Maple 9 Learning Guide - Maplesoft

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90 • Chapter 4: <strong>Maple</strong> Organization∫ π0x cos(x) + x dx =∫ π0x cos(x) dx +∫ π0x dxUse the power rule.> Rule[power](%);∫ π0x cos(x) + x dx =∫ π0x cos(x) dx + 1 2 π2Use the Hint command to determine a possible next step for theproblem.> Hint(%);[parts, x, sin(x)]Use the hint with the Rule command.> Rule[%](%%);∫ π0x cos(x) + x dx = −∫ π0sin(x) dx + 1 2 π2Use the sin rule to complete this computation.> Rule[sin](%);∫ π0x cos(x) + x dx = −2 + 1 2 π2Calculating Limits Calculate the limit of (1+1/x) x . Use the Understandcommand to use rules for calculating the Limit without explicitly applyingthem. To add the constant, constant multiple, power, and sum Limitrules to the list of understood rules for the following example, use theUnderstand command.> Understand(Limit, constant, ‘c*‘, power, sum);Limit = [constant, constantmultiple, power, sum]
4.2 The <strong>Maple</strong> Packages • 91> Limit((1 + 1/x)^x, x=infinity);limx→∞ (1 + 1 x )xRequest a hint for the next step of the computation.> Hint(%);Creating problem #3Rewrite the expression as an exponential to prepare for usingl‘Hopital’s rule[rewrite, (1 + 1 x )x = e (x ln(1+ 1 x )) ]Use the rule that is returned by Hint.> Rule[%](%%);limx→∞ (1 + 1 x )x = limx→∞ e(x ln(1+ 1 x ))> Hint(%);[exp]> Rule[%](%%);lim (1 + 1x→∞ x )x = e (lim x→∞ x ln(1+ 1 x ))> Hint(%);[lhopital , ln(1 + 1 x )]> Rule[%](%%);limx→∞ (1 + 1 x )x = e (lim x→∞xx+1 )
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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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Page 51 and 52: 3 Finding SolutionsThis chapter int
Page 53 and 54: 3.1 The Maple solve Command • 45s
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Page 57 and 58: 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: 4.2 The Maple Packages • 89To vie
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 and 110: 4.2 The Maple Packages • 101The s
Page 111 and 112: 5 PlottingMaple can produce several
Page 113 and 114: 5.1 Graphing in Two Dimensions •
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
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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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