Maple 9 Learning Guide - Maplesoft

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iv • ContentsExpression Sequences . . . . . . . . . . . . . . . . . . . . 21Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Operations on Sets and Lists . . . . . . . . . . . . . . . . 25Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.6 Expression Manipulation . . . . . . . . . . . . . . . . . . . 33The simplify Command . . . . . . . . . . . . . . . . . . 33The factor Command . . . . . . . . . . . . . . . . . . . . 34The expand Command . . . . . . . . . . . . . . . . . . . . 35The convert Command . . . . . . . . . . . . . . . . . . . 36The normal Command . . . . . . . . . . . . . . . . . . . . 36The combine Command . . . . . . . . . . . . . . . . . . . 37The map Command . . . . . . . . . . . . . . . . . . . . . . 38The lhs and rhs Commands . . . . . . . . . . . . . . . . 39The numer and denom Commands . . . . . . . . . . . . . . 39The nops and op Commands . . . . . . . . . . . . . . . . 40Common Questions about Expression Manipulation . . . 412.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 423 Finding Solutions 43In This Chapter . . . . . . . . . . . . . . . . . . . . . . . 433.1 The Maple solve Command . . . . . . . . . . . . . . . . 43Examples Using the solve Command . . . . . . . . . . . 43Verifying Solutions . . . . . . . . . . . . . . . . . . . . . . 45Restricting Solutions . . . . . . . . . . . . . . . . . . . . . 47Exploring Solutions . . . . . . . . . . . . . . . . . . . . . . 48The unapply Command . . . . . . . . . . . . . . . . . . . 49The assign Command . . . . . . . . . . . . . . . . . . . . 51The RootOf Command . . . . . . . . . . . . . . . . . . . . 533.2 Solving Numerically Using the fsolve Command . . . . . 54Limitations on solve . . . . . . . . . . . . . . . . . . . . . 553.3 Other Solvers . . . . . . . . . . . . . . . . . . . . . . . . . 58Finding Integer Solutions . . . . . . . . . . . . . . . . . . 58Finding Solutions Modulo m . . . . . . . . . . . . . . . . 58Solving Recurrence Relations . . . . . . . . . . . . . . . . 593.4 Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . 59Sorting and Collecting . . . . . . . . . . . . . . . . . . . . 60Mathematical Operations . . . . . . . . . . . . . . . . . . 61Coefficients and Degrees . . . . . . . . . . . . . . . . . . . 62
Contents • vRoot Finding and Factorization . . . . . . . . . . . . . . . 633.5 Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.6 Solving Differential Equations Using the dsolve Command 713.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 774 Maple Organization 79In This Chapter . . . . . . . . . . . . . . . . . . . . . . . 794.1 The Organization of Maple . . . . . . . . . . . . . . . . . 79The Maple Library . . . . . . . . . . . . . . . . . . . . . . 804.2 The Maple Packages . . . . . . . . . . . . . . . . . . . . . 82List of Packages . . . . . . . . . . . . . . . . . . . . . . . . 82Example Packages . . . . . . . . . . . . . . . . . . . . . . 87The Student Package . . . . . . . . . . . . . . . . . . . . . 87Worksheet Examples . . . . . . . . . . . . . . . . . . . . . 88The LinearAlgebra Package . . . . . . . . . . . . . . . . . 94The Matlab Package . . . . . . . . . . . . . . . . . . . . . 96The Statistics Package . . . . . . . . . . . . . . . . . . . . 98The simplex Linear Optimization Package . . . . . . . . 1014.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 1025 Plotting 103In This Chapter . . . . . . . . . . . . . . . . . . . . . . . 103Plotting Commands in Main Maple Library . . . . . . . . 103Plotting Commands in Packages . . . . . . . . . . . . . . 103Publishing Material with Plots . . . . . . . . . . . . . . . 1045.1 Graphing in Two Dimensions . . . . . . . . . . . . . . . . 104Parametric Plots . . . . . . . . . . . . . . . . . . . . . . . 106Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . 108Functions with Discontinuities . . . . . . . . . . . . . . . . 111Functions with Singularities . . . . . . . . . . . . . . . . . 112Multiple Functions . . . . . . . . . . . . . . . . . . . . . . 114Plotting Data Points . . . . . . . . . . . . . . . . . . . . . 116Refining Plots . . . . . . . . . . . . . . . . . . . . . . . . . 1185.2 Graphing in Three Dimensions . . . . . . . . . . . . . . . 119Parametric Plots . . . . . . . . . . . . . . . . . . . . . . . 121Spherical Coordinates . . . . . . . . . . . . . . . . . . . . 121Cylindrical Coordinates . . . . . . . . . . . . . . . . . . . 124Refining Plots . . . . . . . . . . . . . . . . . . . . . . . . . 125Shading and Lighting Schemes . . . . . . . . . . . . . . . 1265.3 Animation . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Animation in Two Dimensions . . . . . . . . . . . . . . . 128
Page 1 and 2: Maple 9Learning GuideBased in part
Page 3: ContentsPreface 1Audience . . . . .
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
Page 53 and 54: 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
Page 331 and 332:
Index • 323by total order, 60spac
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