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1. 2 Choose Matrix from the Insert menu or click Insert Matrix E3 on the Matrix toolbar to open the Insert Rows 8 Matrix dialog box Calne 3 Enter the number of elements for Rows and Columns For example to create a three element vector enter 3 and 1 4 An array with blank placeholders appears in your worksheet Next fill in the array elements You can enter any math expression into the placeholders of an array Simply click in a placeholder and type a number or expression Use the Tab key to move from placeholder to placeholder 33 34 Chapter 5 Range Variables and Arrays Note Arrays created using the Matrix command on the Insert menu are limited to 600 elements Use subscripted expressions data import functions or Data Tables to create larger arrays The effective array size limit depends on the memory available on your computer but is usually at least 1 million elements For more information see online Help Changing the Size of a Vector or Matrix You can change the size of a matrix by inserting and deleting rows and columns editing lines Mathcad begins inserting or deleting with this 1 Click on one of the matrix elements to place it between the element Bee 2 Choose Matrix from the Insert menu Type the number of rows and or columns you want to insert or delete Then press either Insert or Delete For example to delete the column that holds the selected element
2. 2 Ifthe region you want to create is a math region just start typing anywhere you put the crosshair By default Mathcad understands what you type as mathematics See A Simple Calculation below for an example 3 To create a text region choose Text Region from the Insert menu or simply press and then start typing See Chapter 6 Working with Text for a complete description Tip To add a border around a region or regions select the region s then right click and choose Properties from the menu Click on the Display tab and check the box next to Show Border A Simple Calculation Although Mathcad can perform sophisticated mathematics you can easily use it as a simple calculator To try your first calculation follow these steps Click in the worksheet You see a small crosshair 2 Type15 8 104 5 When you type the equal sign or click lon the Calculator toolbar Mathcad computes the result Figure 2 2 This calculation demonstrates the way Mathcad works e Mathcad sizes fraction bars brackets and other symbols to display equations the same way you might see them in a book e Mathcad understands which operation to perform first Mathcad knew to perform the division before the subtraction and displayed the equation accordingly e As soon as you type the equal sign Mathcad returns the result Mathcad processes each equation as you enter it 8 Chapter 2 Getting Started with
3. When you are in Web browsing mode and right click on the Resources window Mathcad displays a menu with commands appropriate for viewing Web pages Many of the buttons on the Resources toolbar remain active when you are in Web browsing mode so that you can copy save or print material you locate on the Web or backtrack to pages you previously viewed When you click fn you return to the Home page for the Resources window or E book Mathcad provides several ways to get support on product features through an extensive online Help system To see Mathcad s online Help at any time choose Mathcad Help from the Help menu click on the Standard toolbar or press F1 To run Help you must have Internet Explorer 6 or higher installed However IE does not need to be set as your default browser To know what Mathcad menu commands do hover over the command and read the status bar at the bottom of your window For toolbar buttons hold the pointer over the button momentarily to see a tool tip You can also get more detailed help on menu commands toolbars built in functions and operators and error messages To do so Mathcad Community on PlanetPTC 17 1 Click an error message a built in function or variable or an operator 2 Press F1 to bring up the relevant Help screen To get help on menu commands dialogs or on any of the toolbar buttons l Press Shift F1 Mathcad changes the pointer into a que
4. You can also set tabs and guidelines by selecting Tabs from the Format menu Type the location then check the Show Guidelines check box You must be viewing the Ruler for guidelines to show up 60 Chapter 7 Mathcad Worksheets Note The tab stops you insert on the ruler specify where the cursor moves when you press the TAB Tip key To remove a tab stop click on its symbol and drag it off the ruler To move a guideline click on the tab stop on the ruler and drag it To remove an alignment guideline right click on it and uncheck Show Guideline To automatically place the next region you create on a guideline press the TAB key in a blank part of the worksheet The red crosshair moves to the next tab or guideline You can change the measurement system used in the ruler by right clicking on the ruler and choosing Inches Centimeters Points or Picas from the menu To change the ruler measurement for all documents make this change to the template Normal xmct Inserting or Deleting Blank Space Tip You can easily insert extra space into your worksheet 1 Click in a blank spot and press Enter repeatedly To delete extra space from your worksheet 1 Click in the space you want to delete Make sure the cursor looks like a red crosshair and that there are no regions to the right or left of the cursor 2 Press Delete to remove blank space below your cursor or Backspace to remove blank space above your cursor
5. 127 128 Chapter 12 3D Plots 2 Select a type of three dimensional graph Make your selections for the appearance and coloring of the plot on subsequent pages of the Wizard Click Finish and a graph region with a blank placeholder appears 4 Enter appropriate arguments a function name data vectors and so on for the 3D plot into the placeholder 5 Click outside the plot or press Enter Creating 3D Plots of Functions Tip You can create various 3D plots from functions using commands from the Insert menu and changing settings through the 3D Plot Format dialog box or you can use the 3D Plot Wizard To learn about creating two and three dimensional images visit PlanetPTC at http communities ptc com community mathcad then search for the Creating Amazing Images with Mathcad 14 E book by Professor Byrge Birkeland Creating a Surface Bar Contour or Scatter Plot Note You can visualize any function of two variables as a surface bar contour or scatter plot in three dimensions Step 1 Define a function or set of functions First define the function in your worksheet in one of the following forms T KELU YY W Fix Wi sings cosi y GEU Y 2 u cosiv YU Y Y COSU 2 COSY ZU Y SNU In the plot of each function above the x and y coordinates and variables will range by default from 5 to 5 with a step size of 0 5 F x y is a function of two variables Each z coordina
6. Inserting Graphics and Other Objects for more on viewing a matrix or three matrices in the case of a color image in the picture operator Chapter 6 Working with Text Inserting Text Text and Paragraph Properties Text Styles Equations in Text gt gt gt gt Text Tools Inserting Text This section describes how to add text to your worksheets Mathcad ignores text when it performs calculations but you can insert working math equations into text regions as described in Equations in Text on page 51 Creating a Text Region To create a text region follow these steps First click wherever you want the text region to begin Then 1 Choose Text Region from the Insert menu or press the double quote key You can also just start typing and once you type a space Mathcad begins a text region The BE crosshair changes into a text cursor and a text box appears 2 Now begin typing Mathcad displays the text and surrounds it with a text box As you type the text cursor moves and Fluid fow example the text box grows 3 When you finish typing click outside the text region The Fluid flaw example text box disappears J Note You cannot leave a text region simply by pressing Enter You must click outside the region press Ctr1 Shift Enter or repeatedly press one of the arrow keys until the cursor leaves the region To insert text into an existing text region e Click anywhere in a text region
7. Tip 1 Click inthe graph and choose Graph gt Trace from the Format menu or click Lae on the ae Graph toolbar to open the X Y Trace dialog box Make sure Track data points is checked eva 2 Click and drag the mouse along the trace ieee rae ate whose coordinates you want to see A dashed crosshair jumps from one point to the next as you move the pointer along the trace Y Value 3 Ifyou release the mouse button you can use the left and right arrows to move to the previous and next data points Use the up and down arrows to select other traces 4 As the pointer reaches each point on the trace Mathcad displays the values of that point in the X Value and Y Value boxes or the Radius and Angle boxes in the Polar Trace dialog box 5 The values of the last point selected are shown in the boxes The crosshair remains until you click Close in the dialog box When Track data points is unchecked in the Trace dialog box you can see a readout of coordinates for any location in a plot not just the data points that created an individual trace Figure 11 11 shows an example of a plot whose coordinates are being read tl fix sin x O0 001 1 x4 X Trace Value O 448 Ka YValue 0 35355 Copy Y Track data points Figure 11 11 Reading coordinates from a graph To copy and paste a coordinate 1 Click Copy X or Copy
8. Uoc y recursive definition 4 1 s 1 expand s tyl Figure 13 5 Defining a variable in terms of itself makes the symbolic processor ignore previous definitions of that variable Using the Symbolics Menu The Symbolics menu commands are useful when a symbolic calculation does not need to be tied to the rest of your worksheet These commands are not live you apply them to selected expressions they do not know about previous definitions and do not automatically update The Symbolics menu commands perform the same manipulations as many of the keywords listed in online Help For example the Symbolics menu command Polynomial Coefficients evaluates an expression just as the keyword coeffs does The basic steps for using the Symbolics menu are the same as for all the menu commands 1 Enter the expression you want to evaluate 2 Surround the expression with the editing lines 3 Choose one of the commands from the Symbolics menu such as Evaluate gt Symbolically The location of the result 5 ce depends on the Evaluation Style you ve selected see Displaying Symbolic Results below Some commands on the Symbolics menu such as Variable gt Solve require that you click on or select a variable rather than the entire expression Displaying Symbolic Results You can choose Evaluation Style from the Symbolics menu to return symbolic results either below to the right or in place of the original expression a
9. You can not delete any excess space if any region extends into the space you are trying to delete To quickly insert or delete a specific number of blank text lines from your worksheet right click in a blank part of the worksheet choose Insert Lines or Delete Lines from the menu and enter the number of lines in the dialog box The dialog box default shows you the maximum number of lines you can delete Separating Regions As you move and edit regions in a Mathcad worksheet they sometimes overlap one another Overlapping regions don t interfere with each other s calculations but they may make your worksheet hard to read 0 PaO A good way to determine whether regions overlap is to choose Regions from the View menu Mathcad displays blank space in gray and leaves the regions in your default background color To return to the default view choose O Oo e fF oO A Oo Ff Regions from the View menu again Layout 61 1 1 1 0 i Px iko To separate all overlapping regions choose J 1 Separate Regions from the Format menu 0 0 Wherever regions overlap this command moves i the regions in such a way as to avoid overlaps Po QO n 0 Note Be careful with the Separate Regions command since moving regions may change the order of calculation You can also drag regions individually add lines by pressing Enter or cut and paste the regions so they don t overlap Highlighting Regions You can make c
10. i Effects Sample Strikeout C Underline ABE L Subscript L Superscript Script Color This iz an OpenType font This same B Black FT font will be used on both your printer and pour screen Many of the options of the Text Format dialog box are also available via the buttons and drop down lists on the Formatting toolbar Formatting 48 Chapter 6 Working with Text Tip Tip Tip When you first insert text its properties are determined by the style called Normal See Text Styles on page 49 to find out how to create and modify text styles Any properties that you change for selected text override the style for that paragraph that text cursor inherits the new properties You can change the following properties of selected text e Font e Font style such as bold and italic e Font size e Effects such as subscripts and superscripts e Color Font sizes are in points Remember that if you enlarge the font size the text region you re in may grow and overlap nearby regions Choose Separate Regions from the Format menu if necessary You can specify that a text region or regions automatically push down following regions as they grow longer by choosing Properties from the Format menu Click the Text tab and select Push Regions Down As You Type As a shortcut for creating subscripts and superscripts in text use the Subscript and Superscript buttons on the For
11. Modifying a Picture You can modify the orientation view zoom and pan factors brightness contrast and grayscale mapping of a picture in Mathcad using the Picture toolbar To do so 1 Click on the picture so you see hash marks around the picture s border as shown at the right 2 The Picture toolbar will pop up Hover over each tool briefly to see its tooltip 3 Ifyou resize the picture by dragging on the border you must right click on it then pick Zoom gt Zoom to Window to make it fit the resized border Online Help See Working with a Picture in online Help for more details Importing a Picture from Another Application You can copy an image from another application and paste it into Mathcad Note Ifyou use the Paste command on the Edit menu or use drag and drop from another application you are pasting a linked OLE object into your Mathcad worksheet See Inserting Objects on page 108 When you double click a linked OLE object you activate the application that created the object and are able to edit the object directly in your Mathcad worksheet You can use the Paste Special command on the Edit menu to paste an image as a noneditable metafile or bitmap A metafile can be resized in Mathcad without loss of resolution whereas a bitmap is usually viewed best only at its original size A device independent bitmap or DIB is stored in a bitmap format that is portable to other operating systems Mathcad sto
12. Press Ctrl Shift for the nth derivative operator Figure 13 7 Evaluating integrals and derivatives symbolically Examples of Symbolic Calculation 149 Tutorial Integrals 1 Click 77 on the Calculus toolbar or press to insert the derivative operator d Alternatively click 7x7 on the Calculus toolbar or press Ctr1 Shift to insert the nth order derivative operator 2 Enter the expression you want to differentiate and the variable with respect to which you are differentiating in the placeholders 3 Click on the Symbolic toolbar or press Ctr1 period for the symbolic equal sign gt 4 Press Enter Figure 13 8 shows how to differentiate an expression without using the derivative operator The Symbolics menu command Variable gt Differentiate differentiates an expression with respect to a selected variable by differentiation yields 4 x A by differentiation yields _ cosht x4 cosht x4 cosh x sinh by integration yields x7 eyptx 2 EpC 2 expts Figure 13 8 Differentiating and integrating with menu commands Click on the x first then choose Variable gt Differentiate or Variable gt Integrate from the Symbolics menu If the expression is one element of an array Mathcad differentiates only that array element To differentiate an entire array differentiate each ele
13. Shift again The first result i td disappears temporarily Enter a second keyword and arguments into the placeholder 4 Press Enter for the second e series x 3 31 1 x 4 ge float 1 3 1 4 1 4 5 x result Continue applying keywords to the intermediate results To apply several keywords and only see the final result 1 Enter the expression you want to evaluate 2 Press Ctr1 Shift period Te 3 Enter the first keyword into the placeholder including any comma delimited arguments 4 Press Ctrl Shift again and enter a second keyword into the placeholder The series 3 second keyword is placed immediately float 1 below the first keyword 5 Continue adding keywords by pressing l Ctrl Shift after each one Press a CEE ER Enter for the final result float 1 146 Chapter 13 Symbolic Calculation Keyword Modifiers Online Help Keyword modifiers are special words that control the behavior of keywords For example you can use the modifier real after the keyword assume to make Mathcad assume that a variable as a real number The following example shows how to simplify an expression using the simplify keyword assuming that a variable is real 1 Type an expression containing the variable you 2 want to assume is real ya 2 Select simplify from the Symbolic toolbar 3 Press Ctrl Shift period to insert a JZ simplify placeholder below simplif
14. To delete a matched pair of parentheses 1 Move the editing lines to one side of the a b c mu l Lag m 2 Press Backspace or Delete Moving Parts of an Expression Tip The menu commands Cut Copy and Paste from the Edit menu are useful for editing complicated expressions Copy and Paste can be used to move parts or all of an expression from one place to another Suppose you want to build the expression cos wt x sin wt x 1 Drag select the argument to the cosine function 2 Select Copy from the Edit menu or right click on the highlighted argument and select Copy 3 Click on the placeholder for the sin function cos w t x sin h 4 Select Paste from the Edit menu or right click i on the placeholder and select Paste CASE Sinia You can drag and drop expressions or even entire math regions into placeholders in other expressions or into any blank space If you re trying to drop the expression into a placeholder be sure to position the pointer carefully over the placeholder Math Styles 29 Deleting Parts of an Expression If you want to remove part of an expression and replace it with what is currently on the Clipboard do not use Cut because doing so puts the removed part on the Clipboard To delete part of an expression without placing it on the Clipboard 1 Drag select the part of the expression in this case the numerator so that it is highlighted in reve
15. gt l 4 6 8 io 12 14 16 fie G REE EE EEE 14 46 4 46 1 HOODA 6 12 14 18 18 20 22 24 26 28 30 7 14 16 18 20 22 24 26 28 30 a2 fe 16 18 2022 24 26 26 30 32 34 2 78 20 22 24 26 26 30 32 34 30 10 12 10 i2 14 Figure 5 7 Copying and pasting results from an output table Column numbers run across the top row while row numbers run down the left edge The highlighted numbers are selected to be copied Type y then paste the copied results from the output table Tip When you display an array as an output table you can export data directly from the table Right click on the output table choose Export from the menu and enter the name of the file the format and the columns and rows to export Working with Arrays There are many operators and functions designed for use with vectors and matrices see Matrix Toolbar and Operators and Vector and Matrix Functions in online Help This section highlights the vectorize operator which permits efficient parallel calculations on the elements of arrays You can also display the values of an array graphically or export them to a data file or another application Performing Calculations in Parallel Any calculation Mathcad can perform with single values it can also perform with vectors or matrices of values There are two ways to do this e Iterate over each element using range variables See Iterative Calculations on p
16. symbol for 19 89 imaginary value 89 implied multiplication 24 86 incompatible units error message 87 increments for ranges 80 indefinite integral 149 indented paragraphs 49 index variables See range variables inequalities as constraints in solve blocks 101 infinity 00 74 in place activation 108 Input Table component 35 Insert 21 Insert Area command 63 Insert key 45 Insert Math Region command 51 Insert Matrix command to create array 33 to resize array 34 Insert Object command 58 92 108 Insert Reference command 65 Insert Unit command 86 90 inserting blank lines 60 equations in text 51 functions 82 graphic objects 108 graphics computationally linked 110 math region 51 minus sign in front of expression 27 parentheses around expression 27 pictures 105 text 45 units 86 insertion point text 45 insertion point crosshair 7 integrals indefinite 149 symbolic evaluation of 149 International System of units SI 84 90 Internet PlanetPTC 17 interrupting calculations in progress 93 iteration with range variables 34 j imaginary unit 19 JPEG 70 keywords symbolic 143 language dictionaries 54 limits axis 11 default range 11 limits evaluating 150 line break in text 46 linear system solver and optimizer 98 systems of equations 98 link to objects 108 to other worksheets 65 66 literal subscripts 75 lockable area See area locked calculations 63 64 Index 159 locking and unlocking an area 63 64
17. 1 Click Lika to open the Search Book dialog box E Search Book Search for differential algebraic equation dielectric constant liquids table listing dielectric constant solids table listing differential algebraic equation differential equations stiff differentiation differentiation of vectors differential nennmetrii Found 1 differential algebraic equation ODEs Simple Pendulum Motion 7 2 Type a word or phrase in the Search for text box Select a word or phrase and click Search to see a list of topics containing that entry and the number of times it occurs in each topic 3 Choose atopic and click Go To Mathcad opens the section containing the entry Click Next to get to the exact location of the entry and any other locations Annotating an E book A Mathcad E book is made up of fully interactive Mathcad worksheets You can freely edit any math region in an E book to see the effects of changing a parameter or modifying an equation You can also enter text math or graphics as annotations in any section of your E book Saving Annotations Changes you make to an E book are temporary your edits disappear when you close the E book To save your edits first check Annotate Book on the Book menu then choose to save changes to the current section save all changes or restore the original E book section Copying Information from an E book There are two ways to copy information from
18. By default the location of the referenced file is stored in the worksheet as an absolute system path or URL To keep the location of the referenced file relative to the Mathcad worksheet containing the reference click Use relative path for reference in the Insert Reference dialog box The reference remains valid even if you move the files as long as you keep the relative folder structure intact To use a relative path you must first save the file containing the reference To update a worksheet containing a reference first make the change on the referenced worksheet and save the source file Next return to the referencing worksheet then click on the reference and press the F9 key Calculate You can change the referenced file by right clicking on the reference choosing Properties and choosing a new file on the Reference tab Hyperlinks You can create a hyperlink from any Mathcad region such as a text region or image to other regions in the same worksheet or other Mathcad worksheets or even to other types of files Hyperlinks allow you to connect groups of worksheets or simply cross reference related areas of a worksheet or worksheets Creating Hyperlinks to a Mathcad File Tip Mathcad can follow a hyperlink to any worksheet whether it is stored on your local system or the Internet To create a hyperlink from one worksheet to another first specify the hyperlink by selecting a piece of text or clicking an image The
19. C Use full width for each section Tools Options Frame ao Stat at page number ahi Header B fea 2 E E ees Footer To add or edit a header or footer Safeguarding an Area of the Worksheet 63 Tip 1 Click the Header or Footer tab To create a different header or footer for the first page of your worksheet check the Different header and footer on first page option and click the Header Page 1 or Footer Page 1 tabs which appear 2 Type the header or footer information into the text boxes Text you type into the Left Center and Right text boxes appears in these positions on the page Click Format in the Tools group to change the header or footer font font style size or alignment Click Use full width for each section if you want text in any of the boxes to extend beyond the width of that third of the worksheet 3 Click the buttons in the Tools group to automatically insert items such as the file name page number current date or time To insert an image click Image in the Tools group and browse to locate a bitmap BMP file Mathcad by default begins numbering at page 1 You can set a different starting page number in the Options group in the Header and Footer dialog box Safeguarding an Area of the Worksheet You can protect an area of your worksheet by locking it you can still edit content in an area even though nobody else can Any math regions inside a locked or co
20. Space ina math region Mathcad assumes you meant to type text rather than math and converts your math region into a text region or moves the blue editing lines to enclose more of an expression When you insert a division sign Mathcad moves everything that comes after the division sign into the denominator To insert a division sign 1 Click in the expression 2 Pressthe keyorclick jonthe Calculator toolbar Mathcad reformats the expression Some operators require only one operand such as the square root absolute value and complex conjugate operators To insert one of these place the blue insertion line on either side of the operand and press the keystroke or button from a math toolbar For example to turn x into x 1 Click next to the x either preceding or following the character 2 Press to insert the square root operator or click J on the Calculator toolbar Applying an Operator to an Expression If you want to apply an operator to an entire expression e Surround the expression in parentheses or e Use the editing lines to specify the expression Although the first method may be more intuitive it is slower since you need to type a pair of parentheses See Inserting Parentheses on page 27 26 Chapter 4 Working with Math The editing lines consist of a horizontal blue underline and a vertical blue insertion line that moves left to right along the blue underline To ma
21. The Mathcad Workspace When you start Mathcad you see a window like that shown in Figure 2 1 Es 4 n T Mathcad Untitled 1 alle ia File Edit View Insert Format Tools Symbolics Window Help 0 X D W amp la w ma p w C 100 Normal r arial ka lio r E U x E E es Jg E gI of i My site So Custom Char X sin cos tan In n Modifiers S e PR PG x float rectangular assume Il j solve simplify substitute factor expand coets collect series parfrac fourier laplace arans invfourier inviaplace invetrans HT rs mn explicit combine contrac rewrite il Trace Window Untitled 1 Press F1 For help MUM Page 1 Figure 2 1 Mathcad with various toolbars displayed 6 Chapter 2 Getting Started with Mathcad Tip Tip Each button in the Math toolbar opens another toolbar of operators or symbols You can insert many operators Greek letters and plots by clicking these buttons Button Toolbar HA Calculator Arithmetic operators Graph Two and three dimensional plot types and graph tools 33 Matrix Matrix and vector operators x Evaluation Equal signs for evaluation and definition F Calculus Derivatives integrals limits and iterated sums and products ie Boolean Comparative and logical operators for Boolean expression 3 Programming Programming constructs of Greek Greek letters Symbolic Symbolic key
22. both text and math regions By default however Mathcad finds and replaces text in text regions only Searching for Text To find a sequence of characters 1 Choose Find from the Edit menu to open the Find dialog Match whole word only Direction L Match case Oun Down Find in text regions Find in math regions Find in collapsed areas 2 Youcan specify whether Mathcad should search in only text only math or only collapsed regions or search in all three The Help topic Finding and Replacing details the characters you can find in math and text regions Many special characters including Greek characters punctuation and spaces can be located only in text or only in math Replacing Characters To find and replace text Text Tools 53 l 2 Spell Checking Choose Replace from the Edit menu to bring up the Replace dialog box Find what Replace with C Match whole word only C Match case C cance W Cancel v Find in text regions cancel Find in math regions V Find in collapsed areas You can specify whether Mathcad should search and replace in only text only math or only collapsed regions or in all three Mathcad can search the text for misspelled words and suggest replacements You can also add commonly used words to your personal dictionary Note Mathcad only spell checks text regions You can spell check over a range of selected text or spell chec
23. expression equal to 0 when finding roots Tip Another way to solve for a variable is to click on the variable you want to solve for and choose Variable gt Solve from the Symbolics menu Solving a System of Equations Symbolically Solve Keyword One way to symbolically solve a system of equations is to use the same solve keyword used to solve one equation in one unknown To solve a system of n equations for n unknowns 1 Press Ctr1 M to create a vector having n rows and 1 column 2 Fill in each placeholder of the vector with one of the n equations making up the system Make sure you press Ctr1 to enter the Boolean equal sign Press Ctr1 Shift period 4 Type solve followed by a comma in the placeholder to the left of the symbolic equal sign gt 5 Press Ctr1 M to create a vector having n rows and 1 column Then enter the variables you are solving for 152 Chapter 13 Symbolic Calculation 6 Press Enter Mathcad displays the n solutions to the system of equations to the right of the symbolic equal sign Figure 13 11 shows an example Use the solve keyword by pressing Ctrl Shift period K 2 7 yea x a 2 11 bj mta solve ______ 4x y b y 8 1 1 8 1 1 Using a solve block Use Ctrl to type the equal sign Given 2 mTy 4x y b a 2 mT b 8 7 1 ib a 8 1 1 Find x y Figure 13 11 Two methods for solving a sy
24. va This is an example of a function that accepts a vector as an argument and returns a scalar result See Chapter 5 Range Variables and Arrays for more information Note User defined function names are font and case sensitive The function f x is different from the function f x and SIN x is different from sin x Mathcad s built in functions however are defined for all fonts except the Symbol font sizes and styles This means that sin x sin x and sin x all refer to the same function Variables in User Defined Functions When you define a function you don t have to define any of the names in the argument list since you are telling Mathcad what to do with the arguments not what they are When you define a function Mathcad doesn t even have to know the types of the arguments whether the arguments are scalars vectors matrices and so on It is only when Mathcad evaluates a function that it needs to know the argument types However if in defining a function you use a variable name that is not in the argument list you must define that variable name above the function definition The value of that 84 Chapter 8 Calculating in Mathcad variable at the time you make the function definition then becomes a permanent part of the function See the example in Figure 8 6 t 4 fit 16 Figure 8 6 The value of a user function depends on its arguments The value of f depends on its argument but not on th
25. 1 Click on a number 30 Chapter 4 Working with Math 2 Choose Equation from the Format menu to see the Equation Format dialog box and select the style name Constants Follow the procedure given above for modifying the Variables style You can also use the Formatting toolbar to change the font font size or font style associated with a math style For example click on a variable then click on the appropriate Formatting toolbar button to make variables bold italic or underlined or to specify the font or point size in the drop down lists Formatting arabes Ties NewRonen vio BTU Note Changing font characteristics particularly font sizes may cause regions to overlap You can separate overlapping regions by choosing Separate Regions from the Format menu To change the default color of all equations in your worksheet 1 Choose Equation from the Format menu 2 Select a color in the Default Equation Color drop down list Applying Math Styles The Variables and Constants styles govern the default appearance of all math in your worksheet These two style names cannot be changed You may however create and apply additional math styles To see what math style is currently assigned to a name or number simply click on the name or number and look at the style window on the Formatting toolbar Alternatively click the name or number and choose Equation from the Format menu The math style appears in th
26. 144 moving parts of 28 selecting several 57 symbolic evaluation of 141 143 Fahrenheit 92 Features In depth 13 File Send command 71 files opening 55 saving 12 Find function 99 152 fixed positioning 70 floating point evaluation keyword 144 font changing in header or footer 63 changing in math 29 changing in text 47 footers 62 Format Style command 50 formatting 2D plots 120 3D plots 135 numbers in matrices 40 results 88 symbolic 147 worksheets 61 Formatting toolbar 6 math styles 30 text styles 50 FRAME for animation 125 functions applying to an expression 82 defining 9 82 optimization 97 recursive 84 solving 97 to find roots of expressions 97 user defined 74 82 Getting Started Primers 13 Given in solve blocks 99 152 global definitions 78 graphics inserting 105 graphing data 118 expressions 115 158 Index functions 115 117 128 in 2D 113 116 in 3D 127 134 vector 118 graphs creating 10 127 134 formatting 11 resizing 114 See also plots 2D Greek letters in equations 74 in text 46 Greek toolbar 20 46 guess for solve blocks 98 guidelines for aligning regions 59 hard page breaks 62 HBK files 14 headers and footers 62 Help See also Resources Window and Technical Support HTML 56 70 hyperlinks 66 deleting removing 67 editing 67 to other file types 68 to regions 67 i imaginary unit 19 image file BMP format 106 in headers and footers 63 imaginary numbers entering 19
27. 2 Defining a matrix of data and plotting it as a 3D bar plot In the default perspective the first row of the matrix extends from the back left corner of the grid to the right while the first column extends from the back left corner out toward the viewer See Formatting a 3D Plot on page 135 to change this default view Creating a Parametric Surface Plot A parametric surface plot is created from three matrices representing the x y and z coordinates of your points in space To create a parametric surface plot 1 Create or import three matrices having the same number of rows and columns 2 Choose Graph gt Surface Plot from the Insert menu 3 Type the names of the three matrices separated by commas and enclosed in parentheses in the placeholder 132 Chapter 12 3D Plots Figure 12 3 shows a parametric surface plot created from the matrices X Y and Z defined above the plot numpts 20 m O numpts n O numpts rie TIT mr tro Ar numpts numpts Sm n R rcosl8y cosin Ym n R r cosl8_ siniomi 2m n sinian Figure 12 3 Defining data for a parametric surface plot Note The underlying parameter space is a rectangular sheet covered by a uniform mesh The three matrices map this sheet into three dimensional space For example the matrices X Y and Z defined in Figure 12 3 carry out a mapping that rolls the sheet into a tube and then joins the ends of the tube to form a torus For spec
28. 3 2568 fix root fix x amp 2 3 0 201 3 256 polyroots coefi 0 201 3 057 Figure 9 1 Finding roots with root and polyroots 97 98 Chapter 9 Solving Note When you specify the optional arguments a and b for the root function Mathcad only finds a Online Help Note root for the function f if f a is positive and f b is negative or vice versa See Figure 9 1 If after many approximations Mathcad still cannot find an acceptable answer it marks the root function with an error message indicating its inability to converge to a result To find the cause of the error try plotting the expression A plot helps to determine whether or not the expression crosses the x axis and if so approximately where In general the closer your initial guess 1s to where the expression crosses the x axis the more quickly the root function converges on an acceptable result For more details and issues on finding roots see Finding Roots in online Help The root function can solve only one equation in one unknown To solve several equations simultaneously use Find or Minerr described in Solve Block Functions on page 99 Finding All Roots To find the roots of a polynomial or an expression having the form v Xbb LEV XZ VIX EV n ia 2 1 0 you can use polyroots rather than root polyroots does not require a guess value and returns all roots at once whether real or complex You must type the coefficients of the
29. A text box now surrounds your text Anything you type gets inserted at the text cursor To delete text from an existing text region click in the text region and e Press Backspace or Delete just as you would in any other word processor To overtype text 1 Place the text cursor to the left of the first character you want to overtype 2 Press Insert to begin typing in overtype mode To return to the default insert mode press Insert again 45 46 Chapter 6 Working with Text Tip You can also overtype text by first selecting it see Selecting Text below Whatever you type next replaces your selection To break a line or start a new line in a text region press Enter Mathcad inserts a hard return and moves the text cursor down to the next line Press Shift Enter to start a new line in the same paragraph When you rewrap the text by changing the width of the text region Mathcad maintains line breaks at these spots in the text We recommend adjusting the width of the text box rather than using returns to shorten a text region Selecting Text Online Help To select text within a text region 1 Click in the text region ease motion for falling body under gravity 2 Drag across the text holding the mouse button Equations of METIE down ely Gravity Mathcad highlights the selected text including any full lines between the first and last characters you selected You can also select text using
30. Advanced Options from the menu to control settings for the conjugate gradient and quasi Newton solvers To override Mathcad s default choice of solving algorithm Create and evaluate a solve block allowing Mathcad to AutoSelect an algorithm Right click on the name of the function that terminates the solve block and remove the check from AutoSelect on the menu Check another solving method on the menu Mathcad recalculates the solution using the method you selected w GuboSelect Linear d Levenberg Marguardt Conjugate Gradient Quasi Newton ab Cut bia Copy ey Paste Properties Disable Evaluation Optimize When solving overdetermined systems such as regression problems the Levenberg Marquardt method performs best if given a vector of residual values set to zero rather than a single sum of squared errors objective function 104 Chapter 9 Solving Chapter 10 Inserting Graphics and Other Objects Overview Overview Inserting Pictures Inserting Objects gt gt OD Inserting Objects Computationally Linked to Your Worksheet To illustrate your Mathcad calculations visually you can add e 2D and 3D graphs e Pictures based on values in a matrix pasted from another application or based on an image file e Objects created by another application AVI files DOC files MDI files and so on e Graphics computationally linked to your calculations Inserting Pict
31. Hyperlinks to Other Files You can create a hyperlink not only from one Mathcad worksheet to another but also from a Mathcad worksheet to any other file type Use this feature to create E books or compound documents that can contain spreadsheets animation files even Web pages Note Double clicking a hyperlink to another file type launches either the application that created the file or an application associated with a file of that type in the Windows Registry However only Mathcad files can be made into pop up windows Distributing Your Worksheets Printing Mathcad worksheets can be distributed in a variety of media including the Internet through email in print format and of course as individual Mathcad documents or as a Mathcad E book You can also print Mathcad worksheets to PDF files if you have the appropriate applications To print a Mathcad worksheet choose Print from the File menu The Print dialog box lets you control whether to print the entire worksheet selected pages or selected regions The particular dialog box you see depends on the printer you ve selected Printing Wide Worksheets Mathcad worksheets can be wider than a sheet of paper since you can scroll as far to the right as you like in a Mathcad worksheet and place equations text and graphics wherever you like As you scroll horizontally however you see gray vertical lines appearing to indicate the right margins of successive pages corresponding t
32. Mathcad e As you type each operator in this case and Mathcad shows a small black rectangle called a placeholder Placeholders hold spaces open for numbers or expressions not yet typed If you click at the end of an equation you see a placeholder for units and unit conversions Once an equation is on the screen you can edit it by clicking in it and typing new letters numbers or operators You can enter many operators and Greek letters by using the math toolbars Chapter 4 Working with Math explains how to edit Mathcad equations Definitions and Variables Mathcad s power and versatility quickly become apparent once you begin to use variables and functions By defining variables and functions you can link equations together and use intermediate results in further calculations Defining Variables These steps show you how to define a variable 1 Type the variable name 2 Typethe colon key orclick jon the Calculator toolbar to insert the definition symbol 3 Type the value to be assigned to the variable The value can be a single number or a more complicated combination of numbers and previously defined variables If you make a mistake click on the equation and press Space until the entire expression 1s between the two blue editing lines Then delete it by choosing Cut from the Edit menu Ctr1 X Or use Mathcad s Undo Ctr1 Z command from the Edit menu to step back through the equati
33. Note Once you ve inserted regions into your worksheet you can align them vertically or horizontally using menu commands nudging with the arrow keys or by using the worksheet ruler Using Menu Commands To align regions horizontally or vertically 1 Select the regions 2 Choose Align Regions gt Across to align horizontally or Align Regions gt Down to align vertically from the Format menu Or click IF and on the Standard toolbar When you align the regions down Mathcad moves the regions so that their left edges are aligned vertically Aligning regions across moves the regions so that their anchor points are aligned horizontally Aligning regions may inadvertently cause regions to overlap Mathcad warns you when this will occur See Separating Regions on page 60 Using the Worksheet Ruler Choose Ruler from the View menu to open the worksheet ruler at the top of the window If your cursor is in a text region the ruler settings apply to that region only otherwise they apply to the whole worksheet You can use alignment guidelines on the ruler to align regions at particular measurements To set alignment guidelines on the ruler 1 Click on the ruler for each position where you want an alignment guideline A tab stop symbol appears 2 Right click ona tab stop symbol and choose Show Guideline from the menu Green guidelines run down the worksheet so that you can align regions vertically
34. Text Text Tools Mathcad Worksheets Worksheets and Templates Rearranging Your Worksheet Layout Safeguarding an Area of the Worksheet Worksheet References Hyperlinks Distributing Your Worksheets CONN UU WW KPH H 8 Calculating in Mathcad Defining and Evaluating Variables Defining and Evaluating Functions Units and Dimensions Working with Results Controlling Calculation Error Messages 9 Solving Solving and Optimization Functions 10 Inserting Graphics and Other Objects Overview Inserting Pictures Inserting Objects Inserting Objects Computationally Linked to Your Worksheet 11 2D Plots Overview of 2D Plotting Graphing Functions and Expressions Plotting Vectors of Data Formatting a 2D Plot Modifying a 2D Plot s Perspective Animations 12 3D Plots Overview of 3D Plotting Creating 3D Plots of Functions Creating 3D Plots of Data Formatting a 3D Plot 13 Symbolic Calculation Overview of Symbolic Math Live Symbolic Evaluation Using the Symbolics Menu Examples of Symbolic Calculation Index 123 124 127 127 128 130 135 141 141 141 147 148 155 About This Guide The Mathcad User s Guide introduces you to Mathcad and what is unique about working in its environment Its audience is new users and those who have used Mathcad occasionally in the past More depth is provided in the documentation listed below Other Documentation In addition to this guide the following documentation may be h
35. The addition operator with two placeholders tu appears 2 Enter 2 in the first placeholder Building Expressions 21 3 Click in the second placeholder or press Tab to move the blue editing lines and enter 6 4 Press or click on the Calculator toolbar to get the result 2 6 9 Building Expressions You can create many mathematical expressions by simply typing For example you type these characters 3 4 5 2 to get the result at the right Mathcad s equation editor is designed to work within the structure of a mathematical expression so that expressions are not so much typed as built Mathcad assembles the parts that make up an expression using the rules of precedence plus some additional rules to simplify entering denominators exponents and expressions in radicals For example when you type orclick on the Calculator toolbar to create a fraction Mathcad stays in the denominator until you press Space to select the entire expression Typing in Names and Numbers When you type in names or numbers Mathcad behaves very much like a standard word processor As you type you see the characters you type appear behind a vertical editing line The left and right arrow keys move this blue insertion line to the left or to the right a character at a time There are however two important differences e As it moves to the right the blue insertion line leaves behind a blue und
36. command 7 Edit menu Links command 110 editing equations annotated example 24 changing a number 25 changing a variable or function name 25 deleting an operator 26 Index 157 deleting parentheses 28 deleting parts of expression 29 inserting an operator 25 making expression an argument to a function 82 moving parts of an expression 28 moving rearranging equations 57 58 editing lines 24 Electronic Books See E books Email 71 endpoints for ranges 80 engineering notation 89 equal sign in numerical calculations 76 in solve blocks 99 symbolic calculations 141 150 151 equality constraints 101 equations as constraints in solve blocks 101 calculating results 9 76 color 30 disabling calculation for 94 dragging and dropping 28 effect of range variables in 79 errors in 94 font 29 global definitions 78 in text 51 locking in area 63 order of evaluation 77 92 processing and calculating 8 92 solving for root 97 solving symbolically 150 152 solving with solve blocks 98 styles 29 units in 84 variable definition 73 error messages correcting 95 in equations 94 tracing the source of 94 with units 87 Evaluate Symbolically command 147 exiting Mathcad 12 expand keyword 144 147 expand nested arrays 89 exponential notation entering 20 exponential threshold 89 exporting worksheets as RTF 71 expressions applying a function to 82 correcting errors in 95 deleting parts of 29 error messages in 94 evaluating 76 expanding
37. data manipulation and engineering design work Calculation standardization and reuse through Mathcad ensures standards compliance By combining calculations graphs text and images in one document Mathcad enables knowledge capture and publication that aid management of large projects Mathcad allows you to document your calculations in the language of mathematics because Mathcad combines a powerful computational engine accessed through conventional math notation with a full featured word processor and graphing tools You can type equations as you re used to seeing them on paper Simply type in your equations then see them display with an instant result along with as much text as you want to accompany the math Mathcad makes it easy to communicate the rationale and assumptions behind your calculations enabling design quality assurance You can use Mathcad equations to solve both symbolical and numerical equations You can place text anywhere on the worksheet and add two and three dimensional graphs to the page You can even illustrate your work with images taken from another application Mathcad takes full advantage of Microsoft s OLE 2 object linking and embedding standard to work with other applications supporting drag and drop and in place activation as both client and server Mathcad lets you easily mix and convert between unit systems catching unit mistakes by checking your worksheets for dimensional consistency You can wor
38. equations in the worksheet choose Calculate Worksheet from the Tools menu or press Ctr1 F9 94 Chapter 8 Calculating in Mathcad Interrupting Calculations To interrupt a computation in progress Tip Mathcad 1 Press Esc The dialog box shown at right appears 2 Click OK to stop the calculation or Cancel to resume J eup processing calculation j Cancel If you click OK the equation that was being processed when you pressed Esc is marked with an error message see Error Messages on page 94 indicating that calculation has been interrupted To resume an interrupted calculation first click in the equation with the error message then press F9 or click on the Standard toolbar If you find that you frequently interrupt calculations to avoid having to wait for Mathcad to recalculate as you edit your worksheet you should switch to manual mode Disabling Equations You can disable a single equation so that it no longer calculates Disabling an equation does not affect Mathcad s equation editing formatting and display capabilities Tip To disable calculation for a single equation in your worksheet l PA 3 4 Click on the equation Choose Properties from the Format menu and click the Calculation tab Under Calculation Options check Disable Evaluation Mathcad shows a small rectangle after the equation to indicate 1 2 that it is disabled KE
39. how the editing lines hold the x between them If you were to type at this point the x would become the first operand of the plus Hl 2 Press Space The editing lines now hold the entire expression a 3 Now type Whatever was held between the editing lines now A becomes the first operand of the a al 4 Inthe remaining placeholder type y Multiplication When writing expressions like ax or a x y are easily understood to mean a times x and a times the quantity x plus y respectively This cannot be done with Mathcad variables for the simple reason that when you type ax Mathcad has no way of knowing whether you mean a times x or the variable named ax Similarly when you type a x y Mathcad cannot tell if you mean a times the quantity x plus y or whether you mean the function a applied to the argument x y To avoid ambiguity in math expressions we recommend that you always press to explicitly indicate multiplication as shown below 1 Type a followed by Mathcad inserts a small dot after the a to indicate multiplication aa 2 Inthe placeholder type the second factor x a x 24 Chapter 4 Working with Math Note In the special case when you type a numerical constant followed immediately by a variable Tip name such as 4x Mathcad interprets the expression to mean the constant multiplied by the variable 4 x Mathcad displays a space a
40. in this example you type 1 in the box next to Columns 0 in the box next to Rows and press Delete Iterative Calculations Mathcad can do repeated or iterative calculations as easily as individual calculations by using a special variable called a range variable Range variables take on a range of values such as all the integers from 0 to 10 Whenever a range variable appears in a Mathcad equation Mathcad calculates the equation not just once but once for each value of the range variable Creating a Range Variable To compute equations for a range of values first create a range variable In the problem below for example you can compute results for a range of values of from 10 to 20 in steps of 1 To do so 1 First type t 10 Click on the 10 in the equation t 10 2 Type 11 The next number in the range is 11 and the step size is 1 3 Type for the range variable operator or click on the Matrix toolbar and then type the last number 20 The last t 10 11 20 number in the range is 20 Mathcad shows the range variable i operator as a pair of dots Iterative Calculations 35 4 Now click outside the equation for t Mathcad begins to compute with defined as a range variable Since now takes sen on eleven different values there must be eleven different results which are displayed in an output table as shown 1 588 10 1 416 10 1 769 105 1
41. number of Mathcad E books and articles which you can download and use are available on PlanetPTC at http communities ptc com community mathcad E books install to a Handbook folder within the Mathcad program folder Once you have restarted Mathcad they will be listed under E books in the Help menu or you can browse to find unlisted E books HBK If you create your own E books you may have to create a Handbook folder Finding Information in an E book As in other hypertext systems you move around a Mathcad E book simply by clicking on icons or underlined text You can also use the buttons on the toolbar at the top of the E book and Resources window to navigate within the E book Button Function fat Links to the home page or welcome page for the E book ii Opens a toolbar for entering a Web address da Backtracks to the document last viewed or reverses backtrack E a Goes backward or forward one section B Displays a list of documents most recently viewed gw Searches the E book Copies selected regions m i Saves current section of the E book Mathcad Resources 15 Button Function Prints current section of the E book Displays Help for the current function dialog or command E book Search In addition to using hypertext links to find topics in an E book you can search for topics or phrases To do so
42. object can be either embedded in or linked to a Mathcad worksheet An object that is linked must exist in an external saved file An object that you embed may be created at the time of insertion or come from an existing file When you edit a linked object any changes you make to the object also update the original file When you edit an embedded object any changes you make to the object affect it only in the Mathcad worksheet The original object in the source application is unchanged Inserting an Object into a Worksheet Tip You insert an object into Mathcad which is an OLE 2 compatible application by using the Object command from the Insert menu by copying and pasting or by dragging and dropping You can edit objects in a Mathcad worksheet simply by double clicking them causing in place activation of the originating application in most cases Use the same methods to insert a Mathcad object into another application and edit it inside that application as you do to insert objects into a Mathcad worksheet Double click the Mathcad object to edit it Ifthe application supports in place activation the menus and toolbars change to Mathcad s Insert Object Command To insert a new or existing file 1 Click in a blank space in your worksheet 2 Choose Object from the Insert menu to bring up the Insert Object dialog box Insert Object Object Type Create New Adobe Acrobat 7 0 Document Adobe Photoshop Image Create from Fi
43. on the data you can paste or export the resulting array of numbers back to its source or into another application To copy just one number from a result array click the number and choose Copy from the Edit menu Copying multiple numbers from a vector or matrix result differs depending on whether the array is displayed as a matrix or as an output table To copy a result array displayed as a matrix 1 Drag select the array to the right of the equal sign to place the entire array between the editing lines 2 Choose Copy from the Edit menu 3 You may only paste an array into a math placeholder or into a blank space in Mathcad 4 You can also paste the array into another application To copy some or all of the numbers from a data table 1 Click on the first number you want to copy 2 Drag the mouse over the other values you want to copy while holding down the mouse button 3 Right click the selected values then choose Copy Selection from the menu To copy all the values in a row or column click on the column or row number shown to the left of the row or at the top of the column Then choose Copy from the Edit menu After you have copied one or more numbers from an output table you can paste them into another part of your worksheet a blank Data Table or into another application Figure 5 7 shows an example of a new matrix created by copying and pasting numbers from an output table Working with Arrays 41 fn Bae ee
44. plot click on it and use the handles that appear along the edges to drag out the edges Mathcad provides several additional options for manipulating the display of a 3D plot e You can rotate the plot to see it from a different perspective e You can set the plot in motion about an axis of rotation so that it spins continuously e You can zoom in or out on a portion of the plot More information can be found in Rotating Spinning or Zooming a 3D Plot in online Help 140 Chapter 12 3D Plots Chapter 13 Symbolic Calculation Overview of Symbolic Math Live Symbolic Evaluation Using the Symbolics Menu gt gt Examples of Symbolic Calculation Overview of Symbolic Math When you evaluate an expression numerically Mathcad returns one or more numbers as shown at the top of Figure 13 1 When Mathcad calculates symbolically however the result of evaluating an expression is generally another expression as shown in the bottom of Figure 13 1 k3 k 0 3 k i fjs Y a k f 2 64 f 5 27 f x oe 46x i 12 4 8 Figure 13 1 A numeric and symbolic evaluation of the same expression The symbolic transformation can yield insight into the underlying expression There are two ways to perform a symbolic transformation on an expression e You can use the symbolic equal sign with keywords e You can use commands from the Symbolics menu Online Help You can make the numeric and symbolic processors work t
45. polynomial into a separate vector as in Figure 9 1 root and polyroots can solve only one equation in one unknown and always return numerical answers To solve an equation symbolically or to find an exact numerical answer in terms of elementary functions use the solve keyword or choose Variable gt Solve from the Symbolics menu See Chapter 13 Symbolic Calculation Linear Nonlinear System Solving and Optimization Mathcad includes many other numerical solving functions Solving a Linear System of Equations Use the solve function to solve a linear system of equations whose coefficients are arranged in a matrix M The argument M for so ve must be a matrix that is neither singular nor nearly singular An alternative to solve is to solve a linear system by using matrix inversion Solve Blocks The general form for using system solving functions in Mathcad is within the body of a solve block There are four steps to creating a solve block 1 Provide an initial guess for each of the unknowns Mathcad solves equations by making iterative calculations The initial guesses give Mathcad a place to start searching for solutions If you expect your solutions to be complex provide complex guess values Solving and Optimization Functions 99 Tip Note 2 Type the word Given in a separate math region below the guess definitions in order to set up a system of constraint equations Be sure you don t type Given ina text regio
46. record the animation the FRAME variable increments by one Enter the playback speed in the Frames Sec box Click Animate You ll see a miniature rendition of your selection inside the dialog box Mathcad redraws this once for each value of FRAME This preview does not necessarily match the playback speed since at this point you re just creating the animation 126 Chapter 11 2D Plots 7 To save your animation clip as a Windows AVI file suitable for viewing in Mathcad or other Windows applications click Save As in the dialog box Playing an Animation Clip E Play Animation a E x As soon as you ve created an animation clip Mathcad opens a playback window To play back the animation clip click the arrow at the lower left corner of the window You can also play back the animation clip on a frame by frame basis either forward or backward by dragging the slider Playing a Previously Saved Animation If you have an existing Windows AVI file you can play it within Mathcad To do so 1 Choose Animation gt Playback from the Tools menu to bring up the Play ee ae E Play Animati EE Animation dialog box The window is mmanen BEIE collapsed since no animation clip has been opened 2 Click on the button to the right of the play button and choose Open from the menu Use the Open File dialog box to locate and open the AVI file you want to play Online Help See Creating Animations in on
47. to bring up the 3D Plot Format dialog box In the Display As section of the General tab click the tab labeled Plot 2 and select Surface from the array of plot types Both the contour plot and the surface plot with default format settings appear in a single graph as shown in Figure 12 6 Figure 12 6 Two plots one contour and one surface shown on the same graph Formatting a 3D Plot You can change the appearance of any 3D plot by using the options available in the 3D Plot Format dialog box To format a 3D plot 136 Chapter 12 3D Plots 1 Double click the plot or click on the plot and choose Graph gt 3D Plot from the Format menu to open the 3D Plot Format dialog box The General page is shown here 3 D Plot Format Backplanes Special Advanced GQuickPlot Data General Ames Appearance Lighting Title View Rotation Tilt Aves Style Perimeter Comer Frames None Show Border Hi Equal Scales Show Box D o fo nm ae 4 T Tist i Zoom Plat 1 Display As Surface Plat Data Paints Bar Plat O Contour Plot Vector Field Plot Patch Plot ja 2 Make the desired changes in each tab of the dialog box 3 Click Apply to see the effect of your changes without closing the dialog box 4 Close the dialog by clicking OK The 3D Plot Format Dialog Box Most options are available for any three dimensional graph although some may de
48. with exactly the same font size and other characteristics as another math style Saving Math Styles You can reuse math style information by saving a worksheet as a template Choose Save As from the File menu and select Mathcad XML Template XMCT as the file type in the Save As dialog box To apply math style information to another worksheet open your template from the File menu and copy the contents of the worksheet to the template See Worksheets and Templates on page 55 Chapter 5 Range Variables and Arrays Creating Arrays Iterative Calculations Accessing Array Elements Displaying Arrays gt gt gt gt SO Working with Arrays Creating Arrays This section describes creating and working with arrays of numbers and math expressions Vectors and Matrices In Mathcad a column of numbers is a vector and a rectangular array of numbers is called a matrix The general term for a vector or matrix is an array The term vector refers to a column vector A column vector is simply a matrix with one column You can also create a row vector by creating a matrix with one row and many columns You may wish to distinguish between the names of matrices vectors and scalars single numbers by font Names of vectors could be set in bold while setting scalars in italic See Math Styles on page 29 Insert Matrix Command To insert a vector or matrix 1 Click in either a blank space or on a math placeholder
49. your worksheet in miniature as it will appear when printed with a strip of buttons across the top of the window Hew Paae Prex Pace Two Page _ZoomIn Zoom Out _close You can use the Zoom In and Zoom Out buttons to magnify the worksheet or you can magnify the worksheet by moving the cursor onto the page so that the cursor changes to a magnifying glass then click the mouse Click again to magnify your worksheet even more Once you re at the maximum magnification clicking on the page de magnifies it You cannot edit the current page or change its format in the Print Preview screen To edit the page or change its format return to the normal view by clicking Close 70 Chapter 7 Mathcad Worksheets Creating PDF Files You can save documents in Adobe s Portable Document Format PDF Once a PDF printer driver is installed choose Print and select the PDF driver from your list of printers Then choose Print to File in the Print dialog box to create a PDF file that can be distributed as is or further manipulated in Acrobat Distiller Creating E books Online Help As described in Chapter 3 Online Resources an E book is a hyperlinked collection of Mathcad worksheets When you open an E book in Mathcad it opens in its own window An E book has a table of contents an index a browse order and search features accessible through buttons on the toolbar in the E book window The worksheets
50. 4 Decimal format Number of decimal places 5 x 5 25740 Show trailing zeros Y 3 142 x tot Scientific format 31 416 x 107 Engineering format w 5 257E 000 Engineering format Show exponents as E 000 Figure 8 10 Several ways to format the same number Displaying Units of Results Tip By default Mathcad displays results in the fundamental units of the current unit system Check Simplify units when possible in the Result Format dialog box to see units in a result expressed in terms of derived units rather than in base units Check Format units to see units in a result displayed as a built up fraction containing terms with positive exponents only rather than as a product of units with positive and negative exponents You can have Mathcad redisplay a particular result in terms of any of Mathcad s built in units To do so 1 Click in the result You ll see an empty placeholder to its right This is the units placeholder 2 Click the units placeholder then choose Unit from the Insert menu or click on the Standard toolbar to open the Insert Unit dialog box 3 Double click the unit in which you want to display the result You can also type a unit s name directly into the units placeholder Unit Systems Mathcad uses SI as the default unit system When you use the equal sign to display a result having units Mathcad automatically displays the units in the result in terms of base or deri
51. 9 5 A solve block for computing the solution of a matrix equation using the Riccati Equation from control theory The table below lists the constraints that can appear in a solve block between the keyword Given and the functions Find Maximize Minerr and Minimize x and y 102 Chapter 9 Solving Note Online Help represent real valued expressions and z and w represent arbitrary expressions Constraints are often scalar expressions but can also be vector or array expressions Condition w 2Z x lt y x gt y x lt y x2y lt x xXAYy xvy x Oy Boolean Toolbar af we A Ei d W E Constraint Equal Less than Greater than Less than or equal to Greater than or equal to Not And Or Xor Exclusive Or Mathcad does not allow the following between Given and Find in a solve block e Constraints with e Range variables or expressions involving range variables of any kind e Assignment statements statements like x 1 You can include compound statements such as 1 lt x lt 3 Mathcad returns only one solution for a solve block There may however be multiple solutions to a set of equations To find a different solution try different guess values or enter an additional inequality constraint that the current solution does not satisfy Tolerances for Solving Mathcad s numerical solvers make use of two tolerance parameter
52. 96 10 You can use one or more range variables to fill up the elements of an array If you use two range variables in an equation for example Mathcad runs through each value of each range variable This is useful for defining matrices For example to define a 5 x 5 matrix whose jth element is i j enter the equations shown in Figure 5 1 I 0 4 j 0 4 si j i 0 il 2 3 4 i 2 a 4 a 2 3 4 5 6 3 64 5 6 4 5 6 E Figure 5 1 Defining a matrix using range variables Enter the subscript operator by clicking key The x equation is evaluated for each value of each range variable for a total of 25 on the Matrix toolbar or by pressing the evaluations The result is the matrix shown at the bottom of Figure 5 1 with 5 rows and 5 columns The element in the ith row and jth column of this matrix is i J Note When used to define an array element an array subscript can only take on integer values For more details on range variables see Range Variables on page 79 Entering a Matrix as a Data Table You can use a data table to get the convenience of a spreadsheet like interface for entering data 36 Chapter 5 Range Variables and Arrays Note Tip 1 Click in a blank spot in your worksheet and choose Data gt Table from the Insert menu 2 Enter the name of the Mathcad variable to which the data will be assigned in the placeholder 3 Click in the data table and ent
53. By default Mathcad creates a 3 layer 256 color or RGB representation of the data in the matrices This setting can be changed however through the Properties dialog box and the Picture toolbar See Modifying a Picture on page 107 Online Help Since the matrices used in picture rendering may be quite large this technique of creating a picture is most useful when you import graphics files using File Access Functions described in online Help For example you can use the READBMP function to read an external graphics file into a matrix then view it as a picture Creating a Picture by Reference to an Image File Mathcad can create a picture directly from a number of image file formats including BMP JPEG GIF TGA and PCX First click in a blank space then 1 Choose Picture from the Insert menu or click ma on the Matrix toolbar 2 Create a string in the placeholder by typing the double quote key then the name of an image file in the current folder or the full path c temp seriesnetwork bmp to an image file g 7 e a 70 appears F b 3 Click outside the picture region The bitmap EE av f Each time you open or recalculate the worksheet the image file is read into the picture region Note Ifyou modify the source image file you must recalculate your worksheet to see the modified image If you move the source image file Mathcad can no longer find the picture Inserting Pictures 107
54. ITED STATES GOVERNMENT RESTRICTED RIGHTS LEGEND This document and the software described herein are Commercial Computer Documentation and Software pursuant to FAR 12 212 a b OCT 95 or DFARS 227 7202 1 a and 227 7202 3 a JUN 95 and are provided to the US Government under a limited commercial license only For procurements predating the above clauses use duplication or disclosure by the Government is subject to the restrictions set forth in subparagraph c 1 11 of the Rights in Technical Data and Computer Software Clause at DFARS 252 227 7013 OCT 88 or Commercial Computer Software Restricted Rights at FAR 52 227 19 c 1 2 JUN 87 as applicable 01012011 Parametric Technology Corporation 140 Kendrick Street Needham MA 02494 USA Contents About This Guide Other Documentation Other Resources Technical Support Welcome to Mathcad What Is Mathcad Getting Started with Mathcad The Mathcad Workspace Regions A Simple Calculation Definitions and Variables Graphs Saving Printing and Exiting Online Resources Mathcad Resources Mathcad Community on PlanetPTC Other Resources Working with Math Inserting Math Building Expressions Editing Expressions Math Styles Range Variables and Arrays Creating Arrays Iterative Calculations Accessing Array Elements Displaying Arrays Working with Arrays Working with Text Inserting Text Text and Paragraph Properties Text Styles Equations in
55. PIC User s Guide Mathcad 15 0 M010 July 2011 Copyright 2011 Parametric Technology Corporation and or Its Subsidiary Companies All Rights Reserved User and training guides and related documentation from Parametric Technology Corporation and its subsidiary companies collectively PTC are subject to the copyright laws of the United States and other countries and are provided under a license agreement that restricts copying disclosure and use of such documentation PTC hereby grants to the licensed software user the right to make copies in printed form of this documentation if provided on software media but only for internal personal use and in accordance with the license agreement under which the applicable software is licensed Any copy made shall include the PTC copyright notice and any other proprietary notice provided by PTC Training materials may not be copied without the express written consent of PTC This documentation may not be disclosed transferred modified or reduced to any form including electronic media or transmitted or made publicly available by any means without the prior written consent of PTC and no authorization is granted to make copies for such purposes Information described herein is furnished for general information only is subject to change without notice and should not be construed as a warranty or commitment by PTC PTC assumes no responsibility or liability for any errors or inaccuracies that may app
56. To do so simply replace with an appropriate number For example To evaluate the function at a particular value such as 3 5 typed 3 5 Mathcad returns the correct value as shown d 3 5 1 54 10 Formatting a Result You can set the display format for any number that Mathcad calculates and displays In the example above the result is in exponential notation Here s how to change the result so it is displayed differently 1 Click in the result 10 Chapter 2 Getting Started with Mathcad 2 Choose Result from the Format menu to open the Result Format dialog box These dialog settings affect how results are displayed including the number of decimal places the use of exponential notation and trailing zeros and so on Result Format Number Format Display Options Unit Display Tolerance Format Number of decimal places 3 Decimal Scientific Show trailing zeros Engineering Show exponents in engineering format Fraction Exponential threshold a P Apply to symbolic results 3 The default format scheme is General with Exponential Threshold set to 3 Only numbers greater than or equal to 10 are displayed in exponential notation Click the arrows to the right of the 3 to increase the Exponential Threshold to 6 4 After you click OK the number changes to reflect the new result format See Formatting Results on page 88 ae Note When you format
57. Y or Copy Radius or Copy Angle in a polar plot 2 Paste the value into your worksheet or any other application Animations You can use Mathcad to create and play short animation clips by using the built in variable FRAME Anything that can be made to depend on this variable can be animated Animations 125 Creating an Animation Clip The built in variable FRAME is used to drive animations To create an animation l Create an expression or plot or a group of expressions whose appearance depends on the value of FRAME This expression need not be a plot It can be anything at all Choose Animation gt Record from the Tools menu to bring up the Record Animation dialog box Record Animation For FRAME From E o 10 FramesS ec FRAME Select an area of your worksheet whose contents are based on the FRAME variable enter starting and ending FRAME values and choose Animate 3 Drag select the portion of your worksheet you want to animate as shown in Figure 11 12 s 0 0 1 30 Record Animation fx For FRAME roxjc FRAME From To a m Frames Sec 3 FRAME 9 Select an area of your worksheet whose contents are based on the FRAME variable enter starting and ending FRAME values and choose Animate Figure 11 12 Selecting an area for animation and seeing the animation inside the dialog box 4 Set the upper and lower limits for FRAME in the dialog box When you
58. a result only the display of the result 1s affected Mathcad maintains full precision internally up to 16 digits Graphs Mathcad provides a variety of two dimensional X Y and polar graphs plus three dimensional contour scatter and surface plots This section describes how to create a simple two dimensional graph showing the points calculated in the previous section First delete the value of tin your worksheet Since you have defined t as a single number you can not use it as a range of numbers in a graph You can define t as a range of values Creating a Basic Graph To create an X Y plot 1 Click in a blank area of your worksheet Graphs 11 A 4 Choose Graph gt X Y Plot from the Insert menu or click L on the Graph toolbar Or type Mathcad inserts a blank X Y plot Fill in the x axis placeholder bottom center with t and the y axis placeholder left center with d t These placeholders can contain a function an expression or a variable name Click outside the plot or press Enter Mathcad automatically chooses axis limits for you To specify the axis limits yourself click in the plot and type over the numbers in the placeholders at the ends of the axes Mathcad also creates the plot over a default range For detailed information on graphs ranges and expressions in plots see Chapter 11 2D Plots Formatting a Graph The default characteristics of a Mathcad graph are numbere
59. able with two different global definitions or with one global and one local definition may make your worksheet difficult to revise or understand in the future Defining and Evaluating Variables 79 Range Variables Iterative processes in Mathcad worksheets depend on range variables For a description of more advanced iterative operations made possible by the programming operators in Mathcad go to the Programming section of online Help Using Range Variables To define a range variable see Creating a Range Variable on page 34 To define a range variable that changes in steps other than 1 see the section Types of Ranges on page 80 Once you define a range variable it takes on its complete range of values every time you use It You cannot define a variable in terms of a range variable For example if after having defined j as shown in Figure 8 4 you now define 7 j 1 Mathcad assumes you are trying to set a scalar variable equal to a range variable and marks the equation with an appropriate error message One application of range variables is to fill up the elements of a vector or matrix You can define vector elements by using a range variable as a subscript For example to define x for each value of j Type x j3 37 2 Space 1 Figure 8 4 shows the vector of values computed by this equation Since j is a range variable the entire equation is evaluated once for each value of j This defines x for each value ofj
60. ad rewraps the text according to the width set by Ctr1 Enter To change the width of an existing text region do the following 1 Click anywhere in the text region A selection box encloses the text region 2 Move the pointer to the middle of the right edge of the text region until it hovers over the handle on the selection rectangle The pointer changes to a double headed arrow You can now change the size of the text region the same way you change the size of any window by dragging the mouse Tip You can specify that a text region or regions occupy the full page width by selecting them and choosing Properties from the Format menu Click the Text tab and check Occupy Page Width As you enter more lines of text into a full width text region any regions that are below are automatically pushed down in the worksheet Text and Paragraph Properties This section describes how to change various font properties and the alignment and indentation of paragraphs within a text region Changing Text Properties To change the font size style position or color of a portion of the text within a text region first select the text Then choose Text from the Format menu to open the Text Format dialog box or right click and choose Font from the menu Text Format Font style Regular FETE Arial Black Italic O Arial Narrow Bold Arial Rounded MT Boh Bold Italic Arial Unicode MS Baskerville Old Face Bauhaus 93
61. age 34 e Use the vectorize operator to perform the same operation on each element of a vector or matrix individually 42 Chapter 5 Range Variables and Arrays Note Mathematical notation often shows repeated operations with subscripts For example to define a matrix P by multiplying corresponding elements of the matrices M and N you write Pi Miz Nij Note that this is not matrix multiplication but multiplication element by element It is possible to perform this operation in Mathcad using subscripts but it is faster to perform the same operation with a vectorized equation The notation is also more compact To apply the vectorize operator to an expression like M N 1 Select the expression by clicking inside it and pressing Space until the right hand side is surrounded by the editing lines P MN 2 Click fM on the Matrix toolbar to apply the vectorize operator an Mathcad puts an arrow over the top of the selected expression P MUN For example suppose you want to apply the quadratic formula to three vectors containing coefficients a b and c Figure 5 8 shows how to use the vectorize operator The vectorize operator appearing as an arrow above the quadratic formula in Figure 5 8 is essential in this calculation Without it Mathcad would interpret a c as a vector dot product and also flag the square root of a vector as illegal But with the vectorize operator both a c and the square root are p
62. an E book into your Mathcad worksheet e You can select text or equations then copy and paste them into your worksheet 16 Chapter 3 Online Resources e You can drag regions from the E book window into your worksheet Select the regions click and hold down the mouse button over one of the regions while you drag the group into your worksheet then release the mouse button Web Browsing Help Note You can also use the Resources window to browse to any location on the Web and open Web pages in addition to Mathcad worksheets and E books posted on the Web When the Resources window is in Web browsing mode Mathcad is using a Web browsing OLE control provided by Microsoft Internet Explorer To browse to any Web page from within the Resources window 1 Click i on the Resources toolbar An additional toolbar with an Address box appears below the Resources toolbar In the Address box type a Uniform Resource Locator URL for a document on the Web To visit PlanetPTC for example type http communities ptc com community mathcad and press Enter 2 Ifyou do not have a supported version of Microsoft Internet Explorer installed you must launch a Web browser The remaining buttons on the Web toolbar have the following functions Button Function Bookmark submenu add or edit bookmarks or open a bookmarked page Reload the current page E3 Interrupt the current file transfer
63. ange variable in a subscript 38 Chapter 5 Range Variables and Arrays Accessing Rows and Columns Although you can use a range variable to access all the elements in a row or column of an array Mathcad provides a column operator for quickly accessing all the elements inacolumn Click t on the Matrix toolbar for the column operator Figure 5 4 shows how to extract the third column of the matrix M 145 5 2 D 6 6 Figure 5 4 Extracting a column from a matrix Note ORIGIN is 0 Thus the superscript 2 refers to the third column of the matrix M To extract a single row from a matrix transpose the matrix using the transpose operator click 4 on the Matrix toolbar and then extract a column using the column operator This is shown on the bottom of Figure 5 4 Changing the Array Origin When you use subscripts to refer to array elements Mathcad assumes the array begins at the current value of the built in variable ORIGIN By default ORIGIN is 0 but you can change its value See Built in Variables on page 75 for details Figure 5 5 shows a worksheet with the ORIGIN set to 1 If you try to refer to the zeroth element of an array in this case Mathcad displays an error message 2 7 ORIGIN 1 Me 2 4 6 36 9 This array index is invalid For thi Va 1 1 We 3 J Figure 5 5 Arrays beginning at element one instead of at element zero Since the ORIGIN is set to 1 there is no longe
64. ariables Calculation Display Array Origin ORIGIN a m Convergence Tolerance TOL o oo 0 001 Constraint Tolerance ETOL 0 001 Seed value For random numbers il PRN File Settings Precision PRNPRECISION Column Width PRNCOLWIDTH Restore Defaults cane Heh You can enter new values for any of these variables Then choose Calculate gt Worksheet from the Tools menu to ensure that all existing equations use the new values The numbers in brackets to the right of the variable names represent the default values for those variables Evaluating Expressions Numerically To evaluate an expression numerically 1 Type an expression containing any valid combination of numbers variables and functions Any variables or functions should be defined earlier in the worksheet ha my 2 Press the key or click on the Calculator toolbar j Mathcad computes the value of the expression and shows my 507 1008 it after the equal sign Tip Whenever you evaluate an expression Mathcad shows a final placeholder at the end of the equation This placeholder is for unit conversions as explained in Working with Results on page 88 As soon as you click outside the region Mathcad hides the placeholder Defining and Evaluating Variables 77 Figure 8 1 shows some results calculated from preceding variable definitions ev 130 435 EE 567 108 Figure 8 1 Calculations for mot
65. arrow cursor changes to a hand cursor when you hover over any hyperlink When you select text Mathcad underlines the text to show a hyperlink Next specify the target worksheet 1 Choose Hyperlink from the Insert menu Mathcad opens the Insert Hyperlink dialog box Hyperlinks 67 2 Click Browse to locate and select the target worksheet You can also enter an Internet address URL Insert Hyperlink Link to file or URL Browse Enter or locate the path to the document you want to link to Thie can be an Internet address URAL a document on your hard dive ora document on your company s network C Display as pop up document Message that appears on the status line when mouse is over link 3 Check Use relative path for hyperlink to store the location of the target worksheet relative to the Mathcad worksheet containing the hyperlink You can move these files as long as you preserve their relative folder structure Note In order for Use relative path for hyperlink to be available you must first save the worksheet in which you are inserting the hyperlink 4 Check Display as pop up document if you want the target worksheet to open in a small pop up window 5 Enter a message to appear on the status line at the bottom of the window when the mouse hovers over the hyperlink To edit a hyperlink click the hyperlinked item and choose Hyperlink from the Insert menu Make any changes you wish in
66. arrow keys and multiple clicks of the mouse button For more information refer to the topic Selecting text in online Help Once you select text you can delete it copy it cut it check the spelling or change its font size style or color To select and move an entire text region or group of regions follow the same steps that you would use with math regions described in Regions on page 7 Greek Letters in Text Tip To type a Greek letter in a text region either e Click on the appropriate letter on the Greek toolbar To see this toolbar click cf on the Math toolbar or choose Toolbars gt Greek from the View menu or e Type the Roman equivalent of the Greek symbol and then press Ctr1 G For example to enter 0 press Ctr1 G Typing Ctr1 G after a letter in a math region also converts it to its Greek equivalent Changing the Width of a Text Region When you start typing in a text region the region grows as you type wrapping only when you reach the right margin or page boundary Choose Page Setup from the File menu to set the location of the right margin To set a width for your whole text region and have lines wrap to stay within that width as you type 1 Type normally until the first line reaches the width you want 2 Type a space and press Ctr1 Enter Text and Paragraph Properties 47 All other lines break to stay within this width When you add to or edit the text Mathc
67. as the color of any ambient light or directed lights shining on it This behavior is identical to the effect of light on object color in the real world Objects reflect and absorb light depending on their color For example a yellow ball reflects mostly yellow light and absorbs others It looks grayish under dim lighting green under blue lighting and bright yellow in bright lighting Light is controlled using the options on the Lighting page of the 3D Plot Format dialog box Online Help For details on the options available on the Lighting page click Help at the bottom of the dialog box Changing One 3D Plot to Another You can change almost any three dimensional plot into another kind of three dimensional plot by using the Display As options on the General tab in the 3D Plot 138 Chapter 12 3D Plots Format dialog box Figure 12 7 shows the same matrix displayed as three different plot types a Ta 29 0 29 Mi j sin 1 cos j i i 10 10 Surface Plot Scatter Plot a o i m ae Tami a spss a Se a THT rh Figure 12 7 The same data displayed in several different 3D plots Note Some three dimensional plots cannot be converted to other forms For example you cannot convert a vector field plot into any other kind of plot Annotations To add text or graphic annotation to a three dimensional plot just drag text or bitmaps directly onto the plot To edit a text annotation on a plo
68. axes See Formatting a 2D Plot on page 120 for how to modify these defaults Resizing a Graph To resize a plot click in the plot to select it Then move the cursor to a handle along the edge of the plot until the cursor changes to a double headed arrow Hold the mouse button down and drag the mouse in the direction that you want the plot s dimension to change Mathcad does not graph complex points To plot the real or imaginary part of a point or expression use the Re and m functions to extract the real and imaginary parts respectively If some points in a function or expression are valid and others are not Mathcad plots only the valid ones If the points are not contiguous Mathcad does not connect them with a line You may therefore see a blank plot if none of the points are contiguous To see the points format the trace to have symbols See Formatting a 2D Plot on page 120 Creating a Polar Plot To create a polar plot 1 Choose Graph gt Polar Plot from the Insert menu or click on the Graph toolbar 2 Fill in both the angular axis placeholder bottom center and the radial axis placeholder left center with a function expression or variable 3 Click outside the plot or press Enter Mathcad creates the plot over a default range using default limits Graphing Functions and Expressions 115 Graphing Functions and Expressions 2D QuickPlots A 2D QuickPlot is a plot created
69. back and forth between these two methods as the need arises Here s how to create the expression a using the first method 1 Press to create the exponent operator or click on the Calculator toolbar You see two placeholders The editing lines hold the exponent placeholder 2 Click in the lower placeholder and type a 3 Click in the upper placeholder and type hu Building Expressions 23 4 Click in the remaining placeholders and type x and y ahty To use the editing lines to create the expression a proceed as follows 1 Type a The editing lines hold the a indicating that a becomes the first al operand of the next operator you type 2 Press to create the exponent operator a becomes the first operand of the exponent The editing lines now hold another placeholder mu ca 3 Type x y in this placeholder aktyl Note that you can type the expression the same way you d say it out loud However even this simple example contains an ambiguity When you say a to the x plus y there s no way to tell if you mean a or a y Although you can always resolve ambiguities by using parentheses doing so can quickly become cumbersome A better way is to use the editing lines to specify the operands The following example illustrates this specification by describing how to create the expression a y instead of a 7 1 Enter a x as you did in the previous example Note
70. ber of decimal places 3 Decima menu or double click the result to open the Result Format dialog box ki C Show trailing zeros Show exponents in engineering Format Exponential threshold 4 P C Apply to symbolic results l Doo ow aS a 3 Change the desired settings See online Help for more details on the various settings in the dialog box To display a result with six decimal places increase Number of decimal places from 3 to 6 n 10 3 141593 x 10 al To redisplay a result using the worksheet default result format settings delete the equal sign and press again Working with Results 89 Note When the format of a result is changed only the appearance of the result changes in the Tip Online Help worksheet Mathcad continues to maintain full precision up to 17 decimal places internally for that result Use the round function if you wish Mathcad to calculate with fewer decimal places If you copy a result Mathcad copies the number only to displayed precision Setting Worksheet Default Format To change the default display of numerical results 1 Click in a blank part of your worksheet 2 Choose Result from the Format menu 3 Change the desired settings in the Result Format dialog box Mathcad changes the display of all results whose formats have not been explicitly specified You can also change the worksheet default by clicking on a particular result choosing Result from
71. browse to find it Modifying a Template To modify an existing template l 2 3 Choose Open from the File menu In the Files of type drop down list select Mathcad Templates Type the name of the template in the File name box or browse to locate it Worksheet templates are saved by default in the Template folder You may now edit the template just like any Mathcad worksheet Tip To modify the default template for a blank worksheet modify the template file Normal xmcet You may want to save the original Normal xmct elsewhere in case you need to retrieve it Note When you modify a template your changes affect only new files created from the modified template The changes do not affect any worksheets created with the template before the template was modified Rearranging Your Worksheet This section describes how to rearrange math images and text in your worksheets Note You can get an overall view of how your worksheet looks by choosing Zoom from the View menu or by clicking 100 on the Standard toolbar and choosing a magnification Or you can use the File gt Print Preview command Selecting Regions To select a single region for editing simply click it to see a selection rectangle around the region To select a single region for moving drag select it To select multiple regions l 2 Press and hold down the mouse Without letting go of the mouse move it to enclose everything you wan
72. cial drop down list and enter a value below You can also set indents using the text ruler Click in a paragraph and choose Ruler from the View menu Move the top or bottom markers in the ruler to set a different indent for the first line or move both markers to indent all the lines in the paragraph Bullets and Numbered Lists To begin the paragraph with a bullet select Bullets from the Bullets drop down list Select Numbers from the drop down list to have Mathcad number successive paragraphs in the region automatically Or click or onthe Formatting toolbar Alignment To align the paragraph at either the left or right edge of the text region or to center the text within the text region use the three alignment buttons in the Paragraph Format dialog box Or click one of the three alignment buttons on the Formatting toolbar Or Tab Stops To specify tabs click the Tabs button in the Paragraph Format dialog box to open the Tabs dialog box Enter numbers into the Tab stop position text box Click Set for each tab stop then click OK You can also set tab stops using the text ruler Click in a paragraph and choose Ruler from the View menu Click in the ruler where you want a tab stop to be A tab stop symbol appears To remove a tab stop click on the tab stop symbol hold the mouse button down and drag the symbol away from the ru
73. cted expression by parentheses wet k E 3 Press Space so that the editing lines hold the parentheses Cwt kz 4 Ifnecessary press the Insert key so that the vertical editing line switches to the left side Kw t k z 5 Now type the name of the function If the function is a built in function you can choose Function from the Insert menu or click ffs on the Standard toolbar and double click the cos w t k z name of the function Defining and Evaluating Functions Note You define a function in much the same way as you define a variable The name goes on the left followed by a definition symbol then an expression on the right The main difference is that the name includes an argument list The example below shows how to define a function called dist x y that returns the distance between the point x y and the origin To make a function definition 1 Type the function name dist 2 Typea left parenthesis followed by one or more names separated by commas Complete this argument list by typing a right parenthesis dist x y It makes no difference whether or not the names in the argument list have been defined or used elsewhere in the worksheet What is important is that these arguments must be names They cannot be more complicated expressions 3 Press or click on the Calculator toolbar to enter ist x y m the definition symbol 4 Type an expression to
74. d exporting Mathcad files in RTF for Microsoft Word HTML for distribution to non Mathcad audiences The Developer s Reference describes using and developing custom Scriptable Object components and Custom Controls The Developer s Reference guides advanced users through Mathcad s Object Model allowing access to Mathcad functionality from another application or OLE container It also explains how to create your own functions in Mathcad in the form of DLLs Resources Window and E books If you learn best from examples want information you can put to work immediately in your Mathcad worksheets or wish to access any page on the Web from within Mathcad open the Resources toolbar or open Tutorials QuickSheets or Reference Tables from the Help menu The Resources window and Mathcad E books appear as custom windows with their own menus and toolbar as shown in Figure 3 1 13 14 Chapter 3 Online Resources f Inside Mathcad Solving and Optimization T 5 File Edit wiew Insert Format Tools Symbolics Book Help oe fe alk H VS s INSIDE MATHCAD TaS SOLVING AND OPTIMIZATION This module introduces Mathcad methods for solving and optimization since different problems require different tools this book covers identifying the type of problem choosing appropriate Mathcad functions for the problem using the appropriate Mathcad functions correctly interpreting the solutions Figure 3 1 E book window and toolbar A
75. d linear axes no grid lines and points connected with solid lines You can change these characteristics by formatting the graph To format the graph you just created l Double click the graph to bring up the Formatting dialog box To learn more about these settings see Chapter 11 2D Plots Click the Traces tab Double click trace 1 in the table cell under Legend Label Type a name for the trace for example Displacement Click the table cell in the Line column and choose a dotted line Choose a line weight of 3 from the next column and the color blue in the Color column Uncheck the Hide Legend check box and select the Bottom left position for the legend Click OK Mathcad shows the graphasa diti dotted line Note thatthe sample line under the d t now reflects the new formatting as does the legend 1600 1400 1200 H 1000 Click outside the graph to deselect it 12 Chapter 2 Getting Started with Mathcad Saving Printing and Exiting After you ve created a worksheet the next step is to save or print it Saving a Worksheet To save a worksheet 1 Choose Save from the File menu Ctr1 S Ifthe file has never been saved before the Save As dialog box appears 2 Type the name of the file in the text box provided To save to another folder locate the folder using the Save As dialog box By default Mathcad saves the file in a native Mathcad fo
76. define the function The expression can contain a name or any previously defined disti y3 4 roe ye functions and variables Once you have defined a function you can use it anywhere below and to the right of the definition Defining and Evaluating Functions 83 When you evaluate an expression containing a function as shown in Figure 8 5 Mathcad 1 evaluates the arguments you place between the parentheses 2 replaces the dummy arguments in the function definition with the actual arguments you place between the parentheses 3 performs the computation specified by the function definition 4 returns the result as the value of the function L5 dist x y ar yf Yes 4 dist fany any gt any Yael dist x1 y1 1 5 distix2 y2 5 dist 43 ys 1 414 Figure 8 5 A user defined function First define the points Next define the function to compute distances to the origin Then insert arguments Note As shown in Figure 8 5 if you type only the name of a function without its arguments Mathcad returns the type signature of the function In this case the function takes two arguments of the same units see Units and Dimensions on page 84 and returns a result with the units of the arguments Any unit is allowed here hence the term any The arguments of a user defined function can represent scalars vectors or matrices For example you could define the distance function as dist v V
77. down from 10 to 1 Ifthe third number in the range definition is not an even number of increments from the starting value the range does not go beyond it For example if you define k 10 20 65 then k takes values 10 20 30 60 Note You can use arbitrary scalar expressions in range definitions However these values must always be real numbers Built in Functions Mathcad provides a large set of built in functions To insert a function 1 Click in a blank area of your worksheet or on a placeholder Defining and Evaluating Variables 81 2 5 Choose Function from the Insert menu or click 9 on the Standard toolbar to open the Insert Function dialog box Insert Function Function Category Bessel Comples Numbers Curve Fitting and Smoothing Data Analysis Differential Equation Soling Expression Type Returns the angle in radians whose cosine is z Principal value for complex z Choose a Function Category or click All to see all functions sorted alphabetically Double click the name of the function you want to insert from the right hand list or click Insert The function and placeholders for its arguments are inserted into the worksheet Fill in the placeholders To apply a function to an expression you have already entered select the expression and follow the steps given above See Chapter 4 Working with Math You can also type the name of a built in functio
78. dynamically connecting Mathcad and other applications see Accessing External Files and Applications in online Help Chapter 11 2D Plots Overview of 2D Plotting Graphing Functions and Expressions Plotting Vectors of Data Formatting a 2D Plot Modifying a 2D Plot s Perspective gt gt gt gt gt Animations Overview of 2D Plotting To visually represent a function or expression of a single variable or vectors of data in Mathcad you can create either a Cartesian X Y plot or a polar plot A typical polar plot shows angular values O versus radial values r Figure 11 1 shows several examples of 2D plots X Y plot of a function X Y plot of data vectors yty i 5 Z Polar plot r 6 38 sings O costs Figure 11 1 Examples of 2D plots 113 114 Chapter 11 2D Plots Creating an X Y Plot Note Note To create an X Y plot 1 Choose Graph gt X Y Plot from the Insert menu click on the Graph toolbar or type Mathcad inserts a blank X Y plot d 2 Fill in both the x axis placeholder bottom center and the y axis placeholder left center with a function expression or variable a 3 Click outside the plot or press Enter Mathcad automatically chooses axis limits To specify the axis limits click in the plot and type over the numbers in the placeholders at the ends of the
79. e Area gt Unlock from the Format menu 3 You will be prompted for a password if it is required To expand a collapsed area 1 Double click the collapsed boundary line Worksheet References 65 Note When you lock an area without a password anyone can unlock it by simply choosing Area gt Unlock from the Format menu Deleting an Area Delete an area just as you would any other region 1 Make sure the area is unlocked You cannot delete a locked area 2 Select either of the two boundary lines of the area by dragging the mouse across it 3 Choose Cut from the Edit menu or press Delete Copying and Pasting Locked Areas Mathcad allows locked areas to be copied and pasted into new documents The pasted area remains locked with the same password and timestamp information but can be transferred into any new Mathcad worksheet To do so first click on an area boundary to select it then copy and paste as you would for any region Worksheet Protection Online Help When distributing a worksheet you may wish to restrict user access to most regions Rather than locking an area you may opt instead to protect your worksheet Mathcad provides three levels of worksheet protection allowing you to prevent users from changing only certain regions or all regions in the worksheet For more information see Protecting Your Worksheets in online Help or Hiding Content and Protecting Your Worksheets in the Tutorials Wor
80. e Greek toolbar or type the equivalent Roman letter and press Ctr1 G See Greek Letters on page 20 e The infinity symbol Insert it by clicking on the Calculus toolbar or by typing Ctrl Shift Z e The following are examples of valid names alpha b xyz700 Al B2 C3 D4 F1 abx Mathcad distinguishes between uppercase and lowercase letters For example diam is a different variable from DIAM Mathcad also distinguishes between names in different fonts as discussed in Math Styles on page 29 Thus Diam is also a different variable from Diam See Variable and Function Names in online Help for restrictions and other details for names in Mathcad Defining and Evaluating Variables 75 Tip Literal Subscripts If you include a period in a variable name Mathcad displays whatever follows the period as a subscript You can use these iteral subscripts to create variables with names like vel and u To create a literal subscript 1 Type the text that appears before the subscript vell 2 Type a period followed by text that is to become the subscript vel init Do not confuse literal subscripts with array subscripts which you generate with the left bracket key or by clicking on the Matrix toolbar They appear similar but behave quite differently in computations A literal subscript is simply a cosmetic part of a variable name An array subscript rep
81. e drop down list in the Equation Format dialog box You can apply a variety of math styles to e individual variable names in an expression or e individual numbers in a math expression but not in computed results which always display in the Constants style For example you may want to show vectors in a bold underlined font 1 Choose Equation from the Format menu 2 Click the down arrow beside the name of the current math styles to see a drop down list of available math styles Equation Format 3 Click on a math style name like User 1 to i ae select it The name User 1 should now halal lens appear in the New Style Name text box Click in this text box and change the name EEG ue to Vectors 4 Click Modify to change this style to a Default Equation Color bold underlined font Math Styles 31 Now you have a math style called Vectors with the desired appearance Now rather than individually changing the font font size and font style for names of vectors you can simply change the math style for all vectors Note All names whether function names or variable names are style sensitive This means that x and x refer to different variables and f x and f x refer to different functions In deciding whether two variable names are the same Mathcad actually checks math styles rather than fonts To avoid using distinct variables that look identical don t create a math style
82. e value of a Since a is not an argument of f the value of f depends on the value of a only at the point where f is defined If you want a function to depend on the value of a variable you must include that variable as an argument If not Mathcad just uses that variable s fixed value at the point in the worksheet where the function is defined Recursive Function Definitions Mathcad supports recursive function definitions you may define the value of a function in terms of a previous value of the function As shown in Figure 8 7 recursive functions are useful for defining arbitrary periodic functions as well as implementing numerical functions like the factorial function Note that a recursive function definition should always have at least two parts e An initial condition that prevents the recursion from going forever Units and Dimensions 85 e A definition of the function in terms of some previous value s of the function A simple recursive function definition factorial n iffms0 1 n factorial n 14 factorial 5 120 Using recursion to define a periodic sawtooth wave fix c 2x period 2 hesi ifi lt period fi hts period 0 01 10 5 VAVAVAA U5 2 4 6 F ki Figure 8 7 Mathcad allows recursive function definitions Note Ifyou do not specify an initial condition that stops the recursion Mathcad generates a stack overflow error message when you try to evaluate the functi
83. ear in this document The software described in this document is provided under written license agreement contains valuable trade secrets and proprietary information and is protected by the copyright laws of the United States and other countries It may not be copied or distributed in any form or medium disclosed to third parties or used in any manner not provided for in the software licenses agreement except with written prior approval from PTC UNAUTHORIZED USE OF SOFTWARE OR ITS DOCUMENTATION CAN RESULT IN CIVIL DAMAGES AND CRIMINAL PROSECUTION PTC regards software piracy as the crime it is and we view offenders accordingly We do not tolerate the piracy of PTC software products and we pursue both civilly and criminally those who do so using all legal means available including public and private surveillance resources As part of these efforts PTC uses data monitoring and scouring technologies to obtain and transmit data on users of illegal copies of our software This data collection is not performed on users of legally licensed software from PTC and its authorized distributors If you are using an illegal copy of our software and do not consent to the collection and transmission of such data including to the United States cease using the illegal version and contact PTC to obtain a legally licensed copy Important Copyright Trademark Patent and Licensing Information See the About Box or copyright notice of your PTC software UN
84. eater than 999 do not use either a comma or a period to separate digits into groups of three Simply type the digits one after another For example to enter ten thousand type 10000 Imaginary and Complex Numbers To enter an imaginary number follow it with 7 or j as in 1i or 2 57 You cannot use i or j alone to represent the imaginary unit You must always type 1i or 13 Otherwise Mathcad thinks you are referring to a variable named either i or 7 When the cursor is outside an equation that contains 1i or 1j however Mathcad hides the 1 Mathcad normally displays imaginary numbers followed by 7 To have Mathcad display imaginary numbers with j choose Result from the Format menu click on the Display Options tab and set Imaginary value to j J See Formatting Results on page 88 for a full description 19 20 Chapter 4 Working with Math Mathcad accepts complex numbers of the form a bi or a bj where a and b are ordinary numbers Exponential Notation To enter very large or very small numbers in exponential notation just multiply a number by a power of 10 For example to represent the number 3 108 type 3 1048 Greek Letters There are two ways to enter a Greek letter e Click the letter on the Greek toolbar Click on the Math toolbar or choose Toolbars gt Greek from the View menu e Type the Roman equivalent of the Greek symbol and then press Ctr1 G For example to e
85. eb at Maintenance users http www ptc com appserver cs search search jsp Single users https www ptc com appserver cs view kdb jsp Mathcad Downloads on the PTC Web Site Users can download additional software from the Free Downloads section of the PTC Web site at http www ptc com community free_downloads htm Items that are locked are only available for maintenance users Chapter 4 Working with Math Inserting Math Building Expressions Editing Expressions Math Styles gt gt OD Inserting Math You can place math expressions anywhere you want in a Mathcad worksheet 1 Click to place the crosshair 2 Type numbers letters and math operators or insert 7 them by clicking buttons on Mathcad s math toolbars 15 14 923 to create a math region 104 5 Mathcad by default understands anything you type at the crosshair cursor as math If you want to create a text region instead see Chapter 6 Working with Text You can also type math expressions in any math placeholder that appears Numbers and Complex Numbers Note Note A single number in Mathcad is called a scalar To enter groups of numbers in arrays see Inserting an Operator on page 20 Types of Numbers Anything beginning with a digit is interpreted as a number by Mathcad As a general rule you enter numbers by simply typing the digits from the keyboard using a period as the decimal point When you enter numbers gr
86. efining data for a contour plot The contour plot is a visual representation of the matrix s level curves Mathcad assumes that the rows and columns represent equally spaced intervals on the axes then linearly interpolates the values of this matrix to form level curves or contours Each level curve is formed such that no two cross By default the z contours are shown on the x y plane Mathcad plots the matrix such that the element in row 0 and column 0 is in the lower left corner Thus the rows of the matrix correspond to values on the x axis increasing to the right and the columns correspond to values along the y axis increasing toward the top Online Help For information on formatting a contour plot see Contour Plots in online Help Graphing Multiple 3D Plots You can place more than one surface curve contour bar or scatter plot on a three dimensional graph For example to create a 3D graph with a contour plot and a surface plot 1 Define two functions of two variables or any combination of two acceptable argument sets for a 3D plot two matrices two sets of three vectors and so on 2 Choose Graph gt Contour Plot from the Insert menu Formatting a 3D Plot 135 3 Enter the name of the function or matrix for the contour plot into the placeholder Then type comma 4 Enter the name of the function or matrix for the surface plot 5 Press Enter to see two contour plots 6 Double click the graph
87. elect Bar Plot Contour Plot or Data Points from the array of plot types Figure 12 1 shows a 3D scatter plot created from the function G and a contour plot created from the function F both defined above Figure 12 1 A scatter plot and a contour plot created from functions of two variables Note All 3D QuickPlots are parametric curves or surfaces In other words all QuickPlots are created from three vectors or matrices of data representing the x y and z coordinates of the plot In the case of a single function of two variables Mathcad internally creates two matrices of x and y data over the default range 5 to 5 with a step size of 0 5 and then generates z data using these x and y coordinates 130 Chapter 12 3D Plots To change the default ranges and grids for the independent variables double click on the graph and select the QuickPlot Data tab on the 3D Plot Format dialog Creating a Space Curve You can visualize any parametrically defined function of one variable as a scatter plot in three dimensions Step 1 Define a function or set of functions First define the function in your worksheet in one of the following forms sin u Riuj 2 u Hi uj cosu Stuy Ta singu cos uy Thuy costu Hu is a vector valued function of one variable R u S u and T u are functions of one variable Note A space curve often represents the path of a particle in motion through space where u is a
88. elpful You can find these resources in the Mathcad Resources window under the Help menu Tutorials include introductory Primers and more extended tutorials e QuickSheets are sample Mathcad worksheets that you can revise for your own use e Online Help provides more extensive details on features and functions Other Resources We provide other resources for learning about Mathcad e Mathcad Community on PlanetPTC where current users answer many questions You can also download E books and Mathcad files The Mathcad community is available at http communities ptc com community mathcad e Updates to the documentation from the References Document section of the PTC Web site Technical Support Contact PTC Technical Support if you encounter problems using the software Contact information for PTC Technical Support is available on the PTC Customer Support Site http www ptc com support Information and a knowledge base of technical support information for Mathcad single users 1s available at http www ptc com support mathcad htm Comments We welcome your suggestions and comments on Mathcad documentation You can submit your feedback to mathcad documentation ptc com Chapter 1 Welcome to Mathcad What Is Mathcad What Is Mathcad Mathcad is the industry standard technical calculation tool for engineers worldwide Mathcad delivers all the solving capabilities functionality and robustness needed for calculation
89. er JPEG or PNG PNG is a lossless format and may result in clearer images for graphs and drawings while JPEG format may create Distributing Your Worksheets 71 Note smaller files or be more compatible with older browser versions All graphs embedded images tables and equations are displayed as images in the output HTML document For further instructions and tips on publishing Web sites with Mathcad see the online Author s Reference under the Help menu in Mathcad Finally you can choose a new title for your page then open the page immediately in your default Web browser You can also save Mathcad documents in HTML by choosing Save As from the File menu and selecting HTML File htm from the Save as type drop down list Options for HTML can be set by choosing Preferences from the Tools menu and modifying choices on the HTML Options tab When you save a Mathcad worksheet in HTML format an HTM file is created plus a folder with the name filename images that contains all the associated image files When copying files to your server don t forget to include the associated image folder Saving Your Worksheet to Microsoft Word Mailing Tip Tip To save a worksheet so you can distribute it in Microsoft Word 1 Scroll to the bottom of your worksheet to update all calculated results or choose Calculate gt Calculate Worksheet from the Tools menu or press Ctr1 F9 2 Choose Save As fr
90. er numbers into the cells Each row must have the same number of columns If you do not enter a number into a cell Mathcad inserts 0 Figure 5 2 shows two data tables Notice that when you create a data table you re actually assigning elements to an array that has the name of the variable you assigned H meani H 5 284 meani 120 140 120 k 68 100 73 5 5 2 5 4 5 6 H Figure 5 2 Using data tables to create arrays of data When you click the table you can edit the values in it using the scroll bars To resize the table move the cursor to one of the handles along the sides of the region so that the cursor changes to a double headed arrow Press and hold down the mouse button and drag the cursor to change the table s dimensions A data table can be used to import from a data source or another application containing data Right click on the top left corner and choose Import from the menu The imported data can be edited in Mathcad as described above You can copy data from a data table as follows first select the data then right click on the data table and choose Copy from the menu You can paste a single number into the table by right clicking a cell and choosing Paste from the menu Choosing Paste Table from the menu overwrites the entire table Accessing Array Elements 37 Accessing Array Elements Subscripts Note Tip You can access all the elements of an array simply by using its variable name
91. erformed element by element 1 3 2 1 2 1 3 b C 2 1 1 2 o 1 er i aE i x i R ae 0 25 D 66li 0 707i las bee c moO oO A A Figure 5 8 Quadratic formula with vectors and the vectorize operator First set up the three coefficients Then compute a root The result should be zero While vectorization is faster than element by element operations for those operations which require it it will be slower than natively vectorized operations Many operations are already performed on an element by element basis such as the addition of two arrays For such operations adding an unnecessary vectorization operator will give the same result but much more slowly Working with Arrays 43 Graphical Display of Arrays In addition to looking at the actual numbers making up an array you can also see a graphical representation of those same numbers There are several ways to do this e For an arbitrary array you can use the various three dimensional plot types discussed in Chapter 12 3D Plots e For an array of integers between 0 and 255 you can look at a grayscale image by choosing Picture from the Insert menu and entering the array s name in the placeholder e For three arrays of integers between 0 and 255 representing the red green and blue components of an image choose Picture from the Insert menu and enter the arrays names separated by commas in the placeholder See Chapter 10
92. erline the horizontal editing line e Unless the equation you ve clicked in has an operator in it already pressing Space turns the math region into a text region It is not possible to turn a text region back into a math region Controlling the Editing Lines Click in an expression e To move the blue insertion line from one side of the expression to the other press Insert e Use the left and right arrow keys to move the vertical editing line one character at a time If your expression contains built up fractions you can also use the up and down arrow keys e Press Space to select larger parts of the expression Each time you press Space the editing lines enclose more and more of the expression until they enclose the entire expression Pressing Space one more time brings the editing lines back to where they started Tip Youcan drag select parts of an expression to work on them The selected part is highlighted with a dark background Whatever you type next overwrites the highlighted part 22 Chapter 4 Working with Math The following example walks you through a short cycle of using Space 1 The two editing lines hold just the single variable d a 2 Pressing Space makes the editing lines grow to hold the entire a b denominator d 3 Pressing Space again makes the editing lines grow so that they now a b hold the entire expression wad 4 At this point the editing lines can t bec
93. erlinks gt gt gt OH gt Distributing Your Worksheets Worksheets and Templates As you use Mathcad you create a worksheet file Mathcad uses XMCD as the file extension for worksheets When you create a new worksheet in Mathcad you can start with Mathcad s default choices or you can use a template that contains customized formats Mathcad comes with a variety of predefined templates You can extend this set by saving any of your Mathcad worksheets as a new template Creating a New Worksheet When you first open Mathcad or click on the Standard toolbar you see an empty worksheet based on the worksheet template Normal xmct You can enter and format equations graphs text and images in the worksheet as well as modify worksheet attributes such as numerical format headers and footers and text and math styles To create a new worksheet based on a template 1 Choose New from the File menu Mathcad displays a list of available worksheet templates Mue LETTPIEVES Blank Worksheet 2 Choose a template other than Calculation Form Blank Worksheet By default creel Mathcad displays worksheet Microsef word templates saved in the Template PEDOT a Specification Form folder within the Mathcad Table of Contents Web Page program folder Click Browse to find a template in another folder 55 56 Chapter 7 Mathcad Worksheets Opening a Worksheet Open an existing worksheet by choosi
94. ertain regions stand out by highlighting them with a colored background 1 Click in a region or select multiple regions 2 Choose Properties from the Format menu 3 Click the Display tab 4 Check Highlight Region Click Choose Color to choose a highlight color other than the default choice Mathcad colors the background of the region Changing the Worksheet Background Color To change the color of the background of your entire worksheet 1 Choose Color from the Format menu 2 Choose Background to see the colors you may choose from Layout Before printing a worksheet you may want to adjust the margins paper options page breaks and headers and footers Setting Margins Paper Size Source and Orientation Mathcad worksheets have user specifiable margins at the left right top and bottom of the worksheet To set these margins choose Page Setup from the File menu Use the four text boxes in the lower right of the Page Setup dialog to specify the distances from the margin to the corresponding edge of the actual sheet of paper You can also use Page Setup settings to change the size source or orientation of the paper See Printing on page 68 for more about printing your Mathcad worksheets 62 Chapter 7 Mathcad Worksheets Tip Page Breaks Tip To use the margin and other page setup settings from the current worksheet in new worksheets save the worksheet as a template as described in Creatin
95. from 0 to 15 aq 1 41 Z 3 10 ay SO 11 122 215 226 Figure 8 4 Using a range variable to define the values of a vector 80 Chapter 8 Calculating in Mathcad Tip Mathcad takes longer to compute equations with ranged expressions since there may be many computations for each equation While Mathcad is computing the mouse pointer changes its appearance See Interrupting Calculations on page 93 Types of Ranges The definition ofj in the previous section ranging from 0 to 15 is an example of the simplest type of range definition But Mathcad permits range variables with values ranging from any number to any other number using any constant increment or decrement To define a range variable with a step size other than 1 type an equation of the form k 1 1 1 2 It appears in your worksheet window as k 1 1 1 2 In this range definition e The variable k is the name of the range variable itself e The number 1 is the first value taken by the range variable k e The number 1 1 is the second value in the range Note that this is not the step size The step size in this example is 0 1 the difference between 1 1 and 1 If you omit the comma and the 1 1 Mathcad assumes a step size of one in whatever direction up or down is appropriate e The number 2 is the last value in the range In this example the range values are constantly increasing If instead you had defined k 10 1 then k would count
96. from an expression or function that represents the y coordinates of the plot Mathcad automatically creates a plot over a default domain for the independent variable from 10 to 10 for an X Y plot and 0 to 360 for a polar plot To create an X Y QuickPlot of a single expression or function 1 Type the expression or function of a single variable you want to plot Click in the expression 1 2 Choose Graph gt X Y Plot from the Insert Zita d menu 3 Click outside the graph or press Enter oir 10 To change the default domain for the independent variable in a 2D QuickPlot change the axis limits on the plot Defining an Independent Variable You can set your own range by defining the independent variable as a range variable before creating the plot 1 Define a range variable See Range Variables on page 79 2 Enter the expression or function you want w O01 2a to plot using that variable Click in the expression 1 3 Choose Graph gt X Y Plot from the Insert menu sinis Oo 4 Type the name of the variable into the x axis placeholder 5 Click outside the graph or press Enter Mathcad plots one point for every value of the range variable and unless you specify otherwise connects each pair of points with a straight line To smooth out the curve make the step size of the range variable smaller 116 Chapter 11 2D Plots Plotting Multiple 2D Curves You can graph several traces on the sa
97. g a New Mathcad Template on page 56 Mathcad provides two kinds of page breaks e Soft page breaks Mathcad uses your default printer settings and your top and bottom margins to insert these page breaks automatically You can see these dotted horizontal lines as you scroll down in your worksheet You cannot add or remove soft page breaks e Hard page breaks You can insert a hard page break by placing the cursor and choosing Page Break from the Insert menu Hard page breaks display as solid horizontal lines in your worksheets To move or delete a hard page break 1 Drag select the hard page break as you would select any other region in your Mathcad worksheet A dashed selection box appears around the page break 2 Choose Delete from the Edit menu or press the Delete key 3 To move the page break just drag it to a new position or delete and reenter Any region that overlaps a soft or hard page break prints by default in pieces on successive pages To separate a region from a hard page break choose Separate Regions from the Format menu However this command does not separate regions from overlapping soft page breaks Choose Repaginate Now from the Format menu to force Mathcad to move soft page breaks above any region that would print in pieces on successive pages Headers and Footers To add or modify headers or footers choose Header and Footer from the View menu Header and Footer Header Footer Left Center a ae
98. g in Mathcad gt gt gt gt gt Defining and Evaluating Variables Defining and Evaluating Functions Units and Dimensions Working with Results Controlling Calculation Error Messages Defining and Evaluating Variables Variables allow you to define values to be used to evaluate expressions and solve equations Defining a Variable A variable definition defines the value of a variable everywhere below and to the right of the definition To define a variable l 2 Type the variable name KE Press the colon key or click on the Calculator toolbar The definition symbol appears with a blank placeholder to KE af the right Type an expression to complete the definition This expression can include numbers and any previously defined variables and KE 1 082 functions The left hand side of a can contain any of the following A simple variable name like x A subscripted variable name like v xX A matrix whose elements are either of the above For example This technique Y allows you to define several variables at once each element on the right hand side is assigned simultaneously to the corresponding element on the left hand side A function name with an argument list of simple variable names For example fix y z Names are described further in the next section A superscripted column matrix name like M 73 74 Chapter 8 Calc
99. guments with Keywords Many keywords take additional arguments that control the operations performed by the keyword For example the keyword series returns the Taylor series of a function By default series returns the terms of the series of order less than 6 which means that the highest power of x that is displayed is x You can change the number of terms returned by adding arguments after series For example to return the terms of the Taylor series for e of order less than 3 1 Type e Press to create a placeholder for El the exponent x e 2 Press Ctr1 Shift period e gt 3 Type series in the placeholder followed by a comma e series a 3 4 Type x in the placeholder to specify the variable followed by a comma e series x a 5 Type 3 in the placeholder to return only the terms of order less than 3 e series x 3 gt j Live Symbolic Evaluation 145 1 6 Press Enter e series 4 3 G1 1 Using More Than One Keyword You can apply several symbolic keywords to a single expression by two different methods To apply several keywords and see the results from each 1 Enter the expression you want to evaluate followed by the first keyword and any comma delimited arguments for the keyword See Using Arguments with Keywords on page 144 2 Press Enter for the first result e series x 3 314 1 4 De 2 3 Click on the result and press Ctr1
100. heet you cannot use the built in unit m for meters anywhere below that definition However Mathcad automatically displays the unit m in any results involving meters Mathcad will warn you if you redefine a built in unit by underlining the redefinition with a wavy green line Fahrenheit and Celsius temperature units as well as decibels and other scalings are not multiplicative These scaling functions are defined in Mathcad and can be used in the units placeholder or in the Postfix Operator on the left hand side of an expression to create conventional unit notation The functions have defined inverses so can also be used in the unit placeholder See the QuickSheet Custom Operators within Mathcad Techniques and Temperature Units and User Defined Default Units within the Features In depth section of the Mathcad Tutorials for samples of temperature scale calculations Working with Results Formatting Results The way that Mathcad displays answers is called the result format You can set the result format for a single calculated result or for an entire worksheet Setting the Format of a Single Result Numerically calculated results are formatted in a worksheet according to the worksheet default result format To modify the format for a single result 1 Click anywhere in the equation n 107 b 142x 107a Result Format Mumber Format Display Options Unit Display Tolerance Format 2 Choose Result from the Format Num
101. ich text format RTF saving to 71 ruler for formatting a worksheet 59 for formatting text 49 measurement system 49 Save As 56 RTF 71 Save as Web Page 70 save to Microsoft Word 71 saving new file 12 162 Index templates 56 57 worksheets 12 55 56 scalar 19 scatter plots 3D formatting 135 See also plots 3D scientific notation 89 scripting 3 search E book 15 in equations 52 in text 52 selecting math expression 21 26 page break 62 regions 57 text 46 selection rectangle 57 Separate Regions command 61 62 separating overlapping regions 60 62 simultaneous equations solving numerically 98 SmartSketch component 110 soft page breaks 62 solve blocks 98 constraints in 101 definition of 98 expressions allowed in 101 finding multiple solutions 102 103 Given in 99 tolerance 102 using to solve numerically 98 using to solve symbolically 152 solve keyword 150 151 solving equations 98 AutoSelect of algorithm 103 linear systems 103 nonlinear systems 103 See also solve blocks with root function 97 with solve blocks 98 152 with Solve for Variable 150 with solve keyword 150 space curves creating 130 See also plots 3D spaces inserting or deleting 60 spell check 53 setting language 54 squiggly green line 88 stack overflow error 84 step size for iteration 80 styles math 29 text 49 subscript button 48 subscripts in text 48 literal 75 non numeric 75 ORIGIN used with 38 start with zero 38 supersc
102. ific information on formatting see Surface Plots in online Help Creating a Three dimensional Parametric Curve A three dimensional parametric curve is created by passing three vectors representing the x y and z coordinates of your points in space to the surface plot To create a three dimensional parametric curve 1 Create or import three vectors having the same number of rows 2 Choose Graph gt Scatter Plot from the Insert menu 3 Type the names of the three vectors separated by commas and enclosed in parentheses in the placeholder Creating 3D Plots of Data 133 Figure 12 4 shows a three dimensional parametric curve created from the vectors P Q and R defined above the plot i 5 4 9 5 x i i104 50 Fyti caostl Qe i slnt2 1 Refi cost sing2 1 Figure 12 4 Defining data for a space curve Online Help For specific information on formatting see Scatter Plots in online Help Creating a Contour Plot To view three dimensional data as a two dimensional contour map you can create a contour plot 1 Define or import a matrix of values to plot 2 Choose Graph gt Contour Plot from the Insert menu to display a blank plot with a single placeholder 3 Type the name of the matrix in the placeholder 134 Chapter 12 3D Plots Figure 12 5 shows a contour plot created from the matrix C defined above the plot fix yi 075 6 Ci j fisi Yil maxi Ci Figure 12 5 D
103. in an E book are live so a reader can experiment directly within the book For details about each step of creating a Mathcad E book see the online Author s Reference under the Help menu It includes tips and techniques for turning a collection of worksheets into a navigable book After you have created an E book others can open it in Mathcad and navigate through it using the toolbar buttons of the E book window For more information on E books and the navigation tools refer to Chapter 3 Online Resources Creating Web Pages and Sites Mathcad worksheets can be output as HTML files for viewing in a Web browser There are a variety of options for specifying how worksheet regions are represented in HTML files All Mathcad text regions are output as standard HTML but you must choose the format in which you would like equations graphs and other types of regions to be stored on a Web page Choose Save as Web Page from the File menu to save a file in HTML format Once you have chosen a file name and location to store your file click Save and a dialog presents you with a set of options for saving your file Options for Web Page Output Save as Web Page Options Display options Save images as PNG C JPEG Quality Lise web page template Browse Page Options Title N File C Program Files Mathsofti Mathcad 14Han screen html View saved page in browser Cancel Choose a format for image export eith
104. ion at constant speed based on simple variable definitions How Mathcad Scans a Worksheet Mathcad scans a worksheet from left to right and top to bottom This means that a variable or function definition involving a affects everything below and to the right of it To see the placement of regions more clearly in your worksheet choose Regions from the View menu Mathcad displays blank space in gray and leaves regions in your background color Figure 8 2 shows examples of how placement of equations in a worksheet affects the evaluation of results In the first evaluation both x and y are highlighted Mathcad shows them in red on screen to indicate that they are undefined This is because the definitions for x and y lie below where they are used Because Mathcad scans from top to bottom it doesn t know the values of x and y when it gets to the first equation The second evaluation on the other hand is below the definitions of x and y By the time Mathcad gets to this equation it has already assigned values to both x and y This variable is undefined Figure 8 2 Mathcad evaluates equations from top to bottom in a worksheet You must define variables above the place where you use them 78 Chapter 8 Calculating in Mathcad Note You can define a variable more than once in the same worksheet Mathcad simply uses the first definition for all expressions until the variable is redefined then uses the new definition G
105. iting a Link Online Help If you ve inserted a linked object into a Mathcad worksheet you can update the link eliminate it or change the source file to which the object is linked To do so choose Links from the Edit menu See the online Help topic Links dialog box for information on each option in the dialog box Inserting Objects Computationally Linked to Your Worksheet If you want to insert an object that is computationally linked to your Mathcad worksheet you can insert a component A component is a specialized OLE object that can receive data from Mathcad and return data to Mathcad linking the object dynamically The SmartSketch component for example allows you to insert Inserting Objects Computationally Linked to Your Worksheet 111 SmartSketch drawings whose dimensions are computationally linked to your Mathcad calculations Depth 6 Amount of water in the ditch Roughness 0 013 Roughness coefficient Bottom 10 Width of the ditch at the bottom Slope 0 01 Slope of the ditch SideAngle 120 Side angle of the ditch Tw SLength Depth Bottom SideAngle Figure 10 1 The SmartSketch component inserted into a Mathcad worksheet An example using the SmartSketch component is shown in Figure 10 1 In addition to the SmartSketch component Mathcad includes several components for exchanging data with Excel and MATLAB Online Help For information on using components to import and export data as well as
106. k an entire worksheet l Choose Spelling from the Tools menu or click 4 on the Standard toolbar Check Spelling Mot Found Change Ta radios Adidas radars radish When Mathcad finds a misspelled word it opens the Check Spelling dialog box The misspelled word is shown along with suggested replacements If Mathcad does not have a suggestion it shows only the misspelled word After the Check Spelling dialog box appears Click Change to change the word to the suggested replacement or to another word that you can select from the list of possible replacements Type a new word into the Change to then click Change Click Ignore or Add to leave the word as is If you click Ignore Mathcad leaves the word alone continues spell checking and ignores all other occurrences of the word If you click Add the word is added to your personal dictionary 54 Chapter 6 Working with Text Foreign Language Spell Check Dictionaries You can load any of eleven different language dictionaries from the Language tab of the Preferences dialog under the Tools menu Under the Spell Check Dialect on the same tab you can choose three different English dialects two Portuguese dialects and two German dialects Chapter 7 Mathcad Worksheets Worksheets and Templates Rearranging Your Worksheet Layout Safeguarding an Area of the Worksheet Worksheet References Hyp
107. k in your preferred unit system or switch to another system for a particular set of equations Mathcad s powerful programming and scripting capabilities are not introduced in this introductory User s Guide Visit online Help the Programming tutorial and the Developer s Reference to learn how to program in Mathcad You can also download the E Book Inside Mathcad Programming from http communities ptc com community mathcad Mathcad provides online Tutorials QuickSheets of working examples of Mathcad functions and applications and Reference Tables with math science and engineering formulas These live worksheets are found under the Help menu or from the Resources toolbar Online Help includes the Author s Reference and Developer s Reference for more advanced usage Mathcad simplifies and streamlines documentation critical to communicating and to meeting business and quality assurance standards By combining equations text and 4 Chapter 1 Welcome to Mathcad graphics in a single worksheet Mathcad makes it easy to keep track of the most complex calculations By saving your worksheets in XML format you can reuse the information in other text based systems or search and report on worksheets without needing to reopen them in Mathcad Chapter 2 Getting Started with Mathcad The Mathcad Workspace Regions A Simple Calculation Definitions and Variables Graphs gt gt gt gt SH Saving Printing and Exiting
108. k through your worksheet To find the source of an error 1 Right click on the region showing the error and choose Trace Error from the menu or click on the region and choose Trace Error from the Trace Error Tools menu 2 Use the buttons in the Trace Error 3 dialog box to navigate through the ee ale regions associated with the region showing the error For example F x p1 Cs 10 click Previous to step back to the previous dependent region 3 Orclick First to jump to the region causing the error Fixing Errors Once you have determined which expression caused the error edit that expression to fix the error or change the variable definitions that led to the error Mathcad first recomputes the edited expression and then recomputes any expressions affected by the fixed expression Note When you define a function Mathcad does not try to evaluate it until you subsequently use it in the worksheet although it does compile and unit balance it If there is an error the use of the function is marked in error even though the real problem may lie in the definition of the function itself possibly much earlier in the worksheet Evaluating the function name and looking at its type signature may help debug the problem Chapter 9 Solving Mathcad supports many functions for solving a single equation in one unknown through large systems of linear nonlinear and differential equations with multiple unknowns The tech
109. ke an operator apply to an expression select the expression by placing it between the two editing lines The following examples show how typing c results in different changes depending on what you select first e The two editing lines hold only the numerator Any operator you a H type applies only to the numerator wad ee l a b q e Typing c applies the operation to the numerator only 4 e The editing lines hold the entire fraction Any operator you type a b applies to the entire fraction vd a b e c applies to the whole fraction I e The editing lines hold the entire fraction Og x a o va mu ZT e Typing c puts the c before the fraction because the blue insertion line was on the eft side I ao CL Deleting an Operator To delete an operator that connects two variable names or constants 1 Click after the operator ou a 2 Press Backspace or if the blue insertion line was before the operator press Delete ie You can then insert a new operator just by typing it in Fractions behave the same way Since we naturally say a over b putting the editing lines after the division bar means putting them just before the b Here s an example 1 Place the vertical editing lines after the division bar te me 2 Press Backspace To delete an operator having only one operand for example x x or x 1 Position the editing li
110. ksheet References Sometimes you want to use formulas and calculations from one Mathcad worksheet inside another Mathcad allows you to reference one worksheet from another that is to access the computations in a worksheet without opening it When you insert a reference to a worksheet you cannot see the formulas of the referenced worksheet but the current worksheet behaves as if you could To insert a reference to a worksheet 1 Click the mouse in a blank part of your worksheet The cursor should look like a crosshair 2 Choose Reference from the Insert menu Insert Reference Insert reference to file Browse Enter or locate the path to the document you want to reference This can be a document on your hard drive or a document on your company s network 66 Chapter 7 Mathcad Worksheets Note 3 Click Browse to locate and select a worksheet You can also enter an Internet address URL to insert a reference to a Mathcad file that is located on the Web To indicate that a reference has been inserted Mathcad pastes a small icon plus the path to the referenced worksheet All definitions in the referenced worksheet are available below or to the right of the icon If you double click the icon Mathcad opens the referenced worksheet in its own window for editing You can move or delete the icon just as you would any other Mathcad region Reference C Program Files Mathsoft Mathcad 14 gsheetiwelcome smed
111. le Authorable Button Bitmap Image Graphical Button Mathcad Document Media Clip C Display As Icon Microsoft Graph Chart Result Inserts a new Adobe Acrobat 7 0 Document aia object into your document Inserting Objects 109 To create a new object 1 Select an application from the Object Type list which shows applications you have installed 2 The source application opens so that you can create the object When you exit the source application the object you created becomes embedded in your Mathcad worksheet To insert an existing file 1 Click Create from File in the Insert Object dialog box Insert Object Create New File Create from File Result Inserts the contents of the file as an object into F pour document so that you may activate it using the program which created it 2 Type the path to the object file or click Browse to locate it 3 Check Link to insert a linked object Otherwise the object is embedded Pasting an Object into a Worksheet You can copy an object from a source application and paste it directly into Mathcad This method is particularly useful when you don t want to insert an entire file To insert an embedded or linked object into a worksheet by copying 1 Open the source application containing the object and copy it 2 Click in the Mathcad worksheet and choose Paste or Paste Special from Mathcad s Edit menu If you choose Pa
112. ler Tip To change the measurement system used in the Paragraph Format dialog box or in the text ruler choose Ruler from the View menu to show the text ruler Then right click the ruler and choose Inches Centimeters Points or Picas from the menu Text Styles Text styles give you an easy way to create a consistent appearance in your worksheets Rather than individually setting specific text and paragraph properties for each paragraph you can apply an available text style Every worksheet has a default Normal text style with a particular choice of text and paragraph properties You can modify existing text styles create new ones of your own and delete ones you no longer need 50 Chapter 6 Working with Text Applying a Text Style to a Paragraph in a Text Region When you create a text region in your worksheet the region is tagged by default with the Normal style You can however apply a different style to each paragraph l Click in the paragraph Choose Style from the Format menu or Text Styles right click on the paragraph and choose TSE Style from the menu to see a list of the paie available text styles Available text styles ra depend on the template used ILEI Select a text style and click Apply Your Subtitle Title paragraph acquires the text and paragraph properties associated with that style Tip You can apply a text style to a text paragraph simply by clicking in the paragraph and choosi
113. licking Space one or more times 2 Press Ctr1 1 to insert the matrix transpose operator 3 Press Ctrl period for the symbolic equal sign 4 Press Enter Mathcad returns the result to the right of the Figure 13 12 shows some examples Figure 13 12 Symbolic matrix operations transposing a matrix finding the inverse and finding the determinant You can also find the transpose inverse or determinant of a matrix by using the Matrix commands on the Symbolics menu Index symbolic equal sign 141 gt vectorize operator 41 parentheses 27 definition 8 73 evaluating expression 9 76 2D plots creating 11 3D Plot Format dialog box 135 aligning output tables 39 regions 59 text 49 Animate command 125 animation 126 creating 125 playback 126 saving 126 speed 125 126 annotation of E book 15 Annotations saving 15 approximations root of expression 97 area collapsing 63 deleting 65 expanding 64 inserting 63 locking and unlocking 63 64 naming 63 password protecting 63 64 arguments of functions 82 arrays calculations by element 41 copying and pasting 40 creating 33 defining with range variables 34 displaying in results 39 extracting a row or column 38 graphical display of 42 nested 89 ORIGIN used with 38 Author s Reference 13 70 Auto on status bar 92 automatic calculation mode 92 autoscaling of axis limits 121 AutoSelect 103 in solving 103 ove
114. line Help for more details about creating and playing animations Chapter 12 3D Plots Overview of 3D Plotting Creating 3D Plots of Functions Creating 3D Plots of Data Formatting a 3D Plot gt gt OD Overview of 3D Plotting Three dimensional plots enable you to visually represent a function of one or two variables and to plot data in the form of x y and z coordinates Mathcad renders 3D plots with OpenGL graphics Inserting a 3D Plot To create a three dimensional plot 1 Define a function of two variables or a matrix of data 2 Choose Graph from the Insert menu and select a 3D plot type or click one of the 3D graph buttons on the Graph toolbar Mathcad inserts a blank 3D plot with axes and an empty placeholder 3 Enter the name of the function or matrix in the placeholder 4 Click outside the plot or press Enter to see the plot For example the surface plot shown below was Fix Wi sings cosi y created in Mathcad from the function When you create a 3D plot from a function it s called a QuickPlot A QuickPlot uses default ranges and grids for the independent variables To change these settings double click on the graph and use the QuickPlot Data page of the 3D Plot Format dialog See Formatting a 3D Plot on page 135 3D Plot Wizard The 3D Plot Wizard provides more control over the format settings of the plot as you insert it 1 Choose Graph gt Plot Wizard from the Insert menu
115. llapsed area continue to affect other equations in the document For example if you define a function inside a locked area you can still use that function anywhere below and to the right of its definition You cannot however change the function s definition unless you unlock the area first Inserting an Area Tip To insert a lockable area into your worksheet 1 Choose Area from the Insert menu Mathcad e inserts the boundaries of the area into the worksheet 2 Select either of these boundary lines just as you d select any region by dragging the mouse across the line or by clicking the line itself 3 Drag the boundary line to increase or decrease the area or select both lines to move the entire area You can have any number of lockable areas in your worksheet The only restriction is that you cannot have one lockable area inside another To name an area in your worksheet click on an area boundary choose Properties from the Format menu and enter a name on the Area tab The Area tab also lets you modify other display attributes of an area such as whether a border or icon appears Locking and Collapsing an Area Lock an area to preserve what s inside of it To lock an area 64 Chapter 7 Mathcad Worksheets Note 1 Click in the area 2 Choose Area gt Lock from the Format menu Lock Area Password optional Cancel Reenter password Collapse area Sllow area to expand and colla
116. lobal Definitions Note Tip Global definitions work exactly like local definitions except that they are evaluated before any local definitions If you define a variable or function with a global definition that variable or function is available to all local definitions in your worksheet regardless of whether the local definition appears above or below the global definition To create a global definition follow these steps 1 Type a variable name or function 2 Press tilde or click on the Evaluation toolbar R ql Type an expression The expression can involve numbers or other globally defined variables and functions 02820562 You can use global definitions for functions subscripted variables and anything else that normally uses the definition symbol A global definition of a variable can be overridden by a local definition of the same variable name with the definition symbol Figure 8 3 shows the results of a global definition for the variable R which appears at the bottom of the figure R 0820562 Figure 8 3 Using the global definition symbol The first set of definitions are used to solve for P Since R is defined globally at the bottom of the worksheet its definition applies everywhere in the worksheet When the local definitions for V and T are changed there is a new result for P It is good practice to allow only one definition for each global variable Defining a vari
117. lsolve function 98 mailing worksheets 71 manual mode 93 margins 61 math region 19 math styles applying 30 editing 29 saving 31 Math toolbar 6 20 Mathcad 2001 20011 11 56 Mathcad Community 17 Mathcad home page 16 Mathcad s Object Model 13 matrices adding deleting rows or columns 34 calculations by element 41 defining by formula 34 defining with two range variables 34 definition of 33 determinant 152 displayed as pictures 105 displayed as scrolling output tables 39 extracting a column 38 extracting elements 37 limits on size 34 40 numbering elements 38 ORIGIN used with 38 plotting in contour plot 134 start with row and column zero 38 subscripts 37 matrix changing size 34 Matrix Determinant command 152 153 Matrix display style 89 Matrix Invert command 153 Matrix Transpose command 152 153 measurement for the ruler 60 metafile 107 Microsoft Internet Explorer 16 Migration Guide 13 minus sign inserting in front of expression 27 MKS units 90 mode See manual mode moving crosshair 7 editing lines 25 insertion point 25 regions 58 moving regions 58 multiple roots finding with polyroots 97 98 multiplication 23 implied 24 86 multiplication operator 23 24 names of variables and functions 74 negating an expression 27 nested arrays expanding 89 nonlinear systems of equations 98 nonscalar value error message 79 nudging regions 58 nudging with arrows 58 number format See result format numbered paragraphs 49 n
118. matting toolbar These buttons work in both math and text regions The subscript button in a math region produces an array subscript not a literal subscript Changing Paragraph Properties A paragraph in a text region is any stream of characters followed by a hard return which you create when you type Enter You can assign distinct properties to each paragraph including alignment indenting for either the first or all lines in the paragraph tab stops and bullets or numbering You can also select multiple paragraphs or text regions to apply settings to more than one paragraph at a time When you type Shift Enter Mathcad inserts a new line within the current paragraph it does not create a new paragraph To change the properties for a paragraph 1 Select the paragraph by clicking in Paragraph Format it by drag selecting it or by triple Indent inches clicking it Left Special none 2 Choose Paragraph from the ight o By Format menu or right click and choose Paragraph from the menu Bullets to open the Paragraph Format Alignment dialog box Left O Rigt O Center Text Styles 49 You can change the following paragraph properties Indent To indent every line in the paragraph the same amount enter numbers in the Left and Right text boxes To indent the first line of the paragraph a different amount than the rest of the lines select First Line or Hanging from the Spe
119. me X Y or polar plot A graph can show several y axis or radial expressions against the same x axis or angular expression See Figure 11 3 Or it can match up several y axis or radial expressions with the corresponding number of x axis or angular expressions See Figure 11 2 To create a QuickPlot containing more than one trace 1 Enter the expressions or functions of a single variable you want to plot separated by commas sin x 2 sinis 2 Click in the expressions then x choose Graph gt X Y Plot from the Insert menu 3 Click outside the graph or press Enter In a QuickPlot with multiple traces you need not use the same independent variable in every y axis or radial axis expression Mathcad provides the appropriate corresponding variable in the x axis or angular axis placeholder To create a graph containing several independent curves 1 Choose Graph gt X Y Plot from the Insert menu 2 Enter two or more expressions separated by commas in the y axis placeholder 3 Enter the same number of expressions separated by commas in the x axis placeholder If you specify more than one independent variable Mathcad matches up the expressions in pairs the first x axis expression with first y axis expression the second with the second and so on It then draws a trace for each pair Figure 11 2 shows an example Figure 11 2 Graph with multiple expressions on both axes Graphing Functions and Expressi
120. ment individually select a variable in that element and choose Variable gt Differentiate from the Symbolics menu See Calculus in the Mathcad tutorial Features In Depth for examples of solving derivatives and integrals To symbolically evaluate a definite or indefinite integral 1 Click IE or J on the Calculus toolbar to insert the definite or indefinite integral operator 2 Fill in the placeholder for the integrand and the placeholders for the limits of integration 150 Chapter 13 Symbolic Calculation Limits Tutorial 3 Place the integration variable in the placeholder next to the d This can be any variable name 4 Click on the Symbolic toolbar or press Ctr1 period for gt 5 Press Enter See Figure 13 7 for examples of integrals evaluated symbolically Mathcad provides three limit operators which can only be evaluated symbolically To use the limit operators 1 Click 4 on the Calculus toolbar or press Ctr1 L to insert the limit operator To insert the operator for a limit from the left or right click Tl or 4 on the Calculus toolbar or press Ctr1 Shift B or Ctr1 Shift A 2 Enter the expression in the placeholder to the right of the lim Enter the limiting variables in the left hand and right hand placeholders below the lim 4 Press Ctr1 period for 5 P
121. mew An easy shortcut for disabling evaluation is to right click on an equation and select Disable Evaluation from the menu To re enable calculation for a disabled equation Ms 2 3 Click on the equation Choose Properties from the Format menu and click the Calculation tab Remove the check from Disable Evaluation Error Messages 95 Error Messages Online Help If Mathcad encounters an error when evaluating an expression it marks the expression with an error message and highlights the offending name or operator in red gits An error message is visible only when you click on the F x gi x 10 associated expression as shown to the right Mathcad cannot process an expression containing an error If the expression is a definition the variable or function remains undefined Any expressions that reference that variable become undefined as well Click on an error message and press F1 for an explanation of the message Finding the Source of an Error When an expression depends upon one or more existing definitions an error you receive in your expression may actually originate in one of those definitions For example in the figure above the error appears on the third region 0 However f x is based on the definition of g x When x is zero g x is the first region that exhibits the error You can try to find the source of an error by examining your worksheet or you can trace the error bac
122. n 3 Now enter the constraints equalities and inequalities in any order below the word Given Make sure you use the Boolean equal symbol on the Boolean toolbar or press Ctr1 for any equality You can separate the left and right sides of an inequality with any of the symbols lt gt lt and 4 Enter any equation that involves one of the functions Find Maximize Minimize or Minerr below the constraints Solve blocks cannot be nested inside each other each solve block can have only one Given and one Find or Maximize Minimize or Minerr You can however define a function like fix Find x at the end of one solve block and refer to this function in another solve block Solve Block Functions Figure 9 2 shows a solve block with several kinds of constraints and ending with a call to the Find function There are two unknowns As a result the Find function takes two arguments x and y and returns a vector with two elements Guess Values Given wn l Findts yi val Results wVal 0 414 yvyal 2 414 Check aval yvalf 6 swal yval 2 Figure 9 2 A solve block with both equalities and inequalities The equations for a circle and line are entered then the inequality constraints are set Find looks for the points of intersection which are checked back in the original equations See the QuickSheet Solve Blocks with Inequality Constraints Unlike most Mathcad functions the
123. n directly into a math placeholder or in a math region Tip Although built in function names are not font sensitive they are case sensitive If you do not use the Insert Function dialog box to insert a function name you must enter the name of a built in function in a math region exactly as it appears in the Insert Function dialog Note Brackets around an argument indicate that the argument is optional Assistance for Using Built in Functions Mathcad offers several sources of assistance for using built in functions The Insert Function dialog box gives you a convenient way to look up a function by category to see the arguments required and to see a brief function description Click in the Insert Function dialog box to open the Help topic associated with a selected function Online Help also available by clicking on the Standard toolbar provides details on the syntax arguments algorithms and behavior of all of Mathcad s built in functions operators and keywords QuickSheets under the Help menu include working examples of many functions 82 Chapter 8 Calculating in Mathcad Applying a Function to an Expression To turn an expression into the argument of a function 1 Click in the expression and press Space until the entire w t k d expression w t k z is held between the editing lines 2 Type the single quote key or click on the Calculator toolbar to enclose the sele
124. n top of a graph Modifying a 2D Plot s Perspective 123 Modifying a 2D Plot s Perspective Mathcad allows you to zoom in on 2D graphs and trace the coordinates of any point on a plot Zooming in on a Plot To zoom in on a portion of a graph 1 Click in the graph and choose Graph gt Zoom from the Format Y2 menu or click A on the Graph min 000613497 masr EE O toolbar to open the Zoom dialog box Moc 0447853 0 344538 2 Click the 2 button then select the Ba oK cancel e graph again 3 Press and hold down the mouse button then drag the mouse A dashed selection outline emerges from the anchor point with coordinates listed in the Min and Max text boxes or the Radius text box of the Polar Zoom dialog box X Zoom k ii 4 When the selection outline encloses the region you want to magnify release the mouse button If necessary click on the selection outline and drag it to another part of the plot 5 Click Zoom to redraw the graph The axis limits are temporarily set to the coordinates specified in the Zoom dialog box To make these axis limits permanent click OK Tox amc x 0 0 0001 1 x fix Figure 11 10 A zoomed in region of an X Y plot redisplayed as an entire plot Getting a Readout of Plot Coordinates To see a readout of coordinates of the specific points that make up a trace 124 Chapter 11 2D Plots
125. nd Paste To drag regions with the mouse 1 Select the regions 2 Place the pointer on any selected region so that the pointer turns into a small hand 3 Press and hold down the mouse 4 Move the mouse The rectangular outlines of the selected regions follow the cursor To move the regions into another worksheet drag the rectangular outlines into the destination worksheet then release the mouse button Nudging Regions with Arrow Keys You can use the arrow keys on your keyboard to nudge selected regions in different directions Press an arrow key once to move the region s one grid space Holding down the arrow key moves the region until the arrow is released You can layer one region on top of another To move a particular region to the top or bottom right click on it and choose Bring to Front or Send to Back from the menu Rearranging Your Worksheet 59 Tip If regions you want to copy are coming from a locked area see Safeguarding an Area of the Worksheet on page 63 or an E book you can copy them simply by dragging them with the mouse into your worksheet Deleting Regions To delete one or more regions 1 Select the regions 2 Choose Cut from the Edit menu or press Ctr1 X Choosing Cut removes the selected regions from your worksheet so that you can paste them elsewhere If you don t want to paste or save the regions choose Delete from the Edit menu or press Ctr1 D instead Aligning Regions
126. nd a dot between the constant and the variable to indicate that the multiplication is implied enabling you to closely approximate the notation in books However Mathcad reserves certain letters such as i for the imaginary unit and o for octal as suffixes for numbers and in these cases does not attempt to multiply the number by a variable name but rather treats the expression as a single number with a suffix You can change the display of the multiplication operator to an x a thin space or a large dot To do so right click on the multiplication operator and choose View Multiplication As Or to change all the multiplication operators in a worksheet and the display of other operators choose Worksheet Options from the Tools menu click on the Display tab and choose from the selections next to Multiplication An Annotated Example An equation is really two dimensional with a structure more like a tree with branches than like a line of text As a result Mathcad has to use a two dimensional editing cursor That s why there are two editing lines a vertical line and a horizontal line Suppose for example that you want to type the slightly more complicated expression x 3 a 4 j y 14 n7 Watch what happens to the editing lines in the following steps 1 Type x 3 a 2 Since the editing lines contain just the 2 only the 2 becomes the numerator if you press the 2 Press Space three times to enclo
127. nd choose whether to add text describing the symbolic method used 148 Chapter 13 Symbolic Calculation Examples of Symbolic Calculation As a general rule you can symbolically evaluate any expression involving variables functions and operators using either the symbolic equal sign or the menu commands Note Functions and variables you define yourself are recognized by the symbolic processor when you use the symbolic equal sign They are not recognized however when you use the Symbolics menu commands Figure 13 6 shows the difference fs Mathcad s symbolic processor alts 5 y recognizes many of its built in math functions and constants rnd x mdtx but not the ones without a commonly accepted meaning Ings PCs Functions and variables you 2 define yourself are recognized when you use the symbolic Z i a equal sign af x eee a singal 4 9 sint 3 Fix af singa amp but not when you use commands from the simplifies to simplifies to Symbollcs menu expcFox a a sinfa Figure 13 6 The symbolic processor recognizes many built in functions User defined functions and variables are only recognized by the symbolic equal sign Derivatives To evaluate a derivative symbolically you can use Mathcad s derivative operator and the live symbolic equal sign as shown in Figure 13 7 Press amp for definite integral Press Ctrl Shift Z for Press Ctrl I for indefinite integral
128. nes just after the operator Ea Editing Expressions 27 2 Press Backspace For certain operators it may not be clear where to put the editing lines For example it is not clear when looking at x or x what before and after mean You may have to experiment to see how Mathcad deals with certain situations Use the Undo command if you need to revise your editing Replacing an Operator To replace an operator after deleting it simply type the new operator To replace an operator between two expressions 1 Position the editing lines just after the operator c 2 Press Backspace An operator placeholder appears o c 3 Type the new operator _ c Inserting a Minus Sign The minus sign that means negation uses the same keystroke as the one that means subtract To determine which one to insert Mathcad looks at where the blue insertion line is If it s on the left Mathcad inserts the negation minus sign If it s on the right Mathcad inserts the subtract minus sign To move the blue insertion line from one side of the blue underline to the other use Insert The following example shows how to insert a minus sign in front of sin a 1 Click on the sin a If necessary press Space to select the entire expression 2 Press Insert to move the vertical editing line all the way to the left aw 3 Type orclick jon the Calculator toolbar to insert a min
129. ng a style from the left most drop down list in the Formatting toolbar To apply a text style to an entire text region first select all the text in the region Modifying an Existing Text Style You can change the definition of a text style by modifying it l Choose Style from the Format menu to open the Text Styles dialog box listing available text styles Select the text style you want to modify and click Modify The Define Style dialog box displays the definitions of that text style Define Style x Based Or gy Description Font Arial Size 10 Left Indent 0 00 Right Indent 0 00 Left Justified 4 Click Font to modify text formats such as the font font size font styling special effects and color Click Paragraph to modify the indenting alignment and other paragraph properties Any text regions previously created with the text style in that worksheet are modified accordingly Creating and Deleting Text Styles You can create new text styles or delete ones you no longer use any text style changes are saved with your worksheet You can base a new text style on an existing text style such that it inherits text or paragraph properties For example you may want to base a new Subheading style on an existing Heading style but choose a smaller font size keeping other properties the same Equations in Text 51 Creating a Text Style To create a new text style 1 Choo
130. ng Open from the File menu Ctr1 O then browse to your files You can also type a path directly into the File Name box including URLs Saving Your Worksheet To save a worksheet choose either Save or Save As from the File menu and enter a file name with an XMCD file extension or one of the other extensions described below The XMCD files are in XML format so the content and data can be read by other applications You can compress the worksheets by saving as XMCDZ compressed XML format Both formats can be opened directly in Mathcad You can save a worksheet in Hypertext Markup Language HTML so that the file can be viewed through a Web browser or in rich text format RTF so that it can be opened by most word processors You can also transform the XML format to HTML or other representations using XMLT language Saving Your Worksheet in an Earlier Format Worksheets created in an earlier version of Mathcad open in the current version but files in the current version of Mathcad can not be opened in earlier versions Mathcad 15 allows you to save a worksheet as Mathcad 11 12 13 or 14 In general regions or features that don t work in an earlier version appear as bitmaps Creating a New Mathcad Template When you create a worksheet based on a template all of the formatting information and any text math and image regions from the template are copied to the new worksheet Templates allow you to maintain consistency across multiple w
131. nge for the independent variable a Plotting Vectors of Data You can plot a vector of data with either an X Y or a polar plot You need to use the vector subscript to specify which elements to plot Some graphs of data vectors are shown in Figure 11 5 Plotting a Single Vector of Data To create an X Y plot of a single vector of data 1 Define a range variable such as i that references the subscript of each element of the vector you want to plot For example for a vector with 10 elements your subscript range variable is 7 0 9 2 Choose Graph gt X Y Plot from the Insert menu Enter i in the bottom placeholder and the vector name with the subscript y for example in the placeholder on the left Type to create the subscript Note Subscripts must be integers greater than or equal to ORIGIN meaning that the x axis or angular variable used in the graphs in Figure 11 5 can run through whole number values only If you want to plot fractional or negative values on the x axis plot a function or plot one vector against another as described in the next section Plotting Vectors of Data 119 Tip Ifyou have a handful of data points you can use a data table to create a vector as shown in the second graph in Figure 11 5 or Figure 11 7 See Entering a Matrix as a Data Table on page 35 i 0 20 weiss 0 45120 Figure 11 5 Graphing a vector Plotting One Data Vector Against Another To plot all the element
132. niques described here generate numeric solutions Chapter 13 Symbolic Calculation describes a variety of techniques for solving equations symbolically Solving and Optimization Functions Finding Roots Tip Finding a Single Root The root function solves a single equation in a single unknown given a guess value for the unknown Or you can give root a range a b in which the solution lies and no guess is required The function returns the value of the unknown variable that makes the equation equal zero and lies in the specified range by making successive estimates of the variable and calculating the value of the equation The guess value you supply for x becomes the starting point for successive approximations to the root value If you wish to find a complex valued root start with a complex guess When the magnitude of Ax evaluated at the proposed root is less than the value of the tolerance parameter TOL Mathcad returns a result Plotting the function is a good way to determine how many roots there are where they are and what initial guesses are likely to find them As described in Built in Variables on page 75 you can change the value of the tolerance and hence the accuracy of the solution found by root by including definitions for TOL in your worksheet You can also change the tolerance by using the Built in Variables tab when you choose Worksheet Options from the Tools menu Mais eo 10x 2 root fix x 5 4
133. ns inserted into text have the same properties as those in the rest of your worksheet Inserting an Equation into Text You can place an equation into text either by creating a new equation inside a text region or by pasting an existing equation into a text region To add a new equation into text The universal gravitational constant G has 1 Click to start the equation the value and can be used to determine the acceleration of a less massive object toward a more massive object 2 Choose Math Region from the The universal gravitational constant G has Insert menu or press the value and can be used to determine Ctr1 Shift Atoinserta the acceleration of a less massive object math placeholder toward a more massive object 3 Type in the equation 52 Chapter 6 Working with Text Text Tools 4 When you ve finished typing The universal gravitational constant G has click on any text to return to the it om text region Mathcad adjusts ene a a eel kas ane the line spacing in the text can be used to determine the acceleration region to accommodate the of a less massive object toward a more embedded math region massive object You can also paste an existing equation into a text region or right click to start an equation Mathcad s text tools are similar to those in word processors Find and Replace Online Help Mathcad s Find and Replace commands on the Edit menu are capable of working in
134. nter 0 press Ctr1 G Note Although many uppercase Greek letters look like ordinary capital letters they are not the same Mathcad distinguishes between Greek and Roman letters even if they appear the same Tip The Greek letter n can also be typed by pressing Ctr1 Shift P Inserting an Operator Tip Operators are symbols like and that link variables and numbers together to form expressions The variables and numbers linked together by operators are called operands For example in an expression like aes the operands for the are x and y You can use standard keystrokes like and to insert operators or insert operators from the math toolbars For example you can insert a derivative operator by clicking d7 on the Calculus toolbar or by typing Choose Toolbars from the View menu to open the math toolbars Online Help contains a complete listing of operators their keystrokes and descriptions You can find the keyboard shortcut for an operator by hovering the mouse pointer over a button in a math toolbar and reading the tooltip When you insert a Mathcad operator into a blank space a mathematical symbol with empty placeholders appears You must enter a valid math expression in each placeholder of an operator in order to calculate a result Here is a simple example 1 Click in a blank space and click on the Calculator toolbar or simply type
135. o the settings for your printer The sections of the worksheet separated by the gray vertical lines print on separate sheets of paper yet the page number at the bottom of the Mathcad window does not change as you scroll to the right Distributing Your Worksheets 69 Tip Tip ie 4 s 5 a 5 1 S gt a b i Ba ae 7 Prints As You can think of the worksheet as being divided into vertical strips Mathcad begins printing at the top of each strip and continues until it reaches the last region in this strip It prints successive strips left to right Note that certain layouts will produce one or more blank pages You can control whether a wide worksheet is printed in its entirety or in a single page width To do so choose Page Setup from the File menu to open the Page Setup dialog box To prevent printing anything to the right of the right margin check Print single page width You can customize the display of some operators including the the bold equals the derivative operator and the multiplication operator Before you print choose Worksheet Options from the Tools menu and click on the Display tab to change the appearance of these operators for people unfamiliar with Mathcad notation Print Preview Tip To check your worksheet s layout before printing choose Print Preview from the File menu or click L on the Standard toolbar The Mathcad window shows the current section of
136. o the first major tick mark beyond the end of the data so that every point being plotted is displayed e With Autoscale off the axis limits are set exactly at the data limits Specifying Other Limits To override Mathcad s automatic limits by entering limits directly on the graph 1 Click the graph to select it You will see a number by each axis limit enclosed in corner symbols as illustrated in the selected plot in Figure 11 8 2 Click on each number and type a number to replace it 122 Chapter 11 2D Plots 3 When you click outside the graph Mathcad redraws it with the new axis limits 11 1 9 4 f s singe x 1 5 Figure 11 8 In the graph on the left Mathcad has automatically generated data limits at 0 5 and 2 499 which are visible when you select the graph The graph on the right displays the new y axis limits manually set at 0 6 and 2 0 Adding Custom Titles Labels and Other Annotations To annotate your graph by moving text on top of it 1 Create a text region or add a graphic object in your worksheet 2 Drag the text or object onto your 2D graph and position it Figure 11 9 shows a graph with both a text region point of inflection and a graphic object an arrow superimposed on it 1 Inflection pt sinis Figure 11 9 Mathcad graph with annotations Note Ifyou choose Separate Regions from the Format menu all overlapping regions in your worksheet separate including the annotations o
137. ogether so that an expression is simplified before the numeric processor calculates it See Symbolic Optimization in online Help Note Foracomputer symbolic operations are in general much more difficult than the corresponding numeric operations In fact many complicated functions and deceptively simple looking functions have no closed forms as integrals or roots Live Symbolic Evaluation One advantage to using the symbolic equal sign sometimes together with keywords and modifiers is that it is live just like numeric processing in Mathcad That is 141 142 Chapter 13 Symbolic Calculation Mathcad first checks all the variables and functions making up the expression being evaluated to see if they ve been defined earlier in the worksheet Then the expression is evaluated symbolically Whenever you make a change to the worksheet the results automatically update This is useful when the symbolic and numeric equations in the worksheet are tied together Unlike the equal sign which always gives a numeric result the symbolic equal sign is capable of returning expressions You can use it to symbolically evaluate expressions variables functions or programs To use the symbolic equal sign 1 Enter the expression you want to evaluate le 2 ay A 2 Click on the Symbolic toolbar or press d 3 Ctr1 period to get the symbolic equal sign a 2K gt iy 3 Press Enter Mathcad di
138. om the File menu In the Save As dialog box choose Rich Text Format File rtf from the Save as type drop down list 4 Enter a file name and then click Save When you open an RTF file with Microsoft Word you can edit the text However you are no longer able to edit math regions and graphs which have become pictures The regions do not appear in their correct position across the page unless you choose Print Layout from Word s View menu Any regions that are to the right of the right margin in Mathcad are not visible in Microsoft Word For optimal conversion to Word you should set your margins in Mathcad to the same defaults as Word 1 25 on left and right and 1 top and bottom or start with the Mathcad template Microsoft Word from File gt New Dragging and dropping a region or regions from Mathcad to Microsoft Word inserts a Mathcad object into Word See Inserting Objects on page 108 You can also simply select text in a Mathcad text region copy the text in Mathcad then Paste into Microsoft Word to move your text to Word If you use a Microsoft s Mail API MAPI compatible email application you can create email messages from within Mathcad Clicking File gt Send launches an email message with a copy of the active Mathcad worksheet as an attachment The settings in your mail system determine how Mathcad worksheets are attached to or encoded in the mail message Chapter 8 Calculatin
139. ome any longer Pressing a b Space brings the editing lines back to the starting point of the cycle 4 pmi Notice there never was an intermediate step in which the editing lines held just the numerator Nor was there ever a step in which the editing lines held just the a or just the b in the numerator The sequence of steps the editing lines go through as you press Space depends on where you start The arrow keys move the editing lines through the expression in the indicated direction Keep in mind that the idea of up and down or left and right may not always be obvious particularly when the expression becomes very complicated or if it involves summations integrals and other advanced operators Typing in Operators The key to working with operators is learning to specify what variable or expression is to become an operand There are two ways to do so e You can type the operator first then fill in the placeholders with operands or e You can use the editing lines to specify what variable or expression you want to select The first method is like building a skeleton and filling in the details later This method may be easier to use for very complicated expressions or when you have operators like summation that require many operands but don t have a natural typing order The second method is more like straight typing so it can be much faster when expressions are simple You may find yourself switching
140. on Online Help The programming operators in Mathcad also support recursion See Recursion in Help Units and Dimensions One of Mathcad s strengths is units and unit conversion Units are used just like built in variables To assign units to a number or expression just multiply it by the name of the unit Mathcad recognizes most units by their common abbreviations By default Mathcad uses the SI unit system the International System of Units in the results of any calculation but you may use any supported units you wish in creating your expressions You can change the default system of units to MKS CGS U S or None under the Unit Systems tab of Worksheet Options in the Tools menu See Displaying Units of Results on page 89 for how to set a unit system for results For example type expressions like the following mass 75 kg acc 100 m s 2 acc g 9 8 m s 2 F mass acc acc g 86 Chapter 8 Calculating in Mathcad Tip Figure 8 8 shows how these equations appear in a worksheet mass 75 kq m acc 100 9 5 acc_g 9 8 F mass acc acc_q F 8 235 x 10 N mass 75kg mass 75kg Figure 8 8 Equations using units Mathcad treats the multiplication as implied when you type an expression like mass 75kg If you define a variable that consists of a number followed immediately by a unit name you can omit the multiplication symbol Mathcad inserts a very small space and treat
141. on Variables in Mathcad worksheets are defined from top to bottom and left to right on a page Once you have defined a variable like you can compute with it anywhere below and to the right of the definition Now enter another definition 1 Press Enter This moves the crosshair below the first definition acc 9 8 2 To define acc as 9 8 type acc 9 8 Definitions and Variables 9 Calculating Results Now that the variables acc and t are defined you can use them in other expressions t 10 1 Click the mouse below the two definitions 2 Type acc 2 Space t 2 Berean 3 Press the equal sign ace Taai This equation calculates the distance traveled by a falling body in time with acceleration acc When you press the equal sign Mathcad returns the result Mathcad updates results as soon as you make changes For example if you click on the 10 on your screen and change it to another number Mathcad changes the result as soon as you press Enter or click outside of the equation Defining a Function To add a function definition to your worksheet 1 First define the function d t by typing d t d th a 2 Complete the definition by typing this expression acc 9 1600 acc 2 Space t 2 Enter a rece gt The definition you just typed defines a function The function name is d and the argument of the function is t You can use this function to evaluate the expression for different values of t
142. onal analysis Mathcad displays an appropriate error message For example suppose you had defined acc as 100 m s instead of 100 m s as shown at right mass 75 kg Since acc is in units of velocity and acc 100 2 g is in units of acceleration it is inappropriate to add them together When you attempt to do so Mathcad displays an error message that specifies how the dimensions mismatch Other unit errors are usually caused by one of the following e An incorrect unit conversion e A variable with the wrong units e Units in exponents or subscripts for example v3 gepe OF 277 e Units as arguments to inappropriate functions for example sin 2 s Defining Your Own Units You may want to define your own units or use your own abbreviation for a unit Define your own units in terms of existing units in exactly the same way you define a variable in terms of an existing variable Figure 8 9 shows how to define new units as well as how to redefine existing units 10 6 A 10 m us 10 s week 7 day kilo 1 kg f ix107 lm week 6 048 x 1075 week 0 019 yr us 1 667 x 10 min Figure 8 9 Defining your own units Top half Defining new units for a worksheet Bottom half Results from the redefined units 88 Chapter 8 Calculating in Mathcad Note Note Since units behave just like variables you may run into unexpected conflicts For example if you define the variable m in your works
143. one of the Alignment options from the menu Changing the Display of Arrays Table versus Matrix You can prevent Mathcad from displaying large matrices as output tables You can also change matrices to output tables To do so 1 Click on the output table or matrix 2 Choose Result from the Format menu 3 Click on the Display Options tab 4 Choose Matrix or Table in the Matrix display style drop down box 40 Chapter 5 Range Variables and Arrays To display all the results in your worksheet as matrices or as tables regardless of their size click an empty space in your worksheet perform steps 2 through 4 and then click OK Note Mathcad cannot display extremely large arrays in matrix form You should display a large array as an output table Changing the Format of Displayed Elements To format the numbers in the array just click on the displayed array and choose Result from the Format menu then modify the settings When you click OK Mathcad applies the selected format to all the numbers in the table vector or matrix It is not possible to format the numbers individually Copying and Pasting Arrays You can copy an array of numbers directly from a tabular application such as Excel or an ASCII file that contains rows and columns into a Mathcad array All data characteristics including text numerics complex numbers or empty cells are preserved Once you ve performed computations or manipulations
144. ons 117 Cleans a j xj sin sy 10 Figure 11 3 Graph with multiple y axis expressions Note All traces on a graph share the same axis limits For each axis all expressions and limits on that axis must have compatible units Creating a Parametric Plot A parametric plot is one in which a function or expression is plotted against another function or expression with the same independent variable You can create either an X Y or polar parametric plot To create an X Y parametric plot 1 Choose Graph gt X Y Plot from the Insert menu 2 In both the x axis and y axis placeholders enter a function or expression 3 Press Enter Mathcad produces a QuickPlot over a default range for the independent variable Figure 11 1 shows an example of a parametric plot If you don t want Mathcad to use a default range for the plot define the independent variable as a range variable before creating the plot Mathcad plots one point for each value of the independent variable and connects each pair of points with a straight line 118 Chapter 11 2D Plots Figure 11 4 shows two functions of O plotted against each other The range variable 0 was previously defined See Range Variables on page 79 re coscei 1 J r0 cos iG rfa singes Figure 11 4 Graphing one function against another For the X Y plot the independent variable 9 is defined as a range variable For the polar plot Mathcad chooses a ra
145. or axes and traces add titles and labels and control other settings for a graph Formatting a 2D Plot 121 1 Double click the graph to open the graph formatting dialog box Formatting Currently Selected X Plot Primary Y Axis Secondary Y Axis Log scale Log scale Grid lines I Grid lines a i Numbered Ii Nurmbered W Auto scale W Auto scale Show markers Ml Show markers Ml Iv Auto grid Iv Auto grid Number of grids Number of grids Axis Style Boxed Equal scales C Crossed f None coe oy te 2 Use the Axes tab to determine the appearance of the axes grid lines and markers Use the Traces tab to set the color type symbols and width of the traces Use the Labels tab to insert labels on the axes X Y plots only and specify a title for your plot The Number Format tab allows you to format the displayed precision of the numbers on the axes Use the Defaults tab to specify the default appearance of your graphs 3 Click Apply to see the effect of your changes without closing the dialog box Tip Ifyou double click an axis on a graph a formatting dialog box for that axis alone appears Online Help Click Help in the bottom of the dialog box for details on particular formatting options Setting Axis Limits 2D graphs by default are set with Auto scale on You can use the Axes page of the graph formatting dialog box to turn Auto scale off e With Auto scale on each axis limit is set t
146. or you can access the elements individually or in groups You access individual elements of a vector or matrix by using the subscript operator Insert the subscript operator by clicking n on the Matrix toolbar or by typing To access an element of a vector enter one number in the subscript To access a matrix element enter two numbers separated by a comma To refer to the ith element of a vector type v i In general to refer to the element in the ith row jth column of matrix M typeM i j Figure 5 3 shows examples of how to define individual matrix elements and how to view them Mo o 1 Mo 1 4 Mo 2 5 My o 4 My 2 6 1 3 5 I OU 6 Figure 5 3 Defining and viewing matrix elements Since the array ORIGIN is zero there is a zeroth row and a first row but no second row When you define vector or matrix elements you may leave gaps in the vector or matrix For example if v is undefined and you define v3 as 10 then vo v and v are all undefined Mathcad fills these gaps with zeros until you enter specific values for them as shown in Figure 5 3 Be careful of inadvertently creating very large vectors and matrices by defining individual elements You can use this kind of subscript notation in Mathcad to perform parallel calculations on the elements of an array See Performing Calculations in Parallel on page 41 If you want to define or access a group of array elements at once you can use a r
147. orksheets A template specifies e Definitions of all math styles Chapter 4 e Definitions of all text styles Chapter 6 e Margins for printing see Layout on page 61 e Numerical result formats and values for Mathcad s built in variables Chapter 8 e Names of Mathcad s basic units and the default unit system Chapter 8 e The default calculation mode Chapter 8 e Ruler visibility and measurement system see Aligning Regions on page 59 e Regions you d like created by default in new worksheets for example a collapsed area with extra unit definitions and calculations you use across worksheets e File properties including title author description and keywords e Graphic elements such as company logos and headings To create a new template 1 Create a new worksheet and set the above values manually or use the Mathcad default values 2 Add the equations text and graphics you want to appear in all new files Rearranging Your Worksheet 57 Then save this worksheet as a template To do so l 2 3 4 Choose Save As from the File menu Browse to the Template folder within the Mathcad program folder In the Save as type drop down list select Mathcad XML Template XMCT Type a name in the File name box Your template is added to the list of templates that appears when you choose New from the File menu If you do not save your template to the Template folder you can
148. ormatting 61 gathering in an E book 70 including by reference 65 opening 56 order of evaluation 77 printing 12 68 referencing in another worksheet 65 saving 12 55 56 saving as templates 56 57 saving in an earlier format 56 sending by Email 71 World Wide Web accessing 16 bookmarks for browsing 16 Mathcad home page 16 PlanetPTC 17 toolbar 16 XMCD 56 XMCD file 55 XMCDZ 56 XMCT file 55 XML 3 56 XML template 57 X Y plots creating 10 11 114 formatting 120 See also plots 2D zero threshold 89 zeros of expressions or functions See roots zooming 2D plots 123
149. pend on the plot type Some options in the 3D Plot Format dialog box work together to control the appearance of a plot For example the choices on the Appearance page the Lighting page and the Special and Advanced pages together control the color of a plot Fill Color The color of a plot is primarily determined by its fill color You can apply color to a plot by filling its surfaces or contours with either a solid color or a colormap A plot s color and shading are also affected by lighting as described below Lines Mathcad provides many ways to control the appearance of the lines on a three dimensional plot You can draw the lines so they form a wireframe or you can draw only the contour lines You can also control the weight and color of the lines on a plot Online Help For more specifics on formatting 3D plots see the online Help topic 3D Plot Format Dialog Box Appearance Tab Points You can draw and format points on most three dimensional plots since all 3D plots are constructed from discrete data points The exceptions are vector field plots contour plots bar plots and patch plots Points are most useful on a 3D scatter plot since points are the main focus of the plot Use the Point Options section of the Appearance tab of the 3D Plot Format dialog box Formatting a 3D Plot 137 Lighting The color of a three dimensional plot is a result of color you use to fill its surface lines and points as well
150. print preview 69 wide worksheets 68 processing equations 8 92 results of 92 programming 3 properties region 61 67 QuickPlot 115 127 QuickSheets 13 radians converting to degrees 92 radix of displayed results 89 range variables array calculations with 41 creating arrays with 34 defining 34 79 80 how Mathcad evaluates equations with 79 setting endpoints and increments 80 recursion 84 redefinition warning 88 Reference Tables 13 references and relative paths 66 to other worksheets 65 regions 7 aligning 59 copying 58 deleting 59 dragging 58 dragging across documents 58 equation 7 hyperlinking to 67 locking 63 moving 58 overlapping 60 properties 67 properties of 58 putting borders around 7 selecting 57 separating 60 tags creating 67 text 7 45 unlocking 64 viewing 7 60 region to region hyperlinking 67 relative paths for references 66 relative positioning 70 Release Notes 17 Repaginate Now command 62 replacing characters in math or text 52 replacing operators 27 resizing graphs 114 pictures 107 Resources Window 13 accessing worksheets on Web 16 bookmarks 16 Web browsing in 16 resources online 13 Result Format dialog box 10 89 results calculating 9 calculating with equations 76 copying 92 formatting 9 88 rich text format RTF 71 root function 97 roots finding 97 finding symbolically 150 151 numerical approximations used 98 of polynomials 98 row vector 33 RTF file 56 See also r
151. pse while locked Show lock timestamp 3 Enter a password if desired in the Lock Area dialog box Type any combination of letters numbers and other characters 4 Check Collapse area to hide the locked regions from view Check Show lock timestamp to display the lock date and time above and below the locked area 5 To hide the collapsed area right click on it and choose Properties then the Area tab Uncheck all boxes to completely hide the area If you drag over a hidden area you will see two dashed lines indicating its position The area is now locked and by default shows padlocks on the boundaries and a timestamp When you lock a region you can choose to allow other users to expand and collapse it even though it remains locked Right clicking on an area to open the Area tab in the Properties dialog allows the area to be collapsed and expanded even when it is locked If you forget the password for an area you will find yourself permanently locked out Keep in mind that the password is case sensitive To collapse an area without locking it first 1 Click in the area 2 Choose Area gt Collapse from the Format menu A collapsed area appears by default as a single line in your worksheet Unlocking and Expanding an Area If you want to make changes to a region inside a locked area you have to unlock it If the area is collapsed you must also expand it To unlock a locked area 1 Click in the area 2 Choos
152. putations the mouse pointer changes its appearance and the word WAIT appears on the message line This can occur when you enter or calculate an equation when you scroll during printing or when you enlarge a window to reveal additional equations In all these cases Mathcad evaluates pending calculations from earlier changes Each expression being evaluated is surrounded by a green rectangle This highlighting makes it easy to follow the progress of a calculation Calculating in Manual Mode In manual mode Mathcad does not compute equations or display results until you specifically request recalculation Therefore you don t have to wait for Mathcad to calculate as you enter equations or scroll around a worksheet Mathcad keeps track of pending computations while you re in manual mode As soon as you make a change that requires computation the word Calc appears on the status line to remind you that the results you see in the window are not up to date and that you must recalculate them to ensure accuracy Update the screen by choosing Calculate Now from the Tools menu clicking on the Standard toolbar or pressing F9 Mathcad performs necessary computations to update all results visible in the worksheet window When you scroll down to see more of the worksheet the word Calc reappears on the message line to indicate that you must recalculate to see up to date results To force Mathcad to recalculate all
153. putations 92 93 personal dictionary spell checker 53 pi T 24 75 entering 20 value 74 picture operator 43 105 pictures border on 107 creating from bitmap file 106 creating from matrix 105 formatting 107 pasted from Clipboard 107 resizing 107 placeholder 8 19 placeholder for an operator 27 PlanetPTC 17 Playback command 126 Playback animation 126 plots 2D autoscaling of axis limits 121 changing perspective 123 creating 10 11 114 formatting 120 graphing expressions 115 graphing functions 115 graphing vectors 119 multiple traces on 116 read out of coordinates 123 resizing 114 setting axis or data limits 121 titles and labels 120 traces on 116 tracing coordinates on 123 zooming 123 plots 3D 127 3D Plot Format dialog box 136 3D Plot Wizard 127 annotations 138 color 136 137 contour plots 133 converting 137 creating 127 134 fill color 136 fogplots 3D formatting 135 graphic annotations on 138 graphing functions 128 lighting 137 lines 136 multiple plots on 134 OpenGL graphics 127 parametric surface plots 131 132 QuickPlot 127 resizing 114 rotating 139 space curves 130 surface plots 128 130 text on 138 zooming 139 Index 161 PNG 70 polar plots creating 114 formatting 120 See also plots 2D polynomial finding the roots of 98 polyroots function 98 predefined built in variables 75 Print Preview command 69 printing 12 blank pages in 69 page settings for 61 68 pagination 62 68
154. r a zeroth row or column in either the matrix or the vector Displaying Arrays 39 Displaying Arrays Mathcad automatically displays matrices and vectors having more than nine rows or columns as output tables rather than as matrices or vectors Smaller arrays are displayed by default in traditional matrix notation Figure 5 6 shows an example l i me 7 3 i 0 2 j 0 2 ne a 1 571 0 571 0 429 A 2412 1 412 0 412 2 45 1 46 0 46 a a odolo isi 0 571 1571 0 571 Figure 5 6 The top results display as a matrix while the bottom results display as an output table Note An output table displays a portion of an array To the left of each row and at the top of each column there is a number indicating the index of the row or column Right click on the output table and select Properties from the menu to control whether row and column numbers appear and to choose the font If your results extend beyond the table you can scroll through the table using scroll bars To resize an output table 1 Click the output table Handles appear along the sides of the table 2 Move the mouse pointer to one of these handles so that it changes to a double headed arrow 3 Press and hold down the mouse button and drag the table in the direction you want the dimensions to change Tip You can change the alignment of the table with respect to the expression on the left hand side of the equal sign Right click on the table then choose
155. res the color depth the number of colors in the image at the time you paste it into a worksheet You can safely resave any worksheets that contain color images on systems with different color displays Tip When you import images the image information is stored as part of the Mathcad worksheet increasing the file size You may be able to reduce the size of the file by saving it as XMCDZ compressed XML format Formatting a Image Resizing an Image To resize an image region 1 Click inside the image region to select it 2 Move the mouse pointer to one of the handles along the edge of region so that the pointer changes to a double headed arrow 3 Press and hold down the left mouse button while dragging the mouse in the direction you want the image region to be stretched 108 Chapter 10 Inserting Graphics and Other Objects Tip When you change the size of the image region the image inside may be distorted To preserve the aspect ratio of the original image drag diagonally on the handle in the lower right corner Choose Properties from the Format menu to open the Properties dialog box to restore an image to its original size or place a border around it Inserting Objects OLE Object Linking and Embedding technology in Microsoft Windows makes it possible to insert static pictures of objects into Mathcad or Mathcad objects into other applications so that they can be fully edited in their originating applications An
156. resents a reference to an array element When you click on a name with a literal subscript a period displays in front of the subscript See Chapter 5 Range Variables and Arrays Built in Variables Note Note Some built in variables have conventional values like z and e and some are system variables that control how Mathcad works Mathcad treats the names of all built in units as predefined variables See Units and Dimensions on page 84 Although Mathcad s predefined variables already have values when you start Mathcad you can still redefine them For example if you want to use a variable called e with a value other than the one Mathcad provides enter a new definition like e 2 The variable e takes on the new value everywhere in the worksheet below and to the right of the new definition Or create a global definition for the variable as described in Global Definitions on page 78 Mathcad s predefined variables are defined for all fonts sizes and styles This means that if you redefine e as described above you can still use e for example as the base for natural logarithms 76 Chapter 8 Calculating in Mathcad You can modify some of Mathcad s built in variables without having to explicitly define them in your worksheet To do so choose Worksheet Options from the Tools menu and click the Built In Variables tab Worksheet Options Unit System Dimensions Compatibility Built In V
157. ress Enter Mathcad returns a result for the limit or an error message if the limit does not exist Figure 13 9 shows some examples of evaluating limits 3 b 3 b A a ni 2 a a im sing 3 30 e Figure 13 9 Evaluating limits from both the right and left See Calculus in the Mathcad tutorial Features In Depth for examples of working with limits Solving an Equation for a Variable To solve an equation symbolically for a variable use the keyword solve 1 Type the equation Make sure you click on the Boolean toolbar or press Ctr1 to create the bold equal sign Examples of Symbolic Calculation 151 Note When solving for the root of an expression there is no need to set the expression equal to zero See Figure 13 10 for an example 2 Press Ctrl Shift period Mathcad displays a placeholder to the left of the symbolic equal sign gt 3 Type solve in the placeholder followed by a comma and the variable for which to solve 4 Press Enter for the result Mathcad inserts the result to the right of the Note that if the variable was squared in the original equation you may get two results back displayed in a vector Figure 13 10 shows an example J TE at I 20 L Sl 2 C solve r a4 1 82 2P a4 solve x z t l e 1 soalve t in Figure 13 10 Solving equations and finding roots You don t need to set the
158. ript to get column from matrix 38 superscript button 48 surface plots creating 128 130 formatting 135 parametric 131 133 See also plots 3D symbolic equal sign 141 evaluation 141 keywords 143 Symbolics menu commands 147 Symbolics menu using 147 tab stops in a worksheet 59 tables of data 35 tabs in a paragraph 49 tag region creating 67 temperature conversions 92 templates 55 creating new 56 modifying 57 used to save calculation mode 93 using to create a worksheet 55 text 45 alignment 49 bullets in 49 changing font 47 color 48 Greek letters in 46 inserting equations in 51 moving 46 Occupy Page Width option 47 Push Regions Down As You Type option 48 regions 45 selecting 46 spell checking 53 styles 49 tools 52 Index 163 text box 45 text regions 45 changing width 46 creating 45 how to exit 45 text ruler 49 text styles 49 applying 50 creating 50 modifying 50 text tools 52 tilde used in global definitions 78 time in header or footer 63 TOL variable 75 76 and solve blocks 102 tolerance See TOL variable and CTOL variable toolbar Formatting 6 Math 6 Standard 6 toolbars customizing 6 E books 14 Web 16 Tools text 52 top to bottom evaluation 77 traces on 2D plots 116 tracing the source of an error 94 transpose of matrix 152 trigonometric functions 92 with degrees and radians 92 Tutorials 13 typing over text 45 U S Customary units 90 undefined variable 94 undefined
159. rmat Mathcad XML KMCD or compressed Mathcad XML XMCDZ You also have the option of saving in other formats HTML RTF for Microsoft Word or XMCT as templates for new Mathcad worksheets or in previous Mathcad versions including MCD To save as HTML you can also choose Save as Web Page under the File menu Note If you save a Mathcad file as HTML or RTF you can not reopen the file back into Mathcad Printing To print choose Print from the File menu or click on the Standard toolbar To preview the printed page choose Print Preview from the File menu or click Lh on the Standard toolbar Exiting Mathcad To quit Mathcad choose Exit from the File menu If you have moved any toolbars Mathcad remembers their locations for the next time you open the application Chapter 3 Online Resources Mathcad Resources Mathcad Community on PlanetPTC Other Resources Mathcad Resources Help Menu Resources Tutorials includes Getting Started Primers and Features In Depth QuickSheets are live examples that you can manipulate to see how to use Mathcad functions graphs and programming features Reference Tables provide you with physical constant tables chemical and physical data and mathematical formulas in Mathcad format Mathcad Help contains complete help on every feature and function in Mathcad with links to live Mathcad examples The Author s Reference covers creating E books in Mathcad an
160. rriding 103 AVI files creating 126 playback 126 background color 61 bar plots 3D formatting 135 base of results decimal octal binary 89 base units 90 binary numbers 89 bitmaps copying from other applications 107 creating pictures from 106 blank lines inserting or deleting 60 blank pages in printouts 69 BMP files 63 106 bookmarks 16 Boolean operators 101 border around a region 7 built in variables 75 bulleted paragraphs 49 Calc on status line 93 calculation 9 controlling 92 disabling for individual equation 94 equations 9 76 locking 63 order in worksheets 77 result format 88 calculator using Mathcad as 7 Celsius 92 CGS units 90 characters deleting or inserting in math 25 Clipboard 28 closing Mathcad See exiting Mathcad collapsing an area 63 colon as definition symbol 73 color in equations 30 in text 48 of worksheet background 61 color images displaying 105 column vector 33 complex keyword 144 complex numbers 19 display of 89 entering 19 imaginary unit symbol 89 compressed files 56 155 156 Index computing results 9 76 constraint in solve blocks 101 tolerance 102 contour plots creating 133 formatting 135 See also plots 3D copy and paste 58 92 108 copying expressions 28 from E book 15 regions 58 results 92 copying regions 58 creating 2D plots 113 116 3D plots 127 134 arrays 33 contour plots 133 E book 70 Portable Document Format PDF files 70 region tags 67
161. rse video 2 Press Delete or Backspace This removes the numerator and leaves behind a placeholder To recover the deleted part press Ctr1 Z to Undo Note Ifyou select an expression with the editing lines instead of drag selecting as shown above you must press Backspace or Delete twice to remove it Math Styles You can use math styles to assign particular fonts font sizes font styles and effects and colors to your math expressions Mathcad has predefined math styles that govern the default appearance of all the math in your worksheet but you can define and apply additional styles Mathcad s predefined math styles are e Variables for all variables letters and operators in math regions e Constants for all numbers in math regions e Math Text Font for title and axes labels in graphs Editing Math Styles To change Mathcad s default style for all Equation Format variables Math Style 1 Click ona variable name in your worksheet cl acetals 2 Choose Equation from the Format menu fee eens The style name Variables is selected variables OOOO O 3 Click Modify to change the font Default Equation Color associated with the Variables style You see a dialog box for changing fonts 4 Any changes you make in the dialog box apply to all variables in your worksheet If you change the Variables style you may also want to change the style used for numbers so that the two match
162. s in calculating solutions in solve blocks e Convergence tolerance The solvers calculate successive estimates of the values of the solutions and return values when the two most recent estimates differ by less than the value of the built in variable TOL A smaller value of TOL often results in a more accurate solution but the solution may take longer to calculate e Constraint tolerance This parameter the built in variable CTOL controls how closely a constraint must be met for a solution to be acceptable For example if the constraint tolerance were 0 0001 a constraint such as x lt 2 would be considered satisfied if in fact the value of x satisfied x lt 2 0001 Procedures for modifying the values of these tolerances are described in Built in Variables on page 75 For more information on solving issues see Find Minerr and Solver Problems in online Help Solving and Optimization Functions 103 Note Solving Algorithms and AutoSelect When you solve an equation by default Mathcad uses an AutoSelect procedure to choose an appropriate solving algorithm The available solving methods are Linear Applies a linear programming algorithm to the problem Guess values for the unknowns are not required Nonlinear Applies either a conjugate gradient Levenberg Marquardt or quasi Newton solving routine to the problem Guess values for all unknowns must precede the solve block Choose Nonlinear gt
163. s of one data vector against all the elements in another enter the names of the vectors in the axis placeholders 1 Define the vectors x and y 2 Choose Graph gt X Y Plot from the Insert menu 3 Enter y in the y axis placeholder and x in the x axis placeholder See Figure 11 6 ype 1 0 1 i Figure 11 6 Graphing two vectors 120 Chapter 11 2D Plots Note Note If the vectors being plotted are not the same length Mathcad plots the number of elements in the shorter vector If you want to plot only certain vector elements define a range variable and use it as a subscript on the vector names In the example above to plot the fifth through tenth elements of x and y against each other 1 Define a range variable such as k going from 4 to 9 in increments of 1 Note that the first elements of the vectors x and y are xq and yo by default 2 Enter y and x in the axis placeholders If you have a set of data values to plot create a vector by reading in data from a data file by pasting in the data or by typing data directly into a data table See Chapter 5 Range Variables and Arrays See Figure 11 7 for an example showing the use of a data table 20 ej sof 120 s sof 2o aj sof 290 Figure 11 7 Plotting vectors from a data table Assign column 0 to vector x Assign column I to vector y Use Ctr1 6 to create the superscript Formatting a 2D Plot You can override Mathcad s default settings f
164. s placeholder For example you can use the units placeholder to display a result as a multiple of z or in engineering notation as a multiple of 10 10 and so on You can also use the units placeholder for dimensionless units like degrees and radians Mathcad treats the unit rad as a constant equal to 1 so if you have a number or an expression in radians you can type deg into the units placeholder to convert the result from radians to degrees Copying and Pasting Numerical Results You can copy a numerical result and paste it in your worksheet or into another application Controlling Calculation 93 To copy more than one number see Copying and Pasting Arrays on page 40 Note The Copy command copies the numerical result only to the precision displayed To copy the result in greater precision double click it and increase Displayed Precision on the Result Format dialog box Controlling Calculation Mathcad starts in automatic mode so that all results are updated automatically The word Auto appears in the message line at the bottom of the window You can disable automatic mode by unchecking Calculate gt Automatic Calculation from the Tools menu The word Auto changes to Calc F9 in the status line You are now in manual mode Tip The calculation mode either manual or automatic is a property saved in your worksheet and template XMCT files Whenever Mathcad needs time to complete com
165. s the multiplication as implied See the definition of mass at the bottom of Figure 8 8 To insert a unit 1 Click in the empty placeholder and choose Unit from the Insert menu or click on the Standard toolbar Mathcad opens the Insert Unit dialog box Insert Unit Dimension Acceleration Activity Angle Area Insert Cancel 15 degree C Calorie fcall5 20 degree C Calorie fcal20 Acre acre Ampere 4 Ampere tamp Angstrom amp ngstran 2 The bottom list shows built in units along with their Mathcad names corresponding to the physical quantity selected in the top list To see all available built in units select All in the top list 3 Double click the unit you want to insert or click the unit you want and then click Insert Mathcad inserts the unit into the empty placeholder Units and Dimensions 87 Note Mathcad performs some dimensional analysis by trying to match the dimensions of your selected result with one of the common physical quantities in the top list If it finds a match all the built in units corresponding to the highlighted physical quantity appear in the bottom list If nothing matches Mathcad simply lists all available built in units on the bottom Dimensional Checking Whenever you enter an expression involving units Mathcad checks it for dimensional consistency If you add or subtract values with incompatible units or violate other principles of dimensi
166. se Style from the Format menu to open the Text Styles dialog box 2 Click New to open the Define Style dialog box 3 Enter a name for the new style in the Name text box If you want to base the new style on one of the existing styles select a style from the Based on drop down list 4 Click the Font button to make choices for text formats for the new style Click the Paragraph button to choose paragraph formats for the new style Your new style now appears in the Text Styles dialog box and you can apply it to any text region When you save the worksheet the new text style is saved with it To use the new text style in future worksheets save your worksheet as a template as described in Chapter 7 Mathcad Worksheets You may also copy the text style into another worksheet simply by copying and pasting a styled region into the new worksheet Note If you base a new text style on an existing text style any changes you later make to the original text style are reflected in the new text style as well Deleting a Text Style To delete a text style 1 Choose Style from the Format menu to open the Text Styles dialog box 2 Select a text style from the list and click Delete Any text regions whose text and paragraph properties were defined by that text style continue to display the properties of the style Equations in Text This section describes how to insert equations into your text regions Equatio
167. se the entire expression so that the whole expression becomes the numerator 3 Now press to create a division bar Note that the numerator is whatever was enclosed between the editing lines when you pressed 4 Now type 4 and click on the Calculator toolbar Then type y 1 under the radical to complete the denominator 5 Press Space twice to make the editing lines hold the radical 6 Press Since the editing lines hold the entire radical the entire radical becomes the first operand when you press 7 Click on the Calculator toolbar or press Ctrl Shift P Editing Expressions 25 Editing Expressions Changing a Name or Number To edit a name or number 1 Click on it The blue insertion line appears 2 Move the blue insertion line by pressing the left and right arrow keys 3 Ifyou type a character it appears just to the left of the blue insertion line Pressing Backspace removes the character to the left Pressing Delete removes the character to the right Inserting an Operator The easiest place to insert an operator is between two characters in a name or two numbers in a constant To insert a plus sign between two characters 1 Place the editing lines where you want the plus sign to be 2 Press the key or click on the Calculator toolbar Note Mathcad inserts spaces automatically around operators when needed If you press
168. solving functions Find Maximize Minerr and Minimize can be entered in math regions with either an initial lowercase or an initial capital letter 100 Chapter 9 Solving Solve blocks can be used to solve parametric systems In Figure 9 3 the solution is cast in terms of several parameters in the solve block besides the unknown variable f 0 02 Given 1 ep 254 2 0 log Vi 3 7 FricFacte 0 R Find ts 2 5 in l O 19 z 00085 in Ry 10000 10000 i Same problem l solved for a vector ffi FricFacle D Rj of answers Figure 9 3 Solving an equation parametrically Solving and Optimization Functions 101 Solve blocks can also take matrices as unknowns and solve matrix equations See Figure 9 4 and Figure 9 5 Two methods for computing a matrix square root nonunique l3 4 4 9 3 4 3 SG Using eigenanalysis Vec eigenvecs M Yals diag eigenvals mM T S Vec a Vals Vac 3 528 0 639 0 38 5 0638 2 915 0 31 0 38 0 31 7 534 Using a solve block initial guess a M Given X EM S1 Find 2 095 2 867 0 623 Sl 2 86 0 55 0 69 0 623 0 69 7 492 Figure 9 4 A solve block for computing the square root of a matrix Note You can improve the solve block result in Figure 9 4 and those of many other sensitive problems by decreasing the CTOL variable State matrices 0 Oo 1 Given JG aeRaE PAC au 1 732 1 1 a Find P Figure
169. space curve 130 surface plots 128 130 text regions 45 variables 8 worksheet templates 55 creating new worksheets 55 crosshair for insertion 7 CTOL variable 76 102 Customer Service Guide 1 dashed selection rectangle 57 data entering into a table 35 data files exporting from an array 41 date in header or footer 63 debugging a worksheet 94 default formats numerical results 88 template 56 worksheet layout 55 defining complex numbers 19 functions 82 global variables 78 multiple definitions of variable 78 numbers 19 range variables 79 See also creating units 87 90 variables 8 73 definite integral 149 definition symbol 73 degrees converting to radians 92 deleting blank lines 60 characters in math 25 hard page breaks 62 hyperlinks 67 operators 26 parentheses 28 parts of an expression 29 regions 59 text 45 derivatives symbolic 148 determinant 152 Developer s Reference 13 device independent bitmap 107 dialects spell checker 54 DIB See device independent bitmap dictionaries spell checker 53 dictionaries languages 54 dimensions 87 disabling equations 94 display of arrays 39 display of operators 24 downloads 17 drag and drop 15 28 58 108 110 dragging regions 58 drawings See pictures e value of 74 75 E books 13 70 annotating 15 copying information from 15 creating 70 finding on the Web 16 moving around in 14 16 searching for information in 15 toolbar 14 16 Edit menu Go to Page
170. splays a simplified version of the original expression If an expression q cannot be simplified further Mathcad simply de i repeats it to the right of the symbolic equal sign Taa S siy The symbolic equal sign is a live operator just like any Mathcad operator When you make a change anywhere above or to the left of it Mathcad updates the result Figure 13 2 shows some examples of how to use the symbolic equal sign You can force the symbolic equal sign to ignore prior definitions of functions and variables by defining them recursively just before you evaluate them as shown in Figure 13 5 on page 147 17 4 17 4 123 Figure 13 2 The symbolic equal sign uses previous definitions If the expression cannot be simplified further the symbolic equal sign does nothing When decimals are used the symbolic equal sign returns decimal approximations Live Symbolic Evaluation 143 Note The symbolic equal sign applies to an entire expression You cannot use the symbolic equal sign to transform only part of an expression Using Keywords The takes the left hand side and places a simplified version of it on the right hand side You can control how the transforms the expression by using one of the symbolic keywords Online Help To do so 1 Enter the expression you want to evaluate y 2 Press Ctrl Shift 2 period 3 Click on the placeholder to the left of the symbolic eq
171. ste the object is pasted in your Mathcad worksheet as one of the following e A matrix if you are pasting numeric data into an empty math placeholder e A text region if you are pasting text e A bitmap or picture metafile if the source application generates graphics e An embedded object if the source application supports OLE If you choose Paste Special you have the option of pasting the object in one of several formats an embedded or linked OLE object a picture metafile or a bitmap 110 Chapter 10 Inserting Graphics and Other Objects Dragging and Dropping an Object into a Worksheet You can also drag an OLE object into a Mathcad worksheet directly from another application However this method of copying does not allow you to create a link to the object Editing an Embedded Object Double click an embedded object in a Mathcad worksheet so that the menus and toolbars change to those of the source application and a hatched border surrounds the object You can use in place activation to edit objects created by applications such as Excel and Word inside Mathcad If the source application does not support in place activation inside Mathcad or the object is linked the behavior is different In the case of an embedded object a copy of the object is placed into a window from the other application or the object is inserted as an icon If the object is linked the source application opens the file containing the object Ed
172. stem of equations symbolically Solving a System of Equations Symbolically Solve Block Another way to solve a system of equations symbolically is to use a solve block similar to numeric solve blocks 1 Type the word Given in a math region stating that what follows is a system of equations You can type Given in any combination of upper and lowercase letters and in any font 2 Enter the equations below the word Given Make sure to press Ctr1 for the Boolean equal sign 3 Enter the Find function with arguments appropriate for your system of equations This function is described in Linear Nonlinear System Solving and Optimization on page 98 4 Press Ctr1 period Mathcad displays the symbolic equal sign 5 Press Enter Mathcad displays the solutions to the system of equations to the right of the symbolic equal sign Figure 13 11 shows an example Most of the guidelines for numeric solve blocks described earlier apply to the symbolic solution of systems of equations The main difference is that when you solve equations symbolically you do not enter guess values for the solutions Symbolic Matrix Manipulation You can use Mathcad to find the symbolic transpose inverse or determinant ofa matrix using a built in operator and the symbolic equal sign To find the transpose of a matrix for example Examples of Symbolic Calculation 153 1 Place the entire matrix between the two editing lines by c
173. stion mark 2 Click a command from a menu Mathcad opens the relevant Help screen 3 Click any toolbar button Mathcad displays the operator s name and a keyboard shortcut in the status bar To resume editing press Esc The pointer turns back into an arrow Mathcad Community on PlanetPTC The Mathcad Community on PlanetPTC allows you to post messages download files and read messages contributed by other Mathcad users You can search for messages containing a key word or phrase be notified of new messages in specific discussions and view messages posted since your last visit PlanetPTC combines some of the best features of an online news group with the convenience of sharing Mathcad worksheets The Mathcad Community is available in the following URL http communities ptc com community mathcad If you wish to contribute files or listings to the resources please email mathcad author ptc com Other Resources Read This First Read This First is available through the Resources Window It contains the latest information on Mathcad updates to the documentation and troubleshooting instructions The most up to date Read This First is posted on the PTC site at Maintenance users http www ptc com appserver cs doc refdoc jsp Single users http www ptc com support mathcad htm Technical Support The Technical Support Knowledge Base contains frequently asked questions sample files and support resources These are posted on the W
174. t select the text and drag it off the plot Then drag the text region back onto the plot Modifying 3D QuickPlot Data When you create a 3D QuickPlot you can change the range and step size of each independent variable by using the settings on the QuickPlot Data page of the 3D Plot Format dialog box To change the range of either independent variable Formatting a 3D Plot 139 Online Help 1 Set the start and end values of either range using the text boxes for each range 2 Click Apply to preview To change the step size the number of grids generated along each variable s axis between the start and end values 1 Use the arrows next to of Grids to increase or decrease the grid value for each range Alternatively you can type in a value in the text box 2 Click Apply to preview your changes The ranges you set for the independent variables in the QuickPlot Data page do not necessarily control the axis limits of the plot unless you are plotting a single function of two variables in Cartesian coordinates In all other cases the axis limits are determined by the x y and z data generated for the QuickPlot by your function s To perform automatic coordinate system conversions on your QuickPlot data 1 Choose Cartesian Spherical or Cylindrical in the Coordinate System section 2 Click Apply to preview your changes Rotating and Zooming on 3D Plots To resize a 3D
175. t inside the selection rectangle Release the mouse to see dashed rectangles around the selected regions 58 Chapter 7 Mathcad Worksheets Tip You can select or deselect a single region or disconnected regions anywhere in the worksheet by holding down the Ctr1 key while clicking on each region Also if you click one region and Shift click another you can select both regions and all regions in between Region Properties Note The Region Properties dialog box allows you to perform different actions depending on the type of region you ve selected e Highlight the region e Display a border around the region e Automatically move everything down in the worksheet below a text region when the region expands e Disable or enable evaluation of a math region e Turn protection on or off for the region You can change the properties for a region or multiple regions by selecting the regions and either choosing Properties from the Format menu or by right clicking on one of the regions and choosing Properties from the menu When you select multiple regions you may only change the properties common to the regions selected If you select both math and text regions you cannot change text only or math only options Moving and Copying Regions Note Once regions are selected you can move or copy them Moving Regions You can move regions by dragging them with the mouse nudging them with the arrow keys or by using Cut a
176. te is determined by the function using these x and y values G u v is a vector valued function of two variables The x y and z coordinates are plotted parametrically according to the definitions in the three elements of the vector using these u and v values X u v Y u v and Z u v are functions of two variables The x y and z coordinates are plotted parametrically according to the three function definitions using these u and v values The function descriptions above assume that you are working in Cartesian coordinates If your function represents spherical or cylindrical coordinates you can automatically convert the function to Cartesian coordinates Double click on the plot go to the QuickPlot Data page of the 3D Plot Format dialog box and click Spherical or Cylindrical under Coordinate System Creating 3D Plots of Functions 129 Step 2 Insert a 3D plot Choose Graph from the Insert menu and select a 3D plot type To create a surface plot from the functions X Y and Z defined above 1 Choose Graph gt Surface Plot from the Insert menu to display a blank 3D plot 2 Type the name of the functions separated by commas and enclosed in parentheses in the placeholder For this example type X Y Z 3 Press Enter XYZ To change your plot to a different plot type 1 Double click on the graph to bring up the 3D Plot Format dialog box 2 Inthe Display As section on the General tab s
177. the Edit Hyperlink dialog box To remove a hyperlink click the hyperlink and choose Hyperlink from the Insert menu Click Remove Link in the dialog box Creating Hyperlinks from Region to Region Before you can link to a specific region in a worksheet you must mark the region with a region tag A tag can be words numbers or spaces but not symbols To create a region tag 1 Right click on the region and select Properties 2 Inthe Properties dialog box under the Display tab type a tag in the Tag textbox Note You can not include a period in the tag name such as Section1 3 you must write Section1 3 To create a hyperlink to a region that has been tagged 1 Click a region or select words in your worksheet and choose Hyperlink from the Insert menu 2 Click Browse to locate and select the target worksheet or enter an Internet address URL You do not have to enter the name of the target worksheet if you are creating a hyperlink to a region within the same worksheet 68 Chapter 7 Mathcad Worksheets At the end of the worksheet path type followed by the region tag The complete path for your target region will look like this C filename region tag If you are in the same file the path to another region will look like this region tag Note that you must include the Note You cannot use the pop up window option when you link from region to region within or between Mathcad worksheets Creating
178. the Format menu changing the settings in the Result Format dialog box and clicking Set as Default Changing the worksheet default result format affects only the current worksheet To use your default result formats in new worksheets save your worksheet as a template as described in Chapter 7 Mathcad Worksheets The Result Format Dialog Box Complete descriptions of options available under the Result Format dialog box can be found in Formatting Results The Number Format page lets you control the number of decimal places trailing zeros exponential threshold scientific or engineering notation or display of your results as fractions or mixed numbers The Display Options page lets you control whether arrays are displayed as tables or matrices whether nested arrays are expanded and whether i or j is used to indicate imaginary numbers You can also specify another radix such as Binary or Octal The Unit Display page gives you options to format units as fractions or simplify the units to derived units The Tolerance page allows you to specify when to hide a real or imaginary part of a result and how small a number has to be for it to display as zero 90 Chapter 8 Calculating in Mathcad Figure 8 10 shows some examples of formatting options w 5 2574 yem io Definitions General format Exponential threshold 15 9 20 Number of decimal places 2 we 5 2574 Decimal format Number of decimal places
179. the last equation in Figure 8 11 AW s is not a unit of force Mathcad therefore inserts m to cancel the extra length dimension mass 75kg acc 100m s7 f acc_g 9 8 m s_ z F mass acc acc_q a 2 Default display using fundamental SI units F 8 235 10 kgms Click on result to see the units placeholder F 9 2935 10 N S Type desired unit in the units placeholder F 8 235 10 dyne You can type combinations of units in the units placeholder 1 Since kW s is not a force unit Mathcad inserts F 8 235m kes an extra m7 to make the units come out right Figure 8 11 A calculated result displayed with different units Mathcad divides the value displayed by the units in the units placeholder when using multiplicative units This ensures that the complete displayed result the number times the expression you entered is a correct value for the equation In the case of scaling units the inverse scaling function is applied to the result Conversions involving an offset or nonlinear transformation such as gauge pressure converted to absolute pressure or degrees Kelvin to Fahrenheit can only be performed by themselves with Mathcad s unit placeholder conversion mechanism Unlike multiplicative units you cannot combine these functions with other units in the placeholder You can enter any variable constant or expression in a units placeholder Mathcad then redisplays the result in terms of the value in the unit
180. time parameter Step 2 Insert a 3D scatter plot To create a space curve from a function or set of functions 1 Choose Graph gt 3D Scatter Plot from the Insert menu to display a blank 3D plot 2 Enter the name of the function or functions in the placeholder separated by commas To create a space curve from the functions R S and T defined above type R S T RST For specific information on formatting see Scatter Plots in online Help Creating 3D Plots of Data You can create 3D plots from data using Insert menu commands and changing settings through the 3D Plot Format dialog or you can use the 3D Plot Wizard Creating a Surface Bar or Scatter Plot Surface bar and scatter plots are useful for visualizing two dimensional data contained in an array as either a connected surface bars above and below the zero plane or points in space Creating 3D Plots of Data 131 To create a surface plot from data 1 Create or import a matrix of values to plot The row and column numbers represent the x and y coordinate values The matrix elements themselves are the z coordinate values plotted as heights above and below the x y plane at z 0 2 Choose Graph gt Surface Plot from the Insert menu 3 Enter the name of the matrix in the placeholder Figure 12 2 shows a 3D bar plot created from a matrix M ee Bee ieee yp 54 0 15 1 Yi ole DeSe Hix yi sin 2x2 y2 Mi j Hiri yi Figure 12
181. ual sign and type any of the keywords from the Symbolic toolbar If the keyword Gro eni d 3 requires any additional arguments separate the arguments from the keyword with commas 4 Press Enter x Ti expand wig ant iay a You can also first enter the expression you want to evaluate Then click on a keyword from the Symbolic toolbar to insert the keyword placeholders for any additional arguments and the symbolic equal sign Finally press Enter for the result Online Help lists and describes all the symbolic keywords available from the Symbolic and Modifier toolbars 144 Chapter 13 Symbolic Calculation Note Many of the keywords take additional arguments such as the name of a variable with respect to which you are performing the symbolic operation Some of the arguments are optional See Figure 13 3 for an example a J X i Oty dx fey i expand 545 464 ese x x acos Q float 4 1 571 x exo a t laplace t at 5 Figure 13 3 By itself the symbolic equal sign simply evaluates the expression but when preceded by an appropriate keyword the symbolic equal sign can change its meaning Note that the keyword float makes the result display as a floating point number if possible The keyword laplace returns the Laplace transform of a function Keywords are case sensitive so they must be typed exactly as shown Unlike variables however they are not font sensitive Using Ar
182. ulating in Mathcad Names Note Online Help A name in Mathcad is simply a sequence of characters you type referring to a variable or function used in computations Built in Names Mathcad s built in names include built in variables and built in functions e Some predefined or built in variables either have a conventional value like 1 3 14159 or e 2 71828 or are used as system variables to control how Mathcad performs calculations See Built in Variables on page 75 e In addition to these predefined variables Mathcad treats the names of all built in units as predefined variables For example Mathcad recognizes the name A as the ampere m as the meter s as the second and so on Choose Unit from the Insert menu or click E on the Standard toolbar to see Mathcad s predefined units See Units and Dimensions on page 84 e Choose Function from the Insert menu or click ft on the Standard toolbar to see Mathcad s built in functions User defined Variable and Function Names Names in Mathcad can contain any of the following characters e Uppercase and lowercase letters e The digits 0 through 9 although they cannot start a name e The underscore _ e The prime symbol Note that this is not the same as an apostrophe You can press Ctr1 F7 to insert it e The percent symbol e Greek letters To insert a Greek letter click a button on th
183. umbers 19 binary 89 complex 19 decimal 89 displayed as zero 89 exponential notation for 20 format for computed results 88 formatting 9 88 imaginary 19 octal 89 radix base for results 89 numerical methods root finding 97 solving and optimization 98 object linking and embedding See OLE Object Model in Mathcad 13 octal numbers 89 OLE 108 110 drag and drop 110 editing links 110 in place activation 108 110 online resources 13 OpenGL 127 operator display 24 operator placeholder 27 operators defined 20 deleting 26 derivative 148 indefinite integral 149 inserting 25 replacing 27 160 Index toolbars 6 optimizers 98 ORIGIN variable 38 output table 39 alignment 39 resizing 39 versus matrix display style 89 overlapping regions 60 overtyping text 45 page breaks inserting and deleting 62 headers and footers 62 length 62 numbering 63 Page Setup dialog box 61 68 paragraphs 48 bullets 49 hanging indent 49 indenting 49 numbers 49 properties 48 tab stops 49 text alignment in 49 parametric plot creating 117 parametric surface plots creating 131 132 See also plots 3D parentheses deleting from expression 28 inserting into an expression 27 password protecting an area hiding an area 63 Paste command 109 Paste Special command 109 pasting bitmaps 107 device independent bitmaps 107 from Clipboard 28 107 metafiles 107 OLE objects 109 PDF Portable Document Format creating 70 pending com
184. ures This section describes techniques for creating and formatting pictures in your worksheet Creating Pictures from Matrices Note You can view any single matrix as a grayscale picture by creating a picture region 1 Click in a blank space 2 Choose Picture from the Insert menu or click on the Matrix toolbar 3 Type the name of a matrix in the placeholder at the bottom of the picture region Mathcad creates a 256 shade grayscale representation of the data in the matrix with each matrix element corresponding to a pixel in the picture Mathcad s picture region assumes a 256 color model with the value 0 represented as black and 255 as white Numbers outside the range 0 255 are reduced modulo 256 and any noninteger value is treated as if its decimal part has been removed To create a color picture in Mathcad you must define three matrices of the same size that describe either e The red green and blue RGB components e The hue saturation and value Smith s HSV color model components or 105 106 Chapter 10 Inserting Graphics and Other Objects e The hue lightness and saturation Otswald s HLS color model components of each pixel in the picture To view any three same size matrices as a color picture 1 Click in a blank space and choose Picture from the Insert menu 2 Type the names of the three matrices separated by commas in the placeholder at the bottom of the picture region
185. us sign sinta a Inserting Parentheses Mathcad places parentheses automatically to maintain the order of operations You may want to place parentheses to clarify an expression or to change the overall structure of the expression You can either insert a pair of parentheses all at once or insert one parenthesis at a time We recommend you insert a pair since this avoids the possibility of unmatched parentheses To enclose an expression with a pair of parentheses 1 Click on the expression and press Space one or more times to a b place it between the editing lines a b 28 Chapter 4 Working with Math Te 2 Type the single quote key or click i on the Calculator 2 b z toolbar The expression is now enclosed by parentheses a b It is sometimes necessary to insert parentheses one at a time using the and keys For example to change b c to a b c 1 Click just to the left of the b Make sure the blue insertion line is on the left as shown Press Insert if necessary to move it over 2 Type and click to the right of the c Make sure the blue insertion line is to the right as shown Press Insert if necessary to move a b q it over 3 Type b c a b e mu l Eg m Deleting Parentheses Whenever you delete one parenthesis Mathcad deletes the matched parenthesis This prevents you from inadvertently creating an expression having unmatched parentheses
186. variables 77 units alternative definitions 90 base units 90 CGS system 90 common sources of error 87 converting calculated results 91 default 84 defining 87 90 dimensional consistency 87 errors in dimensions 87 in equations 84 metric 90 MKS system 90 placeholder 90 prefixes 91 SI 90 simplifying 89 U S customary 90 update worksheet window 93 URL PTC home page 16 User Forums 17 user defined functions 82 evaluating variables in 83 valid names 74 variable in red 77 Variable Differentiate command 148 Variable Integrate command 149 Variable Solve command 151 variables changing the font style of 29 defining 8 73 global definitions of 78 in red 94 matrices 33 names 74 predefined built in 75 range variables 34 79 undefined 94 vectors 33 vector changing size 34 definition of 33 vectorize operator 41 how to type 41 vectors calculations by element 41 displayed as scrolling output tables 39 graphing 119 numbering elements 38 ORIGIN used with 38 start with element zero 38 subscripts 37 undefined elements filled with zeros 38 vectorize operator 41 View Animate command 125 wait message 93 wavy green line 88 Web page options 70 Web pages creating from worksheets 70 formatting 70 164 Index Web pages creating from worksheets 70 Web toolbar 16 Web browsing mode 16 Wizards for inserting 3D plots 127 word processor 21 worksheet ruler 59 worksheet templates 56 worksheets creating 55 exporting as RTF 71 f
187. ved SI units You can display results in units of any of the other built in unit systems in Mathcad CGS U S or MKS or not use a unit system at all To do so choose Worksheet Options from the Tools menu and click the Unit System tab Working with Results 91 Tip Select the default unit system for display of results The SI and US base electrical unit ampere differs from the base electrical unit in MKS coulomb and in CGS statcoulomb The following table summarizes the base units available in Mathcad Unit System Base Units SI m kg s A K cd and mole MKS m kg sec coul K cd and mole CGS cm gm sec statcoul K cd and mole USS ft lb sec A K cd and mole Displays results in terms of fundamental dimensions of None length mass time charge and absolute temperature All built in units are disabled The standard SI unit names such as A for ampere L for liter s for second and S for siemens are generally available in all unit systems except where there are conflicts with system definitions CGS The Insert Unit dialog provides a complete listing of units available for the unit system you have chosen Mathcad includes most units common to scientific and engineering practice When conventional unit prefixes such as m for milli n for nano and so on are not understood by Mathcad you can easily define custom units such as ns as described in Defining Your Own Units on page 87 For e
188. words and modifiers The Standard toolbar provides quick access to many menu commands Standard Dae Savy The Formatting toolbar contains scrolling lists and buttons to specify font characteristics for both equations and text Formatting To learn what a button on any toolbar does hover the mouse over the button until a tooltip appears with a brief description You can choose to show or hide each toolbar from the View menu To detach and drag a toolbar around your window place your cursor on the edge of the toolbar Then hold down the mouse button and drag You can also click on the blue title bar and drag You can customize the Standard and Formatting toolbars To add and remove buttons right click on the toolbar and choose Customize from the menu Regions 7 Working with Worksheets When you start Mathcad you open a Mathcad worksheet You can have as many worksheets open as your available system resources allow If you are working with a longer worksheet use Go to Page from the Edit menu to move quickly through the worksheet Regions Mathcad lets you enter equations text and plots anywhere in the worksheet Each equation piece of text or other element is a region A Mathcad worksheet is a collection of such regions To start a new region in Mathcad 1 Click anywhere in a blank area of the worksheet You see a small crosshair l Anything you type appears at the crosshair
189. xamples of units with prefixes not already built into Mathcad see the Units section of the Tutorials under the Help menu If you click None in the Unit System tab of the Worksheet Options dialog box Mathcad doesn t understand any built in units and displays answers in terms of the fundamental dimensions of length mass time charge and temperature However even if you are working in one of Mathcad s built in unit systems you can always choose to see results displayed in fundamental dimension names rather than the base units of the unit system To do so 1 Choose Worksheet Options from the Tools menu 2 Click the Dimensions tab 3 Check Display dimensions and click OK Unit Conversions There are two ways to convert from one set of units to another e Use the Insert Unit dialog box or e Type units directly into the units placeholder To convert units using the Insert Unit dialog box 1 Click the unit you want to replace 2 Choose Unit from the Insert menu or click on the Standard toolbar 3 Double click the unit you want displayed 92 Chapter 8 Calculating in Mathcad Note Tip Figure 8 11 shows F displayed both in terms of fundamental SI units and in terms of several combinations of units When you enter an inappropriate unit in the units placeholder Mathcad inserts a combination of base units that generate the correct units for the displayed result For example in
190. y A le gt 4 Type assume in the placeholder followed by a fz 5 In the placeholder type a real using J2 Ctr1 for the Boolean equals i comma simplify assume a simplify assume a reall anit 6 Press Enter for the final result 5 ee ea lal assume a Assuming that a is a real number the result is the absolute value of a If you leave out the keyword assume Mathcad returns the result in terms of the complex sign function csgn which gives the sign of the real part ofa complex number ad a simplify a csgnia You can find more details about modifiers and keywords in the online Help topic The Symbolic Toolbar The simplify keyword simplifies expressions using algebraic rules and identities Figure 13 4 shows more examples of simplify w Oy 4 a 4 28 5 simplify 3 x 4 gantal simplify ra sin In a b simplify sin In a b Figure 13 4 The simplify keyword simplifies expressions Using the Symbolics Menu 147 Ignoring Previous Definitions To make Mathcad ignore prior definitions you must define the variable recursively such as x x This exception is illustrated in Figure 13 5 a Mathcad substitutes the value of 3 for x before evaluating this x 1j z 1 expand gt 4z 4 expression Although x is defined to be 3 Mathcad ignores that definition for symbolic evaluation because of the recursive definition

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