Maple 9 Learning Guide - Maplesoft

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110 • Chapter 5: Plotting864–525 10–2–4–6–8–10The polarplot command also accepts parametrized plots. That is,you can express the radius and angle coordinates in terms of a parameter,for example, t. The syntax is similar to a parametrized plot in Cartesian(ordinary) coordinates. See this section, page 106.polarplot( [ r-expr, angle-expr, parameter=range ] )The equations r = sin(t) and θ = cos(t) define the following graph.> polarplot( [ sin(t), cos(t), t=0..2*Pi ] );0.40.2–1 –0.5 0.5 1–0.2–0.4Here is the graph of θ = sin(3r).> polarplot( [ r, sin(3*r), r=0..7 ] );
5.1 Graphing in Two Dimensions • 111420–21 2 3 4 5 6–4Functions with DiscontinuitiesFunctions with discontinuities require extra attention. This function hastwo discontinuities, at x = 1 and at x = 2.⎧⎨ −1 if x < 1,f(x) = 1 if 1 ≤ x < 2,⎩3 otherwise.Define f(x) in <strong>Maple</strong>.> f := x -> piecewise( x
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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
Page 67 and 68: 3.4 Polynomials • 59Solving Recur
Page 69 and 70: 3.4 Polynomials • 61> sort(mul_va
Page 71 and 72: 3.4 Polynomials • 63Table 3.1 Com
Page 73 and 74: 3.5 Calculus3.5 Calculus • 65Mapl
Page 75 and 76: 3.5 Calculus • 67> plot({f(x), p}
Page 77 and 78: 3.5 Calculus • 69> simplify(%);x
Page 79 and 80: 3.6 Solving Differential Equations
Page 85 and 86: _C1 e + _C2 e (−1) − _C3 sin(1)
Page 87 and 88: 4 Maple OrganizationThis chapter in
Page 89 and 90: 4.1 The Organization of Maple • 8
Page 91 and 92: CurveFitting commands that support
Page 93 and 94: 4.2 The Maple Packages • 85Orthog
Page 95 and 96: 4.2 The Maple Packages • 87TypeTo
Page 97 and 98: 4.2 The Maple Packages • 89To vie
Page 99 and 100: 4.2 The Maple Packages • 91> Limi
Page 101 and 102: 4.2 The Maple Packages • 93You ca
Page 103 and 104: 4.2 The Maple Packages • 95The fo
Page 105 and 106: 4.2 The Maple Packages • 97To est
Page 107 and 108: 4.2 The Maple Packages • 99> read
Page 109 and 110: 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: 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 and 162: 5.10 Conclusion5.10 Conclusion •
Page 163 and 164: 6 Evaluation andSimplificationExpre
Page 165 and 166: expand( (x+1)*(y^2-2*y+1) / z / (y-
Page 167 and 168: 6.1 Mathematical Manipulations •
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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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