318 • IndexScientificConstants, 85ScientificErrorAnalysis, 85simplex, 85, 101–102Slode, 85Sockets, 86SolveTools, 86Spread, 86stats, 86, 98–100StringTools, 86Student, 86Student[Calculus1], 86–94Student[LinearAlgebra], 86SumTools, 86tensor, 86TypeTools, 86Units, 87VariationalCalculus, 87VectorCalculus, 87Worksheet, 87XMLTools, 87packages, 80list of, 82loading, 80using commands from, 80padic, 85parametric plots2-D, 1063-D, 121cylinders, 125in polar coordinates, 110spheres, 123parametric solutions, 44partial derivatives, 224, 237limit definition of, 238mixed, 239partial differential equations, 270partial fractions, 173Pascal’s Triangle, 181PDEplot, 274–276PDEs, 270initial conditions, 274plotting, 273PDEtools, 85pi, 12piecewise, 111, 268plain textexporting as, 295playing animations, 128plex, 60plotcolor, 115, 116discont, 111, 113labeldirections, 133labels, 133labelsfont, 133legend, 134linestyle, 115numpoints, 118scaling=constrained, 107style=line, 117symbol, 117symbolsize, 117title, 132, 200titlefont, 133plot3d, 119, 121axes, 133grid, 125lightmodel, 126, 127shading, 126style=hidden, 120plots3-D default shading, 120annotations, 132, 136color functions, 126colors, specifying, 116cones, 125constrained vs. unconstrainedscaling, 107density, 140displaying, 134gray-scale, 127legends, 134
Index • 319lighting schemes, 126line styles, 115modifying attributes, 104point styles, specifying, 117ranges of, 120refining 2-D, 118refining 3-D, 125rotating, 119, 146setting scale, 106shading, 126shell, 122spheres, 122spiral (3-D), 124, 126text, 136titles, 132, 200, 213translating, 146viewing coordinates, 104plots, 85animate, 128, 130arrow, 143cylinderplot, 124sphereplot, 122plotsetup, 298plotting, 103adaptive algorithm for, 118animations, 127, 217circles, 106, 109commands in main library,103commands in packages, 103conformal, 141contours, 140curves in 3-D space, 141cylinders, 124, 125discontinuous functions, 57,111explicit functions, 104, 119histograms, 100implicit functions, 138in separate windows, 298inequalities, 139infinite domains, 105inline, 298interactive plot builder, 152joining points, 117lists of numbers, 279Matrices, 142multiple curves, 114multiple plots, 134objects, 144ODEs, 260on logarithmic axes, 139, 140parametric curves, 106parametric surfaces, 121, 123PDEs, 273points, 116polar coordinates, 108printing, 298professional publishing, 104,298root loci, 142series, 200shaded surface, 120singularities, 112space curves, 141specifying frames, 129, 131specifying range, 105spheres, 123spherical coordinates, 121spirals, 109surfaces, 119tangent, 92tangent function, 113three-dimensional, 119to files, 298topographical maps, 140tubes, 142vector fields, 141visualization component, 143plottools, 85, 144pointplot, 116, 117points, plotting, 116
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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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2.5 Basic Types of Maple Objects
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2.5 Basic Types of Maple Objects
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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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3.6 Solving Differential Equations
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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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5.1 Graphing in Two Dimensions •
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polarplot( r-expr, angle=range )5.1
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5.1 Graphing in Two Dimensions •
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5.1 Graphing in Two Dimensions •
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5.1 Graphing in Two Dimensions •
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5.1 Graphing in Two Dimensions •
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5.2 Graphing in Three Dimensions
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5.2 Graphing in Three Dimensions
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5.2 Graphing in Three Dimensions
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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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6.1 Mathematical Manipulations •
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factor( poly, RootOf(x^2-2) );6.1 M
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6.1 Mathematical Manipulations •
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6.1 Mathematical Manipulations •
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6.1 Mathematical Manipulations •
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6.1 Mathematical Manipulations •
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6.1 Mathematical Manipulations •
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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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6.3 Structural Manipulations • 18
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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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6.3 Structural Manipulations • 18
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term3 := 2 cos(x) 2 sin(x)6.3 Struc
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6.3 Structural Manipulations • 19
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6.3 Structural Manipulations • 19
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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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6.3 Structural Manipulations • 20
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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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7.2 Ordinary Differential Equations
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7.2 Ordinary Differential Equations
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7.2 Ordinary Differential Equations
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odeplot( sol, [t, x(t)], -1..2 );7.
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7.2 Ordinary Differential Equations
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You must evaluate the derivatives a
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7.2 Ordinary Differential Equations
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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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7.2 Ordinary Differential Equations
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- Page 315 and 316: Index!, 8I ( √ −1), 14π, 12~,
- Page 317 and 318: Index • 309combiningpowers, 37pro
- Page 319 and 320: Index • 311integer quotient, 9int
- Page 321 and 322: Index • 313partial, 173fsolve, 54
- Page 323 and 324: Index • 315liesymm, 83lighting sc
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- Page 329 and 330: Index • 321refining 2-D plots, 11
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