User manual MAPLESOFT MAPLE 10

Maple User Manual Copyright © Maplesoft, a division of Waterloo Maple Inc. 2005. Maple User Manual Copyright Maplesoft, Maple, Maple Application Center, Maple Student Center, Maplet, Maple T.A., and MapleNet are all trademarks of Waterloo Maple Inc. © Maplesoft, a division of Waterloo Maple Inc. 2005. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transcribed, in any form or by any means -- electronic, mechanical, photocopying, recording, or otherwise. Information in this document is subject to change without notice and does not represent a commitment on the part of the vendor. The software described in this document is furnished under a license agreement and may be used or copied only in accordance with the agreement. It is against the law to copy the software on any medium except as specifically allowed in the agreement. Windows is a registered trademark of Microsoft Corporation. Java and all Java based marks are trademarks or registered trademarks of Sun Microsystems, Inc. in the United States and other countries. Maplesoft is independent of Sun Microsystems, Inc. All other trademarks are the property of their respective owners. This document was produced using a special version of Maple and DocBook. Printed in Canada ISBN 1-894511-75-1 Contents Preface .................................................................................................... xiii 1 Document Mode ...................................................................................... 1 1.1 Introduction ...................................................................................... 1 1.2 In This Chapter ................................................................................ 3 1.3 Simple Mathematical Expressions ................................................... 4 Rational Expressions (Fractions) ....................................................... 5 Powers ................................................................................................ 5 Products .............................................................................................. 5 Shortcuts for Entering Mathematical Expressions ............................. 6 Other Expressions .............................................................................. 7 1.4 Evaluating Expressions .................................................................... 8 1.5 Editing Expressions and Updating Output ...................................... 9 1.6 Entering Expressions ..................................................................... 10 Palettes ............................................................................................ 10 Symbol Names ................................................................................ 16 1.7 Performing Computations ............................................................. 19 Computing with Palettes ................................................................. 20 Context Menus ................................................................................ 20 Assistants and Tutors ....................................................................... 26 1.8 Document Mode Summary ............................................................ 30 1.9 Getting Help ................................................................................... 32 2 Worksheet Mode ................................................................................... 35 2.1 In This Chapter .............................................................................. 36 2.2 Input Prompt .................................................................................. 37 Suppressing Output .......................................................................... 38 1-D Math Input ................................................................................ 38 Input Separators ............................................................................... 39 2.3 Commands .................................................................................... 40 The Maple Library ........................................................................... 40 Top-Level Commands ...................................................................... 40 Package Commands ........................................................................ 42 2.4 Palettes .......................................................................................... 44 2.5 Context Menus .............................................................................. 46 2.6 Assistants and Tutors ..................................................................... 48 iii iv · Contents Launching an Assistant or Tutor ...................................................... 48 Example: Using the Interactive Plot Builder ................................... 49 2.7 Task Templates .............................................................................. 51 Viewing Task Templates .................................................................. 51 Inserting a Task Template ................................................................ 52 Performing the Task ......................................................................... 53 2.8 Text Regions ................................................................................... 54 2.9 Names ........................................................................................... 55 Assigning to Names ........................................................................ 55 Unassigning Names ........................................................................ 57 Valid Names .................................................................................... 58 2.10 Equation Labels .......................................................................... 59 Displaying Equation Labels ............................................................. 59 Referring to a Previous Result ......................................................... 59 Execution Groups with Multiple Outputs ........................................ 61 Label Numbering Schemes ............................................................. 61 Features of Equation Labels ............................................................ 62 3 Performing Computations .................................................................... 65 3.1 In This Chapter .............................................................................. 65 3.2 Symbolic and Numeric Computation ............................................ 66 Exact Computations ........................................................................ 67 Floating-Point Computations .......................................................... 68 Converting Exact Quantities to Floating-Point Values ................... 69 Sources of Error .............................................................................. 70 3.3 Integer Operations ......................................................................... 71 Non-Base 10 Numbers and Other Number Systems ........................ 74 3.4 Solving Equations .......................................................................... 78 Solving Equations and Inequations ................................................. 78 Other Specialized Solvers ................................................................ 88 3.5 Units, Scientific Constants, and Uncertainty ................................. 96 Units ................................................................................................ 97 Scientific Constants and Element Properties ................................ 105 Uncertainty Propagation ............................................................... 111 3.6 Restricting the Domain ................................................................ 115 Real Number Domain ................................................................... 115 Assumptions on Variables ............................................................. 117 Contents · v 4 Mathematical Computations .............................................................. 123 4.1 In This Chapter ............................................................................ 125 4.2 Algebra ........................................................................................ 126 Polynomial Algebra ...................................................................... 126 4.3 Linear Algebra ............................................................................ 135 Creating Matrices and Vectors ...................................................... 135 Accessing Entries in Matrices and Vectors ................................... 144 Linear Algebra Computations ....................................................... 145 Student LinearAlgebra Package .................................................... 152 4.4 Calculus ....................................................................................... 153 Limits ............................................................................................ 153 Differentiation ............................................................................... 155 Series ............................................................................................. 161 Integration ..................................................................................... 163 Differential Equations .................................................................... 166 Calculus Packages ......................................................................... 166 4.5 Optimization ............................................................................... 168 Point-and-Click Interface .............................................................. 169 Large Optimization Problems ....................................................... 171 MPS(X) File Support .................................................................... 173 Additional Information .................................................................. 173 4.6 Statistics ...................................................................................... 173 Probability Distributions and Random Variables .......................... 173 Statistical Computations ................................................................ 175 Plotting .......................................................................................... 177 Additional Information .................................................................. 179 4.7 Teaching and Learning with Maple ............................................ 180 Student Packages and Tutors ........................................................ 181 5 Plots and Animations .......................................................................... 189 5.1 In This Chapter ............................................................................ 189 5.2 Creating Plots .............................................................................. 190 Interactive Plot Builder ................................................................. 191 Context Menu ................................................................................ 204 Dragging to a Plot Region ............................................................. 207 The plot and plot3d Commands .................................................... 208 The plots Package ......................................................................... 211 vi · Contents Multiple Plots in the Same Plot Region ......................................... 214 5.3 Customizing Plots ....................................................................... 216 Interactive Plot Builder Options ................................................... 216 Context Menu Options .................................................................. 217 The plot and plot3d Options ......................................................... 220 5.4 Analyzing Plots ........................................................................... 222 Point Probe, Rotate, Pan, and Scale Tools ..................................... 222 5.5 Creating Animations ................................................................... 223 Interactive Plot Builder ................................................................. 223 The plots[animate] Command ....................................................... 225 5.6 Playing Animations ..................................................................... 226 Animation Context Bar .................................................................. 226 5.7 Customizing Animations ............................................................. 228 Interactive Plot Builder Animation Options .................................. 228 Context Menu Options .................................................................. 228 The animate Command Options .................................................... 229 5.8 Exporting ..................................................................................... 230 5.9 Code for Color Plates .................................................................. 230 6 Creating Mathematical Documents ..................................................... 231 6.1 In This Chapter ............................................................................ 232 6.2 Document Formatting .................................................................. 233 Quick Character Formatting .......................................................... 233 Quick Paragraph Formatting .......................................................... 235 Copy and Paste ............................................................................... 236 Sections .......................................................................................... 237 Display Hidden Formatting Attributes ........................................... 238 Indentation and the Tab Key .......................................................... 238 Character and Paragraph Styles ..................................................... 239 Document Blocks ........................................................................... 247 Typesetting ..................................................................................... 252 Using Tables for Layout ................................................................. 252 Formatting Lists: Bullets, Numbers, and Indent ............................ 262 Bookmarks ..................................................................................... 264 Inserting Images ............................................................................. 265 Show or Hide Worksheet Content .................................................. 266 6.3 Embedded Components ............................................................... 268 Contents · vii Adding Graphical Interface Components ...................................... 268 Editing Component Properties: General Process ........................... 269 Removing Graphical Interface Components .................................. 269 Example Component Properties .................................................... 270 Printing and Exporting a Document with Embedded Components ................................................................................................. 271 6.4 Creating Graded Assignments ...................................................... 271 Creating a Question ........................................................................ 271 Viewing Questions in Maple .......................................................... 272 Saving Test Content ....................................................................... 272 6.5 Auto-Execute ................................................................................ 272 Setting the Auto-Execute Feature .................................................. 273 Removing the Auto-Execute Setting .............................................. 273 Repeating Auto-Execution ............................................................. 273 Security Levels ............................................................................... 273 6.6 Sketch Regions ............................................................................. 274 Insert a Sketch Pad ......................................................................... 274 Drawing .......................................................................................... 275 Canvas Style of Sketch Pad ............................................................ 275 Erase or Clear Content ................................................................... 276 Selection Tool ................................................................................ 277 6.7 Spell Checking ............................................................................. 277 How to Use the Spellcheck Utility ................................................. 278 Selecting a Suggestion ................................................................... 279 Spellcheck Usage and the Document ............................................. 279 User Dictionary .............................................................................. 279 6.8 Hyperlinks .................................................................................... 281 Inserting a Hyperlink in a Document ............................................. 281 6.9 Worksheet Compatibility ............................................................. 284 7 Maple Expressions .............................................................................. 285 7.1 In This Chapter ............................................................................ 285 7.2 Creating and Using Data Structures ............................................ 285 Expression Sequences ................................................................... 286 Sets ................................................................................................ 287 Lists ............................................................................................... 288 Arrays ............................................................................................ 289 viii · Contents Tables ............................................................................................ 290 Matrices and Vectors ..................................................................... 291 Functional Operators ..................................................................... 292 Strings ........................................................................................... 297 7.3 Working with Maple Expressions ................................................ 298 Low-Level Operations ................................................................... 298 Manipulating Expressions ............................................................. 304 Evaluating Expressions ................................................................. 310 8 Basic Programming ............................................................................ 321 8.1 In This Chapter ............................................................................ 321 8.2 Flow Control ................................................................................ 322 Conditional Execution (if Statement) ........................................... 322 Repetition (for Statement) ............................................................. 325 8.3 Iterative Commands .................................................................... 333 Creating a Sequence ...................................................................... 333 Adding and Multiplying Expressions ........................................... 334 Selecting Expression Operands ..................................................... 335 Mapping a Command over a Set or List ....................................... 336 Mapping a Binary Command over Two Lists or Vectors ............... 336 Additional Information .................................................................. 337 8.4 Procedures ................................................................................... 338 Defining and Running Simple Procedures .................................... 338 Procedures with Inputs .................................................................. 339 Procedure Return Values ............................................................... 339 Displaying Procedure Definitions ................................................. 340 Displaying Maple Library Procedure Definitions ......................... 340 Modules ......................................................................................... 342 9 Maplets ................................................................................................ 343 9.1 In This Chapter ............................................................................ 343 9.2 Simple Maplet .............................................................................. 343 9.3 Using Maplets ............................................................................. 344 Maplet File .................................................................................... 344 Maple Document ............................................................................ 345 9.4 Authoring Maplets ...................................................................... 345 Maplet Builder .............................................................................. 346 Maplets Package ........................................................................... 355 Contents · ix Saving ............................................................................................ 361 10 Input, Output, and Interacting with Other Products ......................... 363 10.1 In This Chapter .......................................................................... 363 10.2 Writing to Files ......................................................................... 363 Saving Data to a File ...................................................................... 363 Saving Expressions to a File .......................................................... 365 10.3 Reading from Files .................................................................... 366 Reading Data from a File ............................................................... 366 Reading Expressions from a File ................................................... 367 10.4 Exporting to Other Formats ...................................................... 369 Exporting Documents ................................................................... 369 MapleNet ........................................................................................ 372 Maple T.A. ..................................................................................... 373 10.5 Connectivity .............................................................................. 374 Translating Maple Code To Other Programming Languages ........ 374 Accessing External Products from Maple ...................................... 374 Accessing Maple from External Products ...................................... 375 Index ...................................................................................................... 379 x · Contents List of Tables Table 1.1: Shortcuts for Entering Mathematical Expressions .................... 6 Table 1.2: Entering a Definite Integral ..................................................... 13 Table 1.3: Symbol Completion Shortcut Keys ......................................... 17 Table 1.4: Summary of Document Mode Tools ....................................... 31 Table 1.5: Maple Help Resources ............................................................ 32 Table 3.1: Select Integer Commands ....................................................... 73 Table 3.2: Modular Arithmetic Operators ................................................ 76 Table 3.3: Overview of Solution Methods for Important Equation Types ........................................................................................................ 78 Table 3.4: Sample Dimensions ................................................................ 98 Table 3.5: Scientific Constants ............................................................... 106 Table 4.1: Maple Resources for Mathematical Computation ................ 123 Table 4.2: Polynomial Arithmetic Operators ......................................... 127 Table 4.3: Polynomial Coefficient and Degree Commands ................... 132 Table 4.4: Select Other Polynomial Commands .................................... 134 Table 4.5: Additional Polynomial Help ................................................. 135 Table 4.6: Matrix and Vector Arithmetic Operators ............................... 146 Table 4.7: Select Matrix and Vector Operators ...................................... 148 Table 4.8: Select LinearAlgebra Package Commands ........................... 150 Table 4.9: Limits .................................................................................... 154 Table 4.10: Student and Instructor Resources ........................................ 180 Table 5.1: Windows of the Interactive Plot Builder ............................... 192 Table 5.2: Displaying a Plot of a Single Variable Expression ................ 193 Table 5.3: Displaying a Plot of Multiple Expressions of 1 Variable ..... 195 Table 5.4: Displaying a Plot of a Multi-variable Expression ................ 196 Table 5.5: Displaying a Conformal Plot ............................................... 198 Table 5.6: Displaying a Plot in Polar Coordinates ................................ 200 Table 5.7: Interactive Plotting ............................................................... 202 Table 5.8: The plot and plot3d Commands ............................................ 208 Table 5.9: Customizing Plots Using Interactive Plot Builder ................ 217 Table 5.10: Customizing 2-D Plots Using the Context Menu ................ 218 Table 5.11: Customizing 3-D Plots Using the Context Menu ................ 219 Table 5.12: Popular Plot Options ........................................................... 220 Table 5.13: Plot Analysis Options .......................................................... 222 xi xii · List of Tables Table 5.14: Creating Animations Using the Interactive Plot Builder ..... 223 Table 5.15: The animate Command ....................................................... 225 Table 5.16: Animation Options .............................................................. 226 Table 5.17: Customizing Animations Using the Context Menu ............ 229 Table 8.1: Default Clause Values ........................................................... 327 Table 8.2: Iterative Commands .............................................................. 333 Table 8.3: The seq Command ................................................................ 333 Table 8.4: The add and mul Commands ................................................ 334 Table 8.5: The select, remove, and selectremove Commands ............... 335 Table 8.6: The map Command ............................................................... 336 Table 8.7: The zip Command ................................................................. 337 Table 10.1: Summary of Content Translation When Exporting to Different Formats .................................................................................................. 371 Preface The Maple Software The MapleTM software is a powerful system that you can use to solve complex mathematical problems. You can also create professional quality documents, presentations, and custom interactive computational tools in the Maple environment. You can access the power of the Maple computational engine through a variety of interfaces. Interface Standard Worksheet Description Full-featured graphical user interface offering features that help you create electronic documents that show all your assumptions, the calculations, and any margin of error in your results; or hide the computations to allow your reader to focus on the problem setup and final results. The advanced formatting features help you create the customized document you need. Because the documents are live, you can edit the parameters and, with the click of a button, compute the new results. The User Manual was created using the Standard Worksheet interface to Maple. An interactive version of this manual is available in the Standard Worksheet interface. From the Help menu, select Manuals, Dictionary, and more>Manuals>User Manual. Basic worksheet environment for older computers with limited memory. Command-line interface, without graphical user interfaces features, for solving very large complex problems or batch processing with scripts. Classic Worksheet Command-line version MaplesoftTM Graphing Calculator Graphical calculator interface to the Maple computational engine. Using it, you can perform simple computations (Microsoft® Windows® only) and create customizable, zoomable graphs. xiii xiv · Preface Interface MapletTM Applications Description Graphical user interface containing windows, textbox regions, and other visual interfaces, which gives you point-and-click access to the power of Maple. You can perform calculations and plot functions without using the worksheet or command-line interfaces. This manual describes how to use the Standard Worksheet interface. Some features are not available in the Classic Worksheet interface and Commandline version. The Standard Worksheet interface has two modes: Document mode and Worksheet mode. Document Mode - Using the Document mode, you can perform quick calculations. You can enter a mathematical expression, and then evaluate, manipulate, solve, or plot with a few keystrokes or mouse clicks. Worksheet Mode - The Worksheet mode is designed for: · Interactive use through Maple commands, which may offer advanced functionality or customized control not available using context menus or other syntax-free methods Programmatic use of the powerful Maple language · Using either mode, you can create high quality interactive mathematical presentations or documents. In This Manual This manual provides an overview of all Maple features including: · · · · · Performing computations Creating plots and animations Creating interactive documents The Maple programming language Using and creating custom Maplet applications Preface · xv · · File input and output, and using Maple with third party products Data structures For a complete list of manuals, study guides, toolboxes, and other resources, visit the Maplesoft Web site at http://www.maplesoft.com. Audience The information in this manual is intended for Maple users who have read the Maple Getting Started Guide. Conventions This manual uses the following typographical conventions. · · · · bold font - Maple command, package name, option name, dialog, menu, and text field italics - new or important concept Note - additional information relevant to the section Important - information that must be read and followed Customer Feedback Maplesoft welcomes your feedback. For suggestions and comments related to this and other manuals, contact doc@maplesoft.com xvi · Preface 1 Document Mode Using the Maple software, you can create powerful interactive documents. You can visualize and animate problems in two and three dimensions. You can solve complex problems with simple point-and-click interfaces or easyto-modify interactive documents. You can also devise custom solutions using the Maple programming language. While you work, you can document your process, providing text descriptions. 1.1 Introduction Maple has two modes: Document mode and Worksheet mode. Using Document mode, you can quickly perform calculations. You can enter a mathematical expression, and then evaluate, manipulate, solve, or plot it with a few keystrokes or mouse clicks. This chapter provides an overview of Document mode. Document mode sample: Find the value of the derivative of at . Integrate over the interval . = Worksheet mode is designed for interactive use through commands and programming using the Maple language. The Worksheet mode supports the features available in Document mode described in this chapter. After review- 1 2 · 1 Document Mode ing the information in this chapter, see Chapter 2, Worksheet Mode (page 35), for information on using Worksheet mode. Worksheet mode sample: Find the value of the derivative of > (1.1) at . > (1.2) > Integrate over the interval . > Important: In every Maple document, you can use Document mode and Worksheet mode. Using either mode: 1.2 In This Chapter · 3 · · You have access to the full mathematical engine. You can create high quality interactive documents: easy-to-use computational tools, presentations, or publications. Interactive document features include: · · · · · Embedded graphical interface components, like buttons, sliders, and check boxes Automatic execution of marked regions when a file is opened Tables Character and paragraph formatting styles Hyperlinks These features are described in Chapter 6, Creating Mathematical Documents (page 231). Note: This chapter was created using Document mode. All other chapters were created using Worksheet mode. 1.2 In This Chapter Section Topics Text and Math Modes Rational Expressions Powers Products Shortcuts for Entering Mathematical Expressions Other Expressions Simple Mathematical Expressions - Introduc- · tion to Math and Text modes, and how to · easily enter simple expressions · · · ·