Maple 9 Learning Guide - Maplesoft

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16 • Chapter 2: Mathematics with Maple: The BasicsFunctionTable 2.2 Select Mathematical Functions in MapleDescriptionsin, cos, tan, etc.trigonometric functionssinh, cosh, tanh, etc. hyperbolic trigonometric functionsarcsin, arccos, arctan, etc. inverse trigonometric functionsexpexponential functionlnnatural logarithmic functionlog[10] logarithmic function base 10sqrtalgebraic square root functionroundround to the nearest integertrunctruncate to the integer partfracfractional partBesselI, BesselJ,Bessel functionsBesselK, BesselYbinomialbinomial functionerf, erfcerror & complementary error functionsHeavisideHeaviside step functionDiracDirac delta functionMeijerGMeijer G functionZetaRiemann Zeta functionLegendreKc, LegendreKc1, Legendre’s elliptic integralsLegendreEc, LegendreEc1,LegendrePic, LegendrePic1hypergeomhypergeometric functionNote: When Maple cannot find a simpler form, it leaves the expressionas it is rather than convert it to an inexact form.> ln(Pi);ln(π)2.3 Basic Symbolic ComputationsMaple can work with mathematical unknowns, and expressions whichcontain them.
2.3 Basic Symbolic Computations • 17> (1 + x)^2;(1 + x) 2> (1 + x) + (3 - 2*x);4 − xNote that Maple automatically simplifies the second expression.Maple has hundreds of commands for working with symbolic expressions.For a partial list, see Table 2.2.> expand((1 + x)^2);1 + 2 x + x 2> factor(%);(1 + x) 2As mentioned in 2.2 Numerical Computations, the ditto operator,%, is a shorthand notation for the previous result.> Diff(sin(x), x);ddx sin(x)> value(%);cos(x)> Sum(n^2, n);∑nn 2> value(%);13 n3 − 1 2 n2 + 1 6 n
Page 1 and 2: Maple 9Learning GuideBased in part
Page 3 and 4: ContentsPreface 1Audience . . . . .
Page 5 and 6: Contents • vRoot Finding and Fact
Page 7: Contents • viiLast-Name Evaluatio
Page 11 and 12: 1 Introduction to MapleMaple is a S
Page 13 and 14: 2 Mathematics with Maple:The Basics
Page 15 and 16: 2.2 Numerical Computations • 7are
Page 17 and 18: 2.2 Numerical Computations • 9Tab
Page 19 and 20: 2.2 Numerical Computations • 11Im
Page 21 and 22: 2.2 Numerical Computations • 13Th
Page 23: 2.2 Numerical Computations • 15Ma
Page 27 and 28: 2.4 Assigning Expressions to Names
Page 29 and 30: 2.5 Basic Types of Maple Objects2.5
Page 31 and 32: 2.5 Basic Types of Maple Objects
Page 33 and 34: {1,2,3,a,b,c} intersect {0,1,y,a};2
Page 35 and 36: third_set := old_set minus {2, 5};2
Page 41 and 42: 2.6 Expression Manipulation • 333
Page 43 and 44: x 2 + x y + y 2(y + x) (x 2 + y 2 )
Page 45 and 46: 2.6 Expression Manipulation • 37T
Page 47 and 48: 2.6 Expression Manipulation • 39>
Page 49 and 50: 2.6 Expression Manipulation • 41C
Page 51 and 52: 3 Finding SolutionsThis chapter int
Page 53 and 54: 3.1 The Maple solve Command • 45s
Page 55 and 56: 3.1 The Maple solve Command • 47A
Page 57 and 58: 3.1 The Maple solve Command • 49>
Page 59 and 60: 3.1 The Maple solve Command • 51>
Page 61 and 62: 3.1 The Maple solve Command • 53f
Page 63 and 64: 3.2 Solving Numerically Using the f
Page 65 and 66: 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
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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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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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Maple 9 Learning Guide - Maplesoft

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