LearningGuide - Maple 9 Learning Guide Based in part on the...

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Maple 9 Learning Guide Based in part on the work of B. W. Char c Maplesoft, a division of Waterloo Maple Inc. 2003
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ii Maplesoft, Maple, Maple Application Center, Maple Student Center, and Maplet are all trademarks of Waterloo Maple Inc. c Maplesoft, a division of Waterloo Maple Inc. 2003. All rights re- served. The electronic version (PDF) of this book may be downloaded and printed for personal use or stored as a copy on a personal machine. The electronic version (PDF) of this book may not be distributed. Information in this document is subject to change without notice and does not repre- sent 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 software on any medium except as speci±cally allowed in the agreement. Windows is a registered trademark of Microsoft Corporation. Java and all Java based marks are trademarks or registered trade- marks 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 that reads and updates L A T E X ±les. Printed in Canada ISBN 1-894511-42-5
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Contents Preface 1 Audience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Manual Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Customer Feedback . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 Introduction to Maple 3 Worksheet Graphical Interface . . . . . . . . . . . . . . . 3 Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Mathematics with Maple: The Basics 5 In This Chapter . . . . . . . . . . . . . . . . . . . . . . . 5 Maple Help System . . . . . . . . . . . . . . . . . . . . . . 5 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Exact Expressions . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Numerical Computations . . . . . . . . . . . . . . . . . . 7 Integer Computations . . . . . . . . . . . . . . . . . . . . 7 Commands for Working With Integers . . . . . . . . . . . 9 Exact Arithmetic—Rationals, Irrationals, and Constants . 10 Floating-Point Approximations . . . . . . . . . . . . . . . 12 Arithmetic with Special Numbers . . . . . . . . . . . . . . 14 Mathematical Functions . . . . . . . . . . . . . . . . . . . 15 2.3 Basic Symbolic Computations . . . . . . . . . . . . . . . . 16 2.4 Assigning Expressions to Names . . . . . . . . . . . . . . 18 Syntax for Naming an Object . . . . . . . . . . . . . . . . 18 Guidelines for Maple Names . . . . . . . . . . . . . . . . . 19 Maple Arrow Notation in De±ning Functions . . . . . . . 19 The Assignment Operator . . . . . . . . . . . . . . . . . . 20 Prede±ned and Reserved Names . . . . . . . . . . . . . . . 20 2.5 Basic Types of Maple Objects . . . . . . . . . . . . . . . . 21 iii
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iv Contents Expression Sequences . . . . . . . . . . . . . . . . . . . . 21 Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Operations on Sets and Lists . . . . . . . . . . . . . . . . 25 Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.6 Expression Manipulation . . . . . . . . . . . . . . . . . . . 33 The simplify Command . . . . . . . . . . . . . . . . . . 33 The factor Command . . . . . . . . . . . . . . . . . . . . 34 The expand Command . . . . . . . . . . . . . . . . . . . . 35 The convert Command . . . . . . . . . . . . . . . . . . . 36 The normal Command . . . . . . . . . . . . . . . . . . . . 36 The combine Command . . . . . . . . . . . . . . . . . . . 37 The map Command . . . . . . . . . . . . . . . . . . . . . . 38 The lhs and rhs Commands . . . . . . . . . . . . . . . . 39 The numer and denom Commands . . . . . . . . . . . . . . 39 The nops and op Commands . . . . . . . . . . . . . . . . 40 Common Questions about Expression Manipulation . . . 41 2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3 Finding Solutions 43 In This Chapter . . . . . . . . . . . . . . . . . . . . . . . 43 3.1 The Maple solve Command . . . . . . . . . . . . . . . . 43 Examples Using the solve Command . . . . . . . . . . . 43 Verifying Solutions . . . . . . . . . . . . . . . . . . . . . . 45 Restricting Solutions . . . . . . . . . . . . . . . . . . . . . 47 Exploring Solutions . . . . . . . . . . . . . . . . . . . . . . 48 The unapply Command . . . . . . . . . . . . . . . . . . . 49 The assign Command . . . . . . . . . . . . . . . . . . . . 51 The RootOf Command . . . . . . . . . . . . . . . . . . . . 53 3.2 Solving Numerically Using the fsolve Command . . . . . 54 Limitations on solve . . . . . . . . . . . . . . . . . . . . . 55 3.3 Other Solvers . . . . . . . . . . . . . . . . . . . . . . . . . 58 Finding Integer Solutions . . . . . . . . . . . . . . . . . . 58 Finding Solutions Modulo m . . . . . . . . . . . . . . . . 58 Solving Recurrence Relations . . . . . . . . . . . . . . . . 59 3.4 Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Sorting and Collecting . . . . . . . . . . . . . . . . . . . . 60 Mathematical Operations . . . . . . . . . . . . . . . . . . 61 Coe±cients and Degrees .
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