Maple 9 Learning Guide - Maplesoft

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102 • Chapter 4: Maple Organization> c3 := 7*x +4*y+11*z maximize(w, {c1,c2,c3});In this case, no answer means that Maple cannot find a solution. You canuse the feasible command to determine if the set of constraints is valid.> feasible({c1,c2,c3});trueTry again and place an additional restriction on the solution.> maximize(w, {c1,c2,c3}, NONNEGATIVE);{z = 1 2 , y = 49 8 , x = 0}4.3 ConclusionThis chapter introduced the organization of Maple and the Maple library.Additionally, examples from five packages were provided. This informationserves as context for references and concepts in the following chapters.
5 PlottingMaple can produce several forms of graphs. Maple accepts explicit, implicit,and parametric forms, and recognizes many coordinate systems.In This Chapter• Graphing in two dimensions• Graphing in three dimensions• Animation• Annotating plots• Composite plots• Special plots• Manipulating graphical objects• Code for color plates• Interactive plot builderPlotting Commands in Main Maple LibraryThe command-line plotting feature of Maple contains plotting functionsin the main library and in packages. The plot and plot3d commandsreside in the main Maple library. These functions can be called any timeduring a Maple session. For details about these commands, refer to the?plot and ?plot3d help pages.Plotting Commands in PackagesMany functions reside in the plots and plottools packages. These packagesmust be accessed by using the long or short form in the commandcalling sequence. For details about these packages, refer to the ?plotsand ?plottools help pages. For command calling sequence information,refer to the ?UsingPackages help page.103
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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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Page 61 and 62: 3.1 The Maple solve Command • 53f
Page 63 and 64: 3.2 Solving Numerically Using the f
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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: 4.2 The Maple Packages • 101The s
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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>
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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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