Maple 9 Learning Guide - Maplesoft

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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 reserved.The electronic version (PDF) of this book may be downloaded andprinted for personal use or stored as a copy on a personal machine. Theelectronic version (PDF) of this book may not be distributed. Informationin this document is subject to change without notice and does not representa commitment on the part of the vendor. The software described inthis document is furnished under a license agreement and may be used orcopied only in accordance with the agreement. It is against the law to copysoftware 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 trademarksof 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 thatreads and updates L A TEX files.Printed in CanadaISBN 1-894511-42-5
ContentsPreface 1Audience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Manual Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Customer Feedback . . . . . . . . . . . . . . . . . . . . . . . . . 21 Introduction to Maple 3Worksheet Graphical Interface . . . . . . . . . . . . . . . 3Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Mathematics with Maple: The Basics 5In This Chapter . . . . . . . . . . . . . . . . . . . . . . . 5Maple Help System . . . . . . . . . . . . . . . . . . . . . . 52.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 5Exact Expressions . . . . . . . . . . . . . . . . . . . . . . 62.2 Numerical Computations . . . . . . . . . . . . . . . . . . 7Integer Computations . . . . . . . . . . . . . . . . . . . . 7Commands for Working With Integers . . . . . . . . . . . 9Exact Arithmetic—Rationals, Irrationals, and Constants . 10Floating-Point Approximations . . . . . . . . . . . . . . . 12Arithmetic with Special Numbers . . . . . . . . . . . . . . 14Mathematical Functions . . . . . . . . . . . . . . . . . . . 152.3 Basic Symbolic Computations . . . . . . . . . . . . . . . . 162.4 Assigning Expressions to Names . . . . . . . . . . . . . . 18Syntax for Naming an Object . . . . . . . . . . . . . . . . 18Guidelines for Maple Names . . . . . . . . . . . . . . . . . 19Maple Arrow Notation in Defining Functions . . . . . . . 19The Assignment Operator . . . . . . . . . . . . . . . . . . 20Predefined and Reserved Names . . . . . . . . . . . . . . . 202.5 Basic Types of Maple Objects . . . . . . . . . . . . . . . . 21iii
Page 1: Maple 9Learning GuideBased in part
Page 5 and 6: Contents • vRoot Finding and Fact
Page 7: Contents • viiLast-Name Evaluatio
Page 11 and 12: 1 Introduction to MapleMaple is a S
Page 13 and 14: 2 Mathematics with Maple:The Basics
Page 15 and 16: 2.2 Numerical Computations • 7are
Page 17 and 18: 2.2 Numerical Computations • 9Tab
Page 19 and 20: 2.2 Numerical Computations • 11Im
Page 21 and 22: 2.2 Numerical Computations • 13Th
Page 23 and 24: 2.2 Numerical Computations • 15Ma
Page 25 and 26: 2.3 Basic Symbolic Computations •
Page 27 and 28: 2.4 Assigning Expressions to Names
Page 29 and 30: 2.5 Basic Types of Maple Objects2.5
Page 31 and 32: 2.5 Basic Types of Maple Objects
Page 33 and 34: {1,2,3,a,b,c} intersect {0,1,y,a};2
Page 35 and 36: third_set := old_set minus {2, 5};2
Page 41 and 42: 2.6 Expression Manipulation • 333
Page 43 and 44: x 2 + x y + y 2(y + x) (x 2 + y 2 )
Page 45 and 46: 2.6 Expression Manipulation • 37T
Page 47 and 48: 2.6 Expression Manipulation • 39>
Page 49 and 50: 2.6 Expression Manipulation • 41C
Page 51 and 52: 3 Finding SolutionsThis chapter int
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3.1 The Maple solve Command • 45s
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3.1 The Maple solve Command • 47A
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3.1 The Maple solve Command • 49>
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3.1 The Maple solve Command • 51>
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3.1 The Maple solve Command • 53f
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3.2 Solving Numerically Using the f
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3.2 Solving Numerically Using the f
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3.4 Polynomials • 59Solving Recur
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3.4 Polynomials • 61> sort(mul_va
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3.4 Polynomials • 63Table 3.1 Com
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3.5 Calculus3.5 Calculus • 65Mapl
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3.5 Calculus • 67> plot({f(x), p}
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3.5 Calculus • 69> simplify(%);x
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3.6 Solving Differential Equations
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_C1 e + _C2 e (−1) − _C3 sin(1)
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4 Maple OrganizationThis chapter in
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4.1 The Organization of Maple • 8
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CurveFitting commands that support
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4.2 The Maple Packages • 85Orthog
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4.2 The Maple Packages • 87TypeTo
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4.2 The Maple Packages • 89To vie
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4.2 The Maple Packages • 91> Limi
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4.2 The Maple Packages • 93You ca
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4.2 The Maple Packages • 95The fo
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4.2 The Maple Packages • 97To est
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4.2 The Maple Packages • 99> read
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4.2 The Maple Packages • 101The s
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5 PlottingMaple can produce several
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5.1 Graphing in Two Dimensions •
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polarplot( r-expr, angle=range )5.1
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5.2 Graphing in Three Dimensions
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5.3 Animation • 127Simultaneous u
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5.3 Animation • 129Specifying Fra
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• a,b - real constants giving the
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5.4 Annotating Plots • 133The Sph
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5.5 Composite Plots • 135> with(p
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a := plot( sin(x), x=-Pi..Pi ):5.6
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5.6 Special Types of Plots • 139T
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5.6 Special Types of Plots • 141A
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5.6 Special Types of Plots • 1431
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5.7 Manipulating Graphical Objects
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5.7 Manipulating Graphical Objects
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hedgehog := [s1, s2, c3, stelhs]:>
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5.8 Code for Color Plates • 151>
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5.10 Conclusion5.10 Conclusion •
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6 Evaluation andSimplificationExpre
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expand( (x+1)*(y^2-2*y+1) / z / (y-
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6.1 Mathematical Manipulations •
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factor( poly, RootOf(x^2-2) );6.1 M
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6.2 Assumptions • 175> assume( a
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6.2 Assumptions • 177∞Logarithm
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6.2 Assumptions • 179a:nothing kn
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6.3 Structural Manipulations • 18
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f := (x, y) → is(x < y)6.3 Struct
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term3 := 2 cos(x) 2 sin(x)6.3 Struc
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y := ln( sin( x * exp(cos(x)) ) );y
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√ z sin(z) + w6.3 Structural Mani
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6.4 Evaluation Rules • 203> eval(
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6.4 Evaluation Rules • 205proc(x:
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6.4 Evaluation Rules • 207The seq
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6.4 Evaluation Rules • 2091Import
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6.4 Evaluation Rules • 211> q :=
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6.5 Conclusion • 213> sum( ’a||
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7 Solving Calculus ProblemsThis cha
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7.1 Introductory Calculus • 217>
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7.1 Introductory Calculus • 219In
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⎡⎧ ⎛1 √⎞1⎨5 − ⎩⎢a
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7.1 Introductory Calculus • 223en
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sol := solve( {err_x=0, err_xi=0},
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7.1 Introductory Calculus • 227If
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7.1 Introductory Calculus • 229>
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7.1 Introductory Calculus • 231{0
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7.1 Introductory Calculus • 233An
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∫ 1+ sin(x) dx27.1 Introductory C
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7.1 Introductory Calculus • 237r
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7.1 Introductory Calculus • 239fy
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7.2 Ordinary Differential Equations
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{y(x) = _C1 },7.2 Ordinary Differen
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Evaluate the result at values for t
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odeplot( sol, [t, x(t)], -1..2 );7.
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You must evaluate the derivatives a
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DEplot( ode, dep-var, range, [ini-c
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DEplot( {eq1, eq2}, [x(t), y(t)], -
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f := unapply( rhs( % ), t );7.2 Ord
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eq := diff(y(t),t) = 1-y(t)*f(t);7.
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7.3 Partial Differential Equations
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8 Input and OutputMaple provides co
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8.1 Reading Files • 279For exampl
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8.2 Writing Data to a File • 281W
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ExportVector( "vectordata.txt", V )
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8.2 Writing Data to a File • 285o
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8.3 Exporting Worksheets • 287•
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8.3 Exporting Worksheets • 289ali
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8.3 Exporting Worksheets • 291\en
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8.3 Exporting Worksheets • 293Exp
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8.3 Exporting Worksheets • 295Pla
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8.3 Exporting Worksheets • 2974.
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8.5 Conclusion • 299Graphics Suit
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9 Maplet User InterfaceCustomizatio
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9.3 How to Start the Maplets Packag
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9.7 How to Activate a Maplet Applic
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Index!, 8I ( √ −1), 14π, 12~,
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Index • 309combiningpowers, 37pro
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Index • 311integer quotient, 9int
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Index • 313partial, 173fsolve, 54
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Index • 315liesymm, 83lighting sc
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Index • 317graphical, 144odeplot,
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Index • 319lighting schemes, 126l
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Index • 321refining 2-D plots, 11
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Index • 323by total order, 60spac
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