Maple 9 Learning Guide - Maplesoft

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154 • Chapter 5: Plotting
6 Evaluation andSimplificationExpression manipulation serves many purposes, for example, convertingoutput expressions into a familiar form to check answers or into a specificform needed by certain Maple routines. The issue of simplification is difficultin symbolic mathematics. What is simple in one context may not bein another context—each individual context can have its own definitionof a simple form.Working with Expressions in MapleMaple provides a set of tools for working with expressions, for performingboth mathematical and structural manipulations.• Mathematical manipulations correspond to a standard mathematicalprocess, for example, factoring a polynomial, or rationalizing the denominatorof a rational expression.• Structural manipulation tools allow you to access and modify parts ofthe Maple data structures that represent expressions and other typesof objects.In This Chapter• Mathematical manipulations• Assumptions• Structural manipulations• Evaluation rules155
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Maple 9Learning GuideBased in part
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ContentsPreface 1Audience . . . . .
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Contents • vRoot Finding and Fact
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Contents • viiLast-Name Evaluatio
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1 Introduction to MapleMaple is a S
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2 Mathematics with Maple:The Basics
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2.2 Numerical Computations • 7are
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2.2 Numerical Computations • 9Tab
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2.2 Numerical Computations • 11Im
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2.2 Numerical Computations • 13Th
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2.2 Numerical Computations • 15Ma
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2.3 Basic Symbolic Computations •
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2.4 Assigning Expressions to Names
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2.5 Basic Types of Maple Objects2.5
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2.5 Basic Types of Maple Objects
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{1,2,3,a,b,c} intersect {0,1,y,a};2
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third_set := old_set minus {2, 5};2
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2.6 Expression Manipulation • 333
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x 2 + x y + y 2(y + x) (x 2 + y 2 )
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2.6 Expression Manipulation • 37T
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2.6 Expression Manipulation • 39>
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2.6 Expression Manipulation • 41C
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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
Page 111 and 112: 5 PlottingMaple can produce several
Page 113 and 114: 5.1 Graphing in Two Dimensions •
Page 117 and 118: polarplot( r-expr, angle=range )5.1
Page 127 and 128: 5.2 Graphing in Three Dimensions
Page 135 and 136: 5.3 Animation • 127Simultaneous u
Page 137 and 138: 5.3 Animation • 129Specifying Fra
Page 139 and 140: • a,b - real constants giving the
Page 141 and 142: 5.4 Annotating Plots • 133The Sph
Page 143 and 144: 5.5 Composite Plots • 135> with(p
Page 145 and 146: a := plot( sin(x), x=-Pi..Pi ):5.6
Page 147 and 148: 5.6 Special Types of Plots • 139T
Page 149 and 150: 5.6 Special Types of Plots • 141A
Page 151 and 152: 5.6 Special Types of Plots • 1431
Page 153 and 154: 5.7 Manipulating Graphical Objects
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Page 157 and 158: hedgehog := [s1, s2, c3, stelhs]:>
Page 159 and 160: 5.8 Code for Color Plates • 151>
Page 161: 5.10 Conclusion5.10 Conclusion •
Page 165 and 166: expand( (x+1)*(y^2-2*y+1) / z / (y-
Page 167 and 168: 6.1 Mathematical Manipulations •
Page 171 and 172: factor( poly, RootOf(x^2-2) );6.1 M
Page 183 and 184: 6.2 Assumptions • 175> assume( a
Page 185 and 186: 6.2 Assumptions • 177∞Logarithm
Page 187 and 188: 6.2 Assumptions • 179a:nothing kn
Page 189 and 190: 6.3 Structural Manipulations • 18
Page 195 and 196: f := (x, y) → is(x < y)6.3 Struct
Page 199 and 200: term3 := 2 cos(x) 2 sin(x)6.3 Struc
Page 205 and 206: y := ln( sin( x * exp(cos(x)) ) );y
Page 207 and 208: √ z sin(z) + w6.3 Structural Mani
Page 211 and 212: 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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