Mathcad User’s Guide with Reference Manual Mathcad 2001i Mathcad User’s Guide with Reference Manual Mathcad 2001i 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 M a t h S oft Σ + √ − = × ∫ ÷ δ 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. English spelling software by Lernout & Haspie Speech Products, N.V. MKM developed by Waterloo Maple Software. VoloView Express technology, copyright 2000 Autodesk, Inc. All Rights Reserved. The Mathcad Collaboratory is powered by WebBoard, copyright 2001 by ChatSpace, Inc. IBM techexplorerTM Hypermedia Browser is a trademark of IBM in the United States and other countries and is used under license. Copyright 1986-2001 MathSoft Engineering & Education, Inc. All rights reserved. MathSoft Engineering & Education, Inc. 101 Main Street Cambridge, MA 02142 USA Mathcad, Axum,andS-PLUS are registered trademarks of MathSoft Engineering & Education, Inc. Electronic Book, QuickSheets, MathConnex, ConnexScript, Collaboratory, IntelliMath, Live Symbolics, and the MathSoft logo are trademarks 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. SmartSketch is a registered trademark of Intergraph Corporation. 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, 2001 Contents How to Use the User’s Guide with Reference Manual 1 The Basics 1: Welcome to Mathcad 3 What Is Mathcad? 3 Highlights of Mathcad 2001i Release 4 System Requirements 6 Installation 6 Contacting MathSoft 7 2: Getting Started with Mathcad 8 The Mathcad Workspace 8 Regions 10 A Simple Calculation 13 Definitions and Variables 14 Entering Text 15 Iterative Calculations 16 Graphs 18 Saving, Printing, and Exiting 20 3: Online Resources 21 Resource Center and Electronic Books 21 Help 26 Internet Access in Mathcad 28 The Collaboratory 28 Other Resources 32 Creating Mathcad Worksheets 4: Working with Math 33 Inserting Math 33 Building Expressions 39 Editing Expressions 43 Math Styles 51 5: Working with Text 54 Inserting Text 54 Text and Paragraph Properties 57 Text Styles 60 Equations in Text 62 Text Tools 63 6: Working with Graphics and Other Objects 65 Overview 65 Inserting Pictures 65 Inserting Objects 70 Inserting Graphics Computationally Linked to Your Worksheet 73 7: Worksheet Management 74 Worksheets and Templates 74 Rearranging Your Worksheet 80 Layout 84 Safeguarding an Area of the Worksheet 86 Safeguarding an Entire Worksheet 88 Worksheet References 89 Hyperlinks 90 Creating Electronic Books 92 Printing and Mailing 93 Computational Factors 8: Calculating in Mathcad 96 Defining and Evaluating Variables 96 Defining and Evaluating Functions 103 Units and Dimensions 106 Working with Results 109 Controlling Calculation 116 Animation 118 Error Messages 120 9: Operators 122 Working with Operators 122 Arithmetic and Boolean Operators 124 Vector and Matrix Operators 127 Summations and Products 129 Derivatives 132 Integrals 134 Customizing Operators 138 10: Built-in Functions 141 Inserting Built-in Functions 141 Core Mathematical Functions 143 Discrete Transform Functions 148 Vector and Matrix Functions 150 Solving and Optimization Functions 156 Statistics, Probability, and Data Analysis Functions 162 Finance Functions 172 Differential Equation Functions 176 Miscellaneous Functions 187 11: Vectors, Matrices, and Data Arrays 192 Creating Arrays 192 Accessing Array Elements 197 Displaying Arrays 199 Working with Arrays 202 Nested Arrays 205 12: 2D Plots 207 Overview of 2D Plotting 207 Graphing Functions and Expressions 209 Plotting Vectors of Data 212 Formatting a 2D Plot 215 Modifying a 2D Plot’s Perspective 218 13: 3D Plots 221 Overview of 3D Plotting 221 Creating 3D Plots of Functions 222 Creating 3D Plots of Data 225 Formatting a 3D Plot 231 Rotating and Zooming on 3D Plots 240 14: Symbolic Calculation 242 Overview of Symbolic Math 242 Live Symbolic Evaluation 243 Using the Symbolics Menu 251 Examples of Symbolic Calculation 253 Symbolic Optimization 263 15: Programming 265 Defining a Program 265 Conditional Statements 267 Looping 268 Controlling Program Execution 271 Error Handling 273 Programs Within Programs 275 16: Extending Mathcad 278 Overview 278 Exchanging Data with Other Applications 278 Scripting Custom OLE Automation Objects 289 Accessing Mathcad from Within Another Application 295 Reference Manual 17: Functions 296 Function Categories 296 Finding More Information 297 About the References 297 Functions 298 18: Operators 426 Accessing Operators 426 Finding More Information 427 About the References 427 Arithmetic Operators 427 Matrix Operators 432 Calculus Operators 435 Evaluation Operators 441 Boolean Operators 445 Programming Operators 447 19: Symbolic Keywords 451 Accessing Symbolic Keywords 451 Finding More Information 452 Keywords 452 Appendices 462 Special Functions 463 SI Units 465 CGS units 467 U.S. Customary Units 469 MKS Units 471 Predefined Variables 473 Suffixes for Numbers 474 Greek Letters 475 Arrow and Movement Keys 476 Function Keys 477 ASCII codes 478 References 479 Index 480 How to Use the User’s Guide with Reference Manual The Mathcad User’s Guide with Reference Manual is organized as follows: The Basics 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. Creating Mathcad Worksheets This section describes in more detail how to create and edit Mathcad worksheets. It leads you through editing and formatting equations, text, and graphics, as well as opening, editing, saving, and printing Mathcad worksheets and templates. Computational Features This section 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. Reference Manual This section lists and describes in detail all built-in functions, operators, and symbolic keywords, emphasizing their mathematical and statistical aspects. As much as possible, the topics in this guide are described independently of each other. This means that once you are familiar with the basic workings of Mathcad, you can simply select a topic of interest and read about it. Online Resources The Mathcad Resource Center (choose Resource Center from the Help menu in Mathcad) provides step by step tutorials, examples, and application files that you can use directly in your own Mathcad worksheets. Mathcad QuickSheets are templates available in the Resource Center that provide live examples that you can manipulate. The Author’s Reference (choose Author’s Reference from the Help menu in Math- cad) provides information about creating Electronic Books in Mathcad. An Electronic Book is a browsable set of hyperlinked Mathcad worksheets that has its own Table of Contents and index. The Developer’s Reference (choose Developer’s Reference from the Help menu in Mathcad) provides information about developing customized Mathcad components, specialized OLE objects in a Mathcad worksheet that allow you to access functions from other applications and data from remote sources. 1 2 / How to Use the User Guide The Developer’s Reference also documents Mathcad’s Object Model, which allows you to access Mathcad’s functionality from another application or an OLE container (see “Online Resources” on page 21 for more details). Notations and Conventions This 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,