expression and generate the corresponding context menu right click Then select the options Plots gt Plot Builder In the resulting dialog box select Animation in the Select Plot Type box Keep all the default selections as shown in the dialog box except for the range of the animation parameter a which should be changed to the range 0 to 2 Then press Plot Click on the resulting plot to open the animation toolbar see
32. ic command package or feature Fromthe Help menu select Maple Help Check for other ready to use TESOUTCeS Example Maple Application Worksheets Center Embedded executable Maple Weh site worksheets that resource for free demonstrate syntax applications or invoke Maplet related to application interfaces mathematics making complex education problems easy to solve science and visualize engineering computer science From the Help and more menu select Manuals Dictionary Go to and more and http maplesoft com then Applications and Examples In the menu ofthe Figure 6 New User Roadmap for Maple 10 Getting Started with Maple 10 Page 6 main Web page click Resources and then Application Center Maple Resources This item in the Manuals Dictionary and more entry for Maple 10 s Help menu opens up a worksheet with additional links to Maple references and resources It even repeats some of the other items listed under Manuals Dictionary and more The items listed for this entry are Tour and New User Roadmap e Tutors Assistants and Task Templates and Maple Calculator e Online Help and Examples e Palettes and Context Menus e Manuals e Web Resources Click on the corresponding links in the Maple Resources worksheet to open the corresponding references Using the Help System This item in the Manuals Dictionary and more entry for Maple 10 s Help menu opens up a worksheet with additional links
33. icking on the vertically downward arrow next to the title of an open Getting Started with Maple 10 Page 49 section or sub section Try these options with this worksheet Before continuing make sure that the two sections are open i e use View gt Expand All Sections and scroll the worksheet to the top To activate the worksheet select Edit gt Execute gt Worksheet This will run all the executable commands in the worksheet You will see the worksheet scrolling down as the commands are executed Scroll the worksheet up and down and stop at one of the graphs Notice that the graphs have sliders attached to them which are associated with parameters used in the equations By clicking on the slider and moving the slider indicator you can change the values of the parameters and modify the plot Try some changes in the parameters by using the sliders Click the Harmonic Oscillator worksheet when done Maplets The ability of adding sliders and other components facilitate sensitivity analysis in a graphical format Such interactive displays are referred to as Maplets Note A self standing application with a GUI Graphics User Interface programmed in Java is referred to as an applet from app an abbreviation for application and let indicating something small or brief The word Maplet is a play on Maple and applets Maplets can be built by adding GUI components to an area of a Maple worksheet To see the available components click on
34. ional window hovering over the interface This window labeled Startup provides links for help on Maple and a random tip on using Maple Click this screen off to get to the main Maple interface In the upper right corner of the main Maple interface you will find a black background window with a list of help references for using Maple This Quick Help window is reproduced below The objective of the Quick Help window is to provide a quick reference to the most useful operations and concepts in Maple If you had clicked off the Quick Help window and would like to recover it simply press the F1 key in your keyboard Getting Started with Maple 10 Page 1 Quick Help Toggle Wath ext F5 Evaluate Enter Evaluate and Display Inline Ctrl Complete SymbolCommand Ctrl Space Navigate Placeholaers Tab Maple Help Ctri F 1 Quick Reference Ctrl F 2 Wath Editor Shortcuts Interactive Assistants Units and Tolerances Assignments Functions Equations Maple Tour Right click on expression to perform operations Press Fd to show this list EJ Shom on new Cocuments Figure 2 Maple s Quick Help window You can click on any of the lines in the Quick Help window to obtain a help window with detailed information on that particular operation For example for information on functions click the line in the Quick Help window This opens a Maple screen entitled Maple 10 Help worksheet help QuickHelpDetails which will show some i
35. mode In this mode the cursor at the top of the worksheet is an italic forward slash and the entry mode is Math The upper left corner of the Maple worksheet will look like this Times Mew Foran wy Figure 7 Cursor and entry mode Math for default new worksheet in Maple 10 Getting Started with Maple 10 Page 11 Math entry mode In this entry mode one can type a mathematical expression or a Maple command An example of a Maple command to try would be plot3d x y x y 2 x x 2 2 y 2 2 axes boxed Type it as shown above However be aware that in Math input Maple will change the asterisks into dots so that the entry line will actually look as wotsd x yi txtyl 2 stxte2 oy x 4 2 y 2 2 axes boxed Press Enter after typing this command to get a plot of the function used as first argument of function plot3d The arguments x 2 2 and y 2 2 represent the ranges of values of x and y respectively to be used in the production of the graph The last argument axes boxed indicates that the three dimensional space where the graphic will be produced will be contained within a coordinate box showing the x y and z axes in the edges The result is the following graph Figure 8 Graph produced with the plot3d command shown above Getting Started with Maple 10 Page 12 Math entry can be used to enter simple arithmetic expressions for example click below the graph
36. n Definition of bivariate functions using the standard mapping notation Definition of multi value or piecewise functions UJI A GO N e Getting Started with Maple 10 Page 53 Table 2 Palette expressions and Maple Input commands for calculus operations naaa gt sumi isk gt product f i k n 3 gt ditti x dx a F Table 3 Palette expressions and Maple Input commands for algebraic operations O a boas ooo e Se ee b Getting Started with Maple 10 Page 54 Table 4 Palette expressions and Maple Input commands for function definition and evaluation Oo Fewo eee x2 gt y A gt piecewise Mal x x gt 0 x Table 5 shows some examples of Greek characters from the Greek palette in Maple 10 an the equivalent reference in Maple Input form Table 5 Greek letters and their references in Maple Input form ee ooo e Se Notice that the letter I upper case gamma is referred to as GAMMA in Maple Input format The name GAMMA actually refers to the gamma function from mathematics see the mathematical dictionary Help gt Manuals Dictionary and more gt Dictionary Upper case Greek letters have names that start with upper case letters in Maple Input format Lower case Greek letters names start with lower case letters in Maple Input format See Table 1 for the list of names of the letters in the Greek alphabet Getting Started with Maple 10 Page 55
37. nce Ctrl F2 gt ow Quick Help Fi what s Mew Startup Dialog Manuals Dictionary and more Maple on the web b About Maple Figure 5 Items in Maple 10 s Help menu Getting Started with Maple 10 Page 4 You are welcome to explore all the entries shown The use of these entries is discussed briefly next Maple Help Cntl F1 Opens Maple s Help window e Take a Tour of Maple Detailed tour of Maple a good start for new users e Quick Reference Cntl F2 Worksheet summarizing basic Maple operation e Quick Help F1 Quick Help window discussed above e Help on Context Help for specific context in a Maple 10 document What s New Highlights new features in Maple 10 version Startup Dialog Launches Startup window discussed above Manuals Dictionary and more Maple and math documents see below Maple on the Web Links to maplesoft s web sites e About Maple Version and other basic information Manuals Dictionary and more The item Manuals Dictionary and more shows the following items a Maple Help Ctrl F Take a Tour of Maple Quick Reference Ctr F2 Quick Help Fi what s Mew Startup Dialog Manuals Dictionary and more New User Roadmap Maple on the vWeb b Maple Resources About Maple Using the Help System Tasks 4oplications and Examples Shortcut keys List of Packages List of Commands Manuals Getting Started Guide Dictionary User Manual On the web
38. nd minima with constraints 7 Statistics Probability and statistical applications 8 Programming and Code Generation Program in Maple translate to C Java etc 9 Dictionary of Math and Engineering discussed earlier 10 Units and Tolerances Using units and quantities with tolerances 11 Education Assessment Maple T A Use Maple for student assessment 12 0penMaple Easy connection to other programs 13 Maplets and MapleNet GUIs for Maple and online deployment For basic mathematics and engineering applications I suggest you cover at least items 1 through 4 in this list Item 5 is applicable to advanced problems in differential equations Item 6 is useful for optimization applications Item 7 is needed for a course on probability and statistics Item 8 will be necessary for writing Maple procedures Item 9 is an excellent reference for most mathematics and engineering applications Item 10 can be applied to laboratory physical measurements for error analysis Items 11 is most useful to instructors to develop online type of assessment activities Item 12 is for advanced applications linking Maple to C FORTRAN or Java programs Maplets in Item 13 are graphic user interfaces GUI for Maple applications while MapleNet is a service provided by maplesoft to post Maple applications online Creating a new worksheet To create a new worksheet use File gt New gt Document mode or simply press Cntl n This will create an empty worksheet in document
39. nformation on how to define functions in Maple This is illustrated in Figure 3 below By scrolling the right hand side window notice that this worksheet contains detailed information on all the topics included in the Quick Help window Maple 10 Help directory tree Also notice that the detailed help worksheet contains a directory tree in the left hand side with folders and documents These are Maple help documents and you can access them from this directory tree by double clicking on a document or folder Notice that the directory tree shows a document entitled Quick Help Detailed Information highlighted This is the help document that you are currently reading You can navigate the directory tree on the left hand side of this window to open other relevant help documents For example if you were interested in learning about the Math Dictionary you would double click on that document in the directory tree Thus we have shown here how to access the Maple Help display through the use of the Quick Help window Remember to recover the Quick Help window simply press F1 Alternatively you can select Help gt Quick Help in the Maple 10 menu bar Getting Started with Maple 10 Page 2 3 Maple 10 Help worksheet help QuickHelpDetails Seles File Edit view History Help s B amp B es F es Search For Topic Text In Document mode toggling between Text and Math modes switches between entering text and entering 2 L 2 x R
40. obtained earlier and type sq Cntl Space click on sqrt the square root symbol 2 3 5 2 3 right arrow key twice gt gt The resulting Maple input is the quantity with the square root in the left hand side of the screen while the output is the quantity shown in blue in the middle of the screen To the right hand side of the screen Maple generates an automatic label 1 to identify the output The section of the Maple screen showing the input output and label is shown next label Figure 9 Example of an arithmetic expression in Math entry form showing input output and label Before continuing with more exercises in the Maple worksheet we ll describe the buttons palette located at the top of the Maple interface Maple tool bar The following figure shows the top of the Maple interface including the menu bar and the tool bar While in your computer the menu bar and tool bar occupy the top of the interface they re shown split in two parts in Figure 10 in order to fit the page width Also the 36 buttons in the tool bar have been labeled with numbers 1 36 to identify their function in the description below Buttons 1 through 8 correspond to typical operations that apply to almost any software i e 1 new file 2 open a file 3 save file 4 print 5 print preview 6 cut selection 7 copy selection to clipboard and 8 paste clipboard contents As with many software applications hovering the cursor over each button
41. on about the Laplace Transform by opening the dictionary and finding the listings under the letter L You should get the information shown in the following figure As additional exercises on the use of the Math Dictionary find the following entries circle of curvature heat equation Napierian logarithm radian Ramanujan factor theorem Babbage s engine Bernoulli equation beta function Cartesian product complex number Laplace equation normal distribution quadratic equation tesselation translation gamma function and Klein bottle Getting Started with Maple 10 Page 3 23 Maple 10 Help Definition Laplacetransform File Edit View History Help Ss amp F H F E Search For Topic Text Laplace transform 5 n the integral transform ResourcesDefintions lt an Table of Contents i gW 7 a 0 Lagrange expansion theorem l l l Lagrange form of the remainder which may be viewed asa form of the Founer Lagrange interpolation formula transform andis used in the solution of diferential Lagrange method of multipliers equations mee also kernel Lagrange multipliers m E iai F HT Figure 4 Maple 10 s Math Dictionary s entry on the Laplace Transform Using Maple 10 s Help The Help item in the Maple 10 s menu bar allows access to many other Help documents for Maple 10 The items available are shown in the figure below Co Maple Help Ctrl F 1 Take a Tour of Maple Quick Refere
42. ots gt x y to see the following plot of a surface in three dimensions Figure 33 Three dimensional surface representing the function x sin x y cos y When one clicks on the graph itself a new graphics toolbar is produced in the Maple interface as shown in the figure below This toolbar include the following items 1 Angle 9 on x y plane measured from the positive x axis to plane of point of view 2 Angle measured from z axis on the line connecting the origin to the point of view 3 Surface style a patch no grid b patch and grid c patch and contours d contour lines only e grid with hidden surfaces f grid with no hidden surfaces g points Axes style a boxed b framed c normal axes d no axes Axes scaling 1 1 scaling if active 6 Plot manipulator same as in two dimensional plots see Figure 29 Ji Ae Getting Started with Maple 10 Page 37 3 4 5 6 1 Sls H 4 G l q a W a bv i b ta e d te v d e f Y g BE Figure 34 Three dimensional graph toolbar By default the plot manipulator is set to rotate as shown above To rotate the plot simply click on it press the left mouse button and drag in any direction You will see the plot rotating in space You will also notice that the values of the angles 9 and change as the graph rotates since for all practical purposes we re changing the location of the point of view i e that point in
43. owing page In these examples I was trying to obtain the symbols a alpha y gamma and the del or nabla operator symbol Maple was successful in recognizing the intended character in each instance Getting Started with Maple 10 Page 30 Symbol Recognition Symbol Recognition Y Symbol Recognition V Y x ua Figure 25 Additional examples of Maple s character recognition feature Two dimensional plotting with context menus An expression in either input or output in Maple containing a single independent variable can be used to produce a plot in two dimensions through the use of context menus For example to plot the function x 2 5 e cos t 2 5 in the interval 0 lt t lt 20 we need only type the expression 2 5 e cos t 2 5 and select the Plots gt 2 D Plot item in the corresponding context menu By default the range is 10 10 By right clicking on the plot itself you can generate a context menu for the plot where the f range can be changed The item to use in the context menu is Axes gt Range as shown in Figure 26 This selection produces the dialog box shown in Figure 27 To adjust the x range we select 0 to 20 The vertical range can be adjusted by selecting the range 2 5 to 2 5 The final version of the graph is shown in Figure 28 Getting Started with Maple 10 Page 31 Ctrl e Ctrl C Ctrl Boxed Scaling Constrained Framed Manipulator w Morrnal Export Mone Default
44. ple 10 Page 25 Examples of ordinary differential equations Example 1 First order linear KO txt 0 3 xfep Ciel homogeneous 7 Example 2 Second order linear yD y i yi 0 l e Chek 2 inf 2 3 homogeneous seed TERE Example 3 Second order linear non e x te x Sanix homogeneous e xj sn x C2 Coe cos x xl Figure 21 Example of a table in a Maple worksheet Using Common Symbols and Greek letters Two of the most useful Maple palettes besides the Expression palette are the Common Symbols and Greek palettes The contents of these two palettes are shown below YF Common Symbols cel J Zk ih A Figure 22 The Common Symbols and Greek Maple 10 palettes Getting Started with Maple 10 Page 26 The Common Symbols palette includes such commonly used symbols such as T The ratio of the length of a circle to its diameter e The basis for the natural logarithms i j I Unit imaginary numbers i j 1 Infinity It also includes the common mathematical symbols Summation Product Integral Union of sets Intersection of sets 2D ea 5 You will also find in this palette comparison symbols e g gt lt etc symbols used in set theory e g G symbols for mathematical logic 4 Y A v gt symbols for number sets C R N Q Z real and imaginary functions for complex numbers SR 3 arithmetic operations x plus minus signs
45. ple input and output and graphs All you need to do is highlight the object you want to delete before using Cntl Delete Try some execution group deleting in your worksheet Inserting a text prompt in an execution group Text could be used to document the operation s in an execution group Use Cntl Shift to insert a text prompt before the current cursor location or Cntl Shift k to insert a text prompt after the current cursor location Alternatively you just can use the options nsert gt Paragraph gt Before Cursor or Insert gt Paragraph gt After Cursor Another possibility is to click the nsert Text button item 11 in Figure 10 available in the toolbar This latter option will actually insert a new text block separate from any execution group Try the different commands listed in this paragraph to insert text in your execution groups or to insert a separate text block Getting Started with Maple 10 Page 52 Inserting and removing sections Use Insert gt Section to insert a section or nsert gt Subsection immediately below the current cursor location If you want to insert a section or sub section encompassing a number of execution groups first highlight the collection of execution groups you want to collect into a section and then press the nsert Section button button 13 in Figure 10 in the toolbar This will indent the selected execution groups into a section or sub section To remove them from a section or subsection use
46. r worksheet below the last operation listed there and type the expression Note Use F5 to toggle to Math input if a text cursor shows up x7 3x7 25 Typex 2 gt 3 x 25 Then before pressing Enter do a right click to obtain the corresponding context menu From this context menu we ll try the following applications Evaluate at a point This option generates the following dialog box Fia Evaluate at a Point Evaluate the expression at the point Figure 17 Dialog box for context menu Evaluate at a Point operation Getting Started with Maple 10 Page 20 Replace the value of x with 2 5 and press OK to get xo 3xt 25 3 38 75 Differentiate Next highlight the original expression namely x 3x 25 and do a copy Cntl C Click on a location below the current one and do a paste Cntl V to make an extra copy of the original expression Then using a context menu right click select the option differentiate gt x to produce xo43x425 3 2x43 Control drag Highlight the original expression namely x 3x 25 cut it and paste it below the last result in your worksheet This time do press Enter to produce a Maple output Next highlight the output and pressing Cntl drag the cursor to a new location below to its original location in the worksheet After a couple of seconds a copy of the output will appear as Maple input at the location where you released the mouse button Integ
47. rate Next using a context menu right click select the option integrate gt x to produce et3axt 253 e oa 251 Exercise 1 Using procedures similar to those detailed above for the context menu operations Evaluate at a point differentiate and integrate and for the same polynomial shown above try the following context menu operations Complete square Solve solve the equation formed by the expression 0 Coefficients gt x Constructions gt Definite Integral gt x Lower Limit 0 Upper Limit 1 Constructions gt Derivative gt x Constructions gt Evaluate at gt x at 1 Constructions gt Limit gt x at 0 Constructions gt Product gt x Lower Limit 1 Upper Limit 10 Constructions gt Sum gt x Lower Limit 1 Upper Limit 10 10 Conversions gt Horner Form gt x 11 Conversions gt To String 12 Integral Transforms gt Fourier Transforms O OND UB WN Getting Started with Maple 10 Page 21 Exercise 2 Enter the following rational fraction as Maple input xi x x4 10 x74 Using context menus try the following operations in Maple 10 Evaluate at a point Factor Normal Solve solve the equation formed by the expression 0 Numerator Denominator Constructions gt Definite Integral gt x Lower Limit 0 Upper Limit 1 Constructions gt Derivative gt x Constructions gt Evaluate at gt x at 1 10 Constructions gt Limit g
48. ration The results is shown next A 1 gt 1 590412451 544 3 gt 1 5904124511259 1464572 Notice that the arrow indicating the operation is shown now below the output Obviously for documentation purposes we need to add some text to the worksheet Adding text to a worksheet To add text to a worksheet click in the location where you want to add the text then press F5 to toggle the input format from Math to Text Type the desired text in that location Select another location to insert more text then repeat the steps indicated Getting Started with Maple 10 Page 19 above For example by inserting text around the previous calculation we can re write this piece of the worksheet as follows Note The text input cursor is a vertical line When a text input is requested the left part of the toolbar will show the Text box highlighted Also we used backspace to remove the arrows from the worksheet The square root 2 5 is approximated by 1 590412451 using 10 digits 5 2 The output of the square root shown as expression 1 below is l f fSl w and this value is approximated as 1590412445 112891465 72 using 20 digits Figure 16 Arithmetic calculation edited by inserting text in a Maple worksheet frame added for emphasis it cannot be produced in Maple Context menus for algebraic expressions Try some context menu operations with algebraic expressions Example 1 Click in a location of you
49. responding to constant values of f i e x Vv c are shown in the x y plane In a density plot instead of showing curves of constant values of f x y different colors or grayscale are shown to indicate the variation in the function f x y Contour plots and density plots as well as a number of other plots can be obtained by using the option Plots gt Plot Builder in a context menu associated with the expression f x y As an example consider the expression x sin x ycos y Type this expression in a Math input format select the expression by clicking on it and do a right click to produce the corresponding context menu Then select the option Plots gt Plot Builder As a result you will get the dialog box shown below Getting Started with Maple 10 Page 46 fia Interactive Plot Builder Select Plot Type Select Plot Type Select Flot 3 D plot 2 D contour plot 2 D density plot 3 D contour plot 2 D gradient vector field plot 2 D implicit plot Select Variable Purpose and Ranges Cancel Figure 42 Dialog box for the Plots gt Plot Builder option on the context menu for an expression of the form x y This dialog box allows us to select from a variety of plots as shown in Figure 42 I have selected the option 2 D contour plot in the Select Plot box This selection shows two parameters at play x and y The dialog box also indicates the default ranges of those parameters 5 to 5 for both of them Keeping t
50. rl R Ctrl L Ctrl Enter Ctrl J Ctrl K Shift Ctrl J Shift Ctrl K Ctrl B Ctrl I Ctrl U Ctrl Ctrl F7 Ctrl Space Fl F2 Ctrl F1 Ctrl F2 Split Sections Join Sections Evaluate Expression Evaluate and Display Zoom Factor 50 Zoom Factor 75 Zoom Factor 100 Zoom Factor 150 Zoom Factor 200 Zoom Factor 300 Zoom Factor 400 Show Region Ranges Show Section Ranges Text Input Mode Maple Input Mode 2 D Math Mode Label Mode Insert Page Break Insert Execution Group After Cursor Insert Execution Group Before Cursor Insert Paragraph After Insert Paragraph Before Bold Style Attribute text or Maple input Italic Style Attribute text or Maple input Underline text or Maple input Enclose Section in Subsection Indent Remove Section Enclosing Selection Outdent Spellcheck Complete Command Quick Help Pop up Menu Context sensitive Help Help Table of Contents Maple Quick Reference Card Getting Started with Maple 10 Page 9 Ctrl Shift 1 Sketch Pencil Ctrl Shift 2 Sketch Highlighter Ctrl Shift 3 Sketch Eraser Ctrl Shift 4 Sketch Selection List of Packages This item opens a worksheet with a listing of all Maple 10 function packages A packages is a collection of related functions which can be loaded at once with the command with List of Commands This item opens a worksheet with a listing of all Maple 10 top level commands
51. sheet Then to enter a title click at the top of the worksheet Use F5 to ensure you re in text mode and select P Title from the input output descriptor located in the toolbar Type the title For this example the top of the worksheet may look as follows hhi ann Lik Text Math P Title vj i B Z U ms bol Recogniti yeaah i es ns Polynomials and Fractions Figure 18 Typing a title in a worksheet To insert sections use Insert gt Section or use the insert section button i e button number 13 in Figure 10 The cursor will remain at the location of the section s title Type Polynomials Then press return press F5 to toggle between Math and Text format and type a few lines in your worksheet describing the section and introducing a polynomial x 2x 5x 3 that will be used in the operations illustrated in the section Then we ll insert a couple of sub sections Evaluate at a point and Integrate by using the insert section button Copy the polynomial into them and evaluate the polynomial at x 2 and integrate with respect to x Document the operations Go back to the upper level of sections in the worksheet and insert a section to be called Fractions below the Polynomials section Insert a few lines introducing the section and define the fraction x x x 10 x74 to be used in the sub sections defined next Within this section insert sub sections entitled Normal fractions and Numera
52. symbolic format is 8 3 This result is shown within the execution group where the command was entered Also after executing this command Maple automatically generated a new execution group immediately below and moved the cursor at the prompt of that new execution group We could use the Expression palette to enter the same integration in formal mathematical mode by clicking on the definite integral button in the palette We need to keep the cursor in front of the new execution group prompt The resulting operations are shown below gt intix x 0 2 gt a 0 led ca L led 00 2 Maple Input format A new execution group prompt will now be available Keeping the cursor in front of the prompt of this new execution group we are going to change the input mode by pressing F5 In Document mode i e in all the examples in the previous sections of this document pressing F5 changed the input mode from Math to text In Worksheet mode however pressing F5 changes the input mode from Math to Text Maple Input This is the preferred input mode in earlier versions of Maple e g before version 8 and it s still available in Maple 10 for those of us like me who learned Maple way before version 10 became available int x x 0 2 i 5 2 As an exercise we ll enter now int x 2 x 0 2 and press Enter The resulting execution group is shown below Note in Maple Input mode you need to end Maple commands with
53. t x at 0 11 Constructions gt Product gt x Lower Limit 1 Upper Limit 10 12 Constructions gt Sum gt x Lower Limit 1 Upper Limit 10 13 Conversions gt Partial fractions gt x 14 Conversions gt To String 15 Integral Transforms gt Fourier Transforms CONDAUBRWNE Exercise 3 Enter the following trigonometric polynomial as Maple input Six cosl x sin x Using context menus try the following operations in Maple 10 Evaluate at a point Factor Solve numerically solve the equation formed by the expression 0 Constructions gt Definite Integral gt x Lower Limit 0 Upper Limit 1 Constructions gt Derivative gt x Constructions gt Evaluate at gt x at 1 Constructions gt Limit gt x at 0 Constructions gt Product gt x Lower Limit 1 Upper Limit 10 Constructions gt Sum gt x Lower Limit 1 Upper Limit 10 O OND UB WN Getting Started with Maple 10 Page 22 Title sections and sub sections When preparing a well documented worksheet we may want to give the worksheet a title and introduce sections and sub sections into the worksheet These items would allows us to organize subjects in a reasonable fashion For example if we re writing a worksheet about polynomials and fractions we could type a title Polynomials and Fractions and then insert a section called Polynomials and one called Fractions To do this exercise create a new work
54. tor amp Denominator Perform such calculations using context menus and document the sessions with text You can insert as much documentation into your worksheet s sections and subsections as you wish in this exercise One possible outcome of this exercise is shown in the following page Getting Started with Maple 10 Page 23 Polynomials and Fractions Polynomials This is a simple polynornual xit2x S5x 3 upon which we perform the following operations Evaluate at a point We use a contex menu to evaluate this polynomual at x 2 xit2x S5x43 39 Integrate We use context menu again to calculate the mndetinte integral of the polynormal boy hp bp oe ey ae ea 1 4 Z Fractions ca Use the traction in the tollowing sub sections x Normal fraction Using the Morea operation trom the context menu Sea r10 x 3x45 x 4 E Numerator Using functions Meameraior inthe context menu 30 2 a woe ITU BH Px 10 x 4 4 Figure 19 Example of a worksheet with a title sections and sub sections Note Click on the arrow defining each section of sub section to open or close that section or sub section Use View gt Expand All Sections or View gt Collapse All Sections to manipulate all sections and sub sections at once Getting Started with Maple 10 Page 24 Using Tables A table can be inserted in a Maple worksheet to organize data or to organize examples in the worksheet Let s try an exercise using tables Open
55. up Shift Enter Soft New Line Alt Shift F6 Cycle through Open Maple Windows For a list of math editing shortcut keys see 2 D Math Shortcut Keys and Hints The following is a list of menu accelerators Shortcut Keys Function l Alt F Open File Menu Alt E Open Edit Menu Alt V Open View Menu Alt Open Insert Menu Alt R Open Format Menu Alt T Open Tools Menu Alt W Open Window Menu Alt H Open Help Menu Alt F D Send Email with attached worksheet Alt F M Recent Documents Menu Ctrl N New Document Worksheet based on Options setting Ctrl O Open Worksheet Ctrl F4 Close Current Worksheet Ctrl S Save Worksheet Ctrl P Print Worksheet Ctrl Shift P Page Setup Alt F4 Exit Maple Ctrl Z Undo Ctrl Y Redo Ctrl X Cut Selection to Clipboard Ctrl C Copy Selection to Clipboard Ctrl V Paste Selection from Clipboard Getting Started with Maple 10 Page 8 Ctrl Delete Ctrl A Ctrl F F5 F3 F4 Delete a line Select All Find Replace Switch between Text and Math mode Split Execution Groups Join Execution Group To split join with the previous execution group place the cursor at the start of the Maple input To split join with the lower execution group place the cursor at the end of the Maple in put Shift F3 Shift F4 Enter Ctrl Ctrl 0 Ctrl 1 Ctrl 2 Ctrl 3 Ctrl 4 Ctrl 5 Ctrl 6 F9 Shift F9 Ctrl T Ctrl M Ct
56. will provide an information balloon with the button operation Getting Started with Maple 10 Page 13 File Edit View Insert Format se E eb 5 7 6 g Teas Ss x i gt Window Help ie la ty ies 1S ag 2a a I OFO 2a 2a 29 30 31 32 33 34 E IU amp z Tools menu bar ay ol p HA 10 C 11 12 EI Pan toolhar menu har ec ye oe 25 26 af F 35 36 toolbar Figure 10 Menu bar and tool bar in a Maple 10 interface The operation of the remaining buttons in the fool bar is listed next by using the identifying numbers shown in Figure 10 9 Undo last operation 10 Redo last undone operation 11 Insert text 12 Insert Maple input 13 Enclose selection into a section or subsection see the Insert menu 14 Remove section or subsection enclosing selection 15 Move back to previous worksheet 16 Move forward to next worksheet 17 Execute entire worksheet 18 Execute selection 19 Stop execution of current operation 20 Debug current operation useful in programming 21 Restart Maple server clears Maple memory 22 Zoom to 100 23 Zoom to 150 24 Zoom to 200 25 Toggle entry of tab characters with tab 26 Open help system 27 Bold characters 28 Italics characters 29 Underlined characters 30 Change font color in characters 31 Change background color in selection 32 Align to th
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