Maple 9 Learning Guide - Maplesoft

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308 • Indexarrays, 27–31declaring 1-D, 27declaring 2-D, 28, 29definition, 27evaluating, 30, 203mapping onto, 38printing, 28selecting elements from 1-Darrays, 27selecting elements from 2-Darrays, 28viewing contents, 28arrow, 143arrow notation, 19assign, 51–53assigned, 206assigning to names, 18, 51assignment operator, 20assignmentsinvalid, 20multiple, 22naming, 18of sets of equations, 51valid names, 19assume, 70, 174–177additionally, 175integer, 175nonnegative, 175assuming, 178assumptions, 70on names, 58, 70removing, 70, 178setting, 174–175viewing, 175audience, 1automatic simplification, 17axes, 133, 134axis labels, 133base n numbersconverting to, 14basic arithmetic, 6basis, 95Bessel functions, 16binary numbersconverting to, 14binomial function, 16boundary conditions, 73calculationsexact vs. floating point, 6calculus, 65–71, 87, 215–240Calculus1 commandsApproximateInt, 93–94, 232–234, 236Hint, 90–92NewtonQuotient, 216Roots, 92Rule, 89–92Tangent, 92Understand, 90capitalization, 12case sensitivity, 12cat, 32catastrophic cancellation, 12changing variables, 30circles, plotting, 106, 109classic worksheet, 3classical dynamics, 243coeff, 62coefficientscollecting, 61extracting, 62, 63polynomial, 62collect, 61, 158distributed, 160colon, 28color functions, 126combinat, 82combine, 164expr, 37power, 37
Index • 309combiningpowers, 37products, 37sums, 37combstruct, 82comma delimited expressions, seeexpression sequencescommand-line version, 3commands, see specific commandnamesseparating, 6terminating, 6common denominator, 36, 165complex numbers, 14complex roots, 54computationsinteger, 7–9referring to previous, 8symbolic, 16concatenation, 201, 211–213expression sequences, 22operator, 22strings, 32conditionsinitial, 242, 274cone, 146cones, plotting, 125conformal, 141constants, 12factoring, 41of integration, 235constrained scaling, in plots, 107content, multivariate polynomial,64context, 82continuation character, 8continuity, extending by, 237contourplot, 140convert, 36, 279base, 14binary, 14exp, 36, 172factorial, 172hex, 14list, 36, 201, 279ln, 172parfrac, 173polynom, 200, 222rational, 173set, 36, 201sincos, 172string, 200trig, 36convertingbetween data structures, 36between temperature scales,36between types, 36between units, 36degrees to radians, 36expressions, 36expressions to functions, 49expressions to L A TEX, 284floating-point to rational, 36radians to degrees, 36rational to partial fractions,36series to polynomials, 36, 66,67, 200, 222solution set to list, 46to floating-point, 13to lists, 47, 279to lists and sets, 201to strings, 200trigonometric to exponential,36coordinatescylindrical, 124polar, 108, 130spherical, 121viewing, 104counting, 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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Page 265 and 266: 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
Page 305 and 306: 8.3 Exporting Worksheets • 2974.
Page 307 and 308: 8.5 Conclusion • 299Graphics Suit
Page 309 and 310: 9 Maplet User InterfaceCustomizatio
Page 311 and 312: 9.3 How to Start the Maplets Packag
Page 313 and 314: 9.7 How to Activate a Maplet Applic
Page 315: Index!, 8I ( √ −1), 14π, 12~,
Page 319 and 320: Index • 311integer quotient, 9int
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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