Maple 9 Learning Guide - Maplesoft

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310 • IndexCurveFitting, 82, 118customer feedback, 2cutout, 148cylinderplot, 124cylindrical coordinates, 124cylindrical coordinates, animations,132D, 236, 242, 255data points, plotting, 116data types, 21decimal forms, 10decimal numbers, 12–14declaring arraysone-dimensional, 27two-dimensional, 28, 29decomposition, polynomial, 64definingdiscontinuous functions, 111functions, 19functions, with arrow notation,52functions, with unapply, 49,72defining arraysone-dimensional, 27two-dimensional, 28, 29definite integrals, 69, 234degree, 62degree of polynomial, 62, 63delaying evaluation, 207denom, 39, 189denominators, 39, 189common, 36, 165isolate, 39densityplot, 140DEplot, 260DEplot3d, 263derivatives, 17, 68, 215limit definition of, 216partial, 224, 237describe, 99DESol, 259determining number of elements(nops), 23, 25DEtools, 83dialog, see Maplet,dialogDiff, 68, 89diff, 196diffalg, 83differential equationsordinary, 71, 241partial, 270solving, 51systems of, 76differentiatingexpressions in a list, 38differentiation, 17, 89difforms, 83Digits, 13digitsin floating-point calculations,default, 13in floating-point calculations,setting, 13in floating-point calculations,setting globally, 13maximum length of floatingpointapproximations, 12maximum length of integers,8Dirac, 16, 73, 266Dirac delta function, 16, 73, 266discontinuous functionsdefining, 111plotting, 57, 111display, 134, 144, 217displayinganimations, 128ditto operator, 8divide, 62division
Index • 311integer quotient, 9integer remainder, 9polynomial, 18, 61dodecahedron, 147Domains, 83double quotes, 32dsolve, 71–77, 241explicit, 243implicit, 243method=laplace, 244startinit, 254type=numeric, 252type=series, 249e (exponential function), 11echo, 281eigenvalues, 97eigenvectors, 97empty_list, 26empty_set, 26equationsleft-hand side, 39right-hand side, 39solving, 43, 54solving systems of, 44error functions, 16errorsfloating-point, 14relative, 12eval, 45, 46, 62, 71, 72, 197, 202evalf, 10, 13, 216evalm, 30evaln, 206evaluatingarrays, 30, 203local variables, 206matrices, 203procedures, 203tables, 203evaluation, 202–213and quoting, 207and substitution, 199assigned, 206at a point, 45delayed, 207evaln, 206forcing full, 204full, 202last-name, 203levels of, 202numerical, 10, 13one-level, 206to a name, 206exact arithmetic, 10exact numbers, analytic description,12exact vs. approximate results, 10–11exp, 12Expand, 158expand, 17, 35, 156vs. simplify, 35–36expanded normal form, 37expandingmodulo m, 158polynomials, 35explicit functions, plotting, 104exponential function, 11, 16exportingas Maple text, 293as Maplet application, 292as plain text, 295HTML with MathML, 287L A TEX, 290RTF, 296ExportMatrix, 282ExportVector, 282expression sequences, 21expression trees, 192expressionsaccessing subexpressions, 40
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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
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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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Page 275 and 276: f := unapply( rhs( % ), t );7.2 Ord
Page 277 and 278: eq := diff(y(t),t) = 1-y(t)*f(t);7.
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Page 285 and 286: 8 Input and OutputMaple provides co
Page 287 and 288: 8.1 Reading Files • 279For exampl
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Page 291 and 292: ExportVector( "vectordata.txt", V )
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Page 295 and 296: 8.3 Exporting Worksheets • 287•
Page 297 and 298: 8.3 Exporting Worksheets • 289ali
Page 299 and 300: 8.3 Exporting Worksheets • 291\en
Page 301 and 302: 8.3 Exporting Worksheets • 293Exp
Page 303 and 304: 8.3 Exporting Worksheets • 295Pla
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Page 307 and 308: 8.5 Conclusion • 299Graphics Suit
Page 309 and 310: 9 Maplet User InterfaceCustomizatio
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Page 313 and 314: 9.7 How to Activate a Maplet Applic
Page 315 and 316: Index!, 8I ( √ −1), 14π, 12~,
Page 317: Index • 309combiningpowers, 37pro
Page 321 and 322: Index • 313partial, 173fsolve, 54
Page 323 and 324: Index • 315liesymm, 83lighting sc
Page 325 and 326: Index • 317graphical, 144odeplot,
Page 327 and 328: Index • 319lighting schemes, 126l
Page 329 and 330: Index • 321refining 2-D plots, 11
Page 331 and 332: Index • 323by total order, 60spac
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Maple 9 Learning Guide - Maplesoft

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