User’s Guide Mathsoft Engineering & Education, Inc. US and Canada All other countries 101 Main Street Knightway House Cambridge, MA 02142 Park Street Bagshot, Surrey Phone: 617-444-8000 GU19 5AQ FAX: 617-444-8001 United Kingdom http://www.mathsoft.com/ Phone: +44 (0) 1276 450850 FAX: +44 (0)1276 475552 i Mathsoft Engineering & Education, Inc. owns both the Mathcad software program and its documentation. Both the program and documentation are copyrighted with all rights reserved by Mathsoft. No part of this publication may be produced, transmitted, transcribed, stored in a retrieval system, or translated into any language in any form without the written permission of Mathsoft Engineering & Education, Inc. U.S. Patent Numbers 5,469,538; 5,526,475; 5,771,392; 5,844,555; and 6,275,866. See the License Agreement and Limited Warranty for complete information. International CorrectSpell software © 1993 by Vantage Research. MKM developed by Waterloo Maple Software. The Mathcad User Forums Collaboratory is powered by WebBoard, copyright 2001 by ChatSpace, Inc. Copyright 1986-2002 Mathsoft Engineering & Education, Inc. All rights reserved. Mathsoft Engineering & Education, Inc. 101 Main Street Cambridge, MA 02142 USA Mathcad is a registered trademark of Mathsoft Engineering & Education, Inc. Mathsoft, MathConnex, QuickPlot, Live Symbolics, IntelliMath and the Collaboratory are trade- marks of Mathsoft Engineering & Education, Inc. Microsoft, Windows, IntelliMouse, and the Windows logo are registered trademarks of Microsoft Corp. Windows NT is a trademark of Microsoft Corp. OpenGL is a registered trademark of Silicon Graphics, Inc. MATLAB is a registered trademark of The MathWorks, Inc. WebBoard is a trademark of ChatSpace, Inc. Other brand and product names referred to are trademarks or registered trademarks of their respective owners. Printed in the United States of America. November, 2002 ii Contents Getting Started About the User’s Guide 1 1: Welcome to Mathcad 3 What Is Mathcad? 3 Highlights of Mathcad 11 Release 4 System Requirements 7 Installation 7 Technical Support 9 2: Getting Started with Mathcad 11 The Mathcad Workspace 11 Regions 13 A Simple Calculation 16 Definitions and Variables 17 Entering Text 18 Iterative Calculations 19 Graphs 21 Saving, Printing, and Exiting 22 3: Online Resources 23 Mathcad Resources 23 Help 28 Collaboratory User Forums 29 Other Resources 32 4: Working with Math 33 Inserting Math 33 Building Expressions 39 Editing Expressions 42 Math Styles 50 5: Vectors, Matrices, and Data Arrays 53 Creating Arrays 53 Accessing Array Elements 56 Displaying Arrays 58 Working with Arrays 61 Nested Arrays 63 6: Working with Text 65 Inserting Text 65 Text and Paragraph Properties 68 Text Styles 71 Equations in Text 72 Text Tools 73 iii 7: Worksheet Management 77 Worksheets and Templates 77 Rearranging Your Worksheet 80 Layout 83 Safeguarding an Area of the Worksheet 85 Safeguarding an Entire Worksheet 87 Worksheet References 88 Hyperlinks 89 Distributing Your Worksheets 91 Calculating with Mathcad 8: Calculating in Mathcad 99 Defining and Evaluating Variables 99 Defining and Evaluating Functions 106 Units and Dimensions 109 Working with Results 112 Controlling Calculation 118 Animation 121 Error Messages 123 9: Solving and Data Analysis 125 Solving and Optimization Functions 125 Differential Equation Solvers 133 Data Fitting 145 10: Inserting Graphics and Other Objects 151 Overview 151 Inserting Pictures 151 Inserting Objects 155 Inserting Graphics Computationally Linked to Your Worksheet 158 11: 2D Plots 161 Overview of 2D Plotting 161 Graphing Functions and Expressions 163 Plotting Vectors of Data 166 Formatting a 2D Plot 168 Modifying a 2D Plot’s Perspective 171 12: 3D Plots 175 Overview of 3D Plotting 175 Creating 3D Plots of Functions 176 Creating 3D Plots of Data 179 Formatting a 3D Plot 184 Rotating and Zooming on 3D Plots 193 iv 13: Symbolic Calculation 195 Overview of Symbolic Math 195 Live Symbolic Evaluation 196 Using the Symbolics Menu 201 Examples of Symbolic Calculation 203 Symbolic Optimization 212 14: Importing and Exporting Data 215 Overview 215 Functions for Reading and Writing Files 215 Exchanging Data with Other Applications 216 Data Input and Output Components 219 Application Components 222 230 15: Extending and Automating Mathcad 231 Overview 231 Programming within Mathcad 231 Building Function DLLs 243 Creating Your Own Components 243 Accessing Mathcad from Within Another Application 248 Functions and Operators 16: Functions 249 Built-in Functions 249 Function Categories 249 Mathcad Functions Listed Alphabetically 260 Functions 260 17: Operators 391 Arithmetic Operators 394 Vector and Matrix Operators 398 Calculus Operators 402 Evaluation Operators 411 Boolean Operators 415 Programming Operators 417 18: Symbolic Keywords 421 Accessing Symbolic Keywords 421 Finding More Information 422 Keywords 422 v Appendices 431 Appendix A: Special Functions 432 Appendix B: SI Units 434 Appendix C: CGS units 436 Appendix D: U.S. Customary Units 438 Appendix E: MKS Units 440 Appendix F: Predefined Variables 442 Appendix G: Suffixes for Numbers 443 Appendix H: Greek Letters 444 Appendix I: Arrow and Movement Keys 445 Appendix J: Function Keys 446 Appendix K: ASCII codes 447 Appendix L: References 448 Index 449 vi About the User’s Guide The Mathcad User’s Guide is organized as follows: ! Getting Started This section contains a quick introduction to Mathcad’s features and workspace, including resources available in the product and on the Internet for getting more out of Mathcad. Be sure to read this section first if you are a new Mathcad user. ! Calculating with Mathcad This section describes in more detail how to create and edit Mathcad worksheets. It describes how Mathcad interprets equations and explains Mathcad’s computational features: units of measurement, complex numbers, matrices, built- in functions, solving equations, programming, and so on. This section also describes how to do symbolic calculations and how to use Mathcad’s two- and three-dimensional plotting features. ! Functions and Operators This section lists and describes in detail all built-in functions, operators, and symbolic keywords, including how to use them in your calculations. Notations and Conventions The User’s Guide uses the following notations and conventions: Italics represent scalar variable names, function names, and error messages. Bold Courier represents keys you should type. Bold represents a menu command. It is also used to denote vector and matrix valued variables. An arrow such as that in “Graph⇒X-Y Plot” indicates a submenu command. Function keys and other special keys are enclosed in brackets. For example, [↑], [↓], [←], and [→] are the arrow keys on the keyboard. [F1], [F2], etc., are function keys; [BkSp] is the Backspace key for backspacing over characters; [Del] is the Delete key for deleting characters to the right; [Ins] is the Insert key for inserting characters to the left of the insertion point; [Tab] is the Tab key; and [Space] is the space bar. [Ctrl], [Shift], and [Alt] are the Control, Shift, and Alt keys. When two keys are shown together, for example, [Ctrl]V, press and hold down the first key, and then press the second key. The symbol [↵] and [Enter] refer to the same key. 1 2 / How to Use the User Guide Additionally, in the Functions and Operators section of this book, the following specific notation is used whenever possible: • x and y represent real numbers. • z and w represent either real or complex numbers. • m, n, i, j, and k represent integers. • S and any names beginning with S represent string expressions. • u, v, and any names beginning with v represent vectors. • A and B represent matrices or vectors. • M and N represent square matrices. • f represents a scalar-valued function. • F represents a vector-valued function. • file is a string variable that corresponds to a filename or path. • X and Y represent variables or expressions of any type. When spaces are shown in an equation, you need not type the spaces. Mathcad automatically spaces equations correctly. Chapter 1 Welcome to Mathcad ! What Is Mathcad? ! Highlights of Mathcad 11 Release ! System Requirements ! Installation ! Technical Support What Is Mathcad? Mathcad is the industry standard technical calculation tool for professionals, educators, and college students worldwide. Mathcad is as versatile and powerful as a programming language, yet it’s as easy to learn as a spreadsheet. Plus, it is fully wired to take advantage of the Internet and other applications you use every day. Mathcad lets you type equations as you’re used to seeing them, expanded fully on your screen. In a programming language, equations look something like this: x=(-B+SQRT(B**2-4*A*C))/(2*A) In a spreadsheet, equations go into cells looking something like this: +(B1+SQRT(B1*B1-4*A1*C1))/(2*A1) And that’s assuming you can see them. Usually all you see is a number. In Mathcad, the same equation looks the way you might see it on a blackboard or in a reference book. And there is no difficult syntax to learn; you simply point and click and your equations appear. But Mathcad equations do much more than look good. You can use them to solve just about any math problem you can think of, symbolically or numerically. You can place text anywhere around them to document your work. You can show how they look with Mathcad’s two- and three-dimensional plots. You can even illustrate your work with graphics taken from another application. Plus, 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 comes with online Tutorials; QuickSheets to show you working examples of Mathcad functions including working with other applications; and Reference Tables with math, science, and engineering formulas all under the Help menu. Online Help includes the Author’s Reference and Developer’s Reference for more advanced usage.