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5.3 Structural Manipulations • 185DE := −sin(t z(t)) sin(y(t)) cos(t) ( d dt y(t))− sin(t z(t)) sin(y(t)) cos(t)− sin(t z(t)) cos(y(t)) sin(t) ( d dt y(t))− sin(t z(t)) cos(y(t)) sin(t) + cos(t z(t)) cos(y(t)) cos(t) z(t)+ cos(t z(t)) cos(y(t)) cos(t) t ( d dt z(t))− cos(t z(t)) sin(y(t)) sin(t) z(t)− cos(t z(t)) sin(y(t)) sin(t) t ( d dt z(t)) + ( d dt x(t))> indets( DE, specfunc(anything, diff) );{ d dt y(t), ddt x(t), ddt z(t)}The following operands of DE contain the derivatives.> select( hastype, DE, specfunc(anything, diff) );−sin(t z(t)) sin(y(t)) cos(t) ( d dt y(t))− sin(t z(t)) cos(y(t)) sin(t) ( d dt y(t))+ cos(t z(t)) cos(y(t)) cos(t) t ( d dt z(t))− cos(t z(t)) sin(y(t)) sin(t) t ( d dt z(t)) + ( d dt x(t))DE has only one operand that is itself a derivative.> select( type, DE, specfunc(anything, diff) );ddt x(t)Maple recognizes many types. For a partial list, refer to ?type andfor more information on structured types, such as specfunc, refer to?type,structured.SubstitutionOften you want to substitute a value for a variable (that is, evaluate anexpression at a point). For example, if you need to solve the problem, “Iff(x) = ln(sin(xe cos(x) )), find f ′ (2),” then you must substitute the value 2for x in the derivative. The command finds the derivative.
186 • Chapter 5: Evaluation and Simplification> y := ln( sin( x * exp(cos(x)) ) );y := ln(sin(x e cos(x) ))> yprime := diff( y, x );yprime := cos(x ecos(x) ) (e cos(x) − x sin(x) e cos(x) )sin(x e cos(x) )Now use the eval command to substitute a value for x in yprime.> eval( yprime, x=2 );cos(2 e cos(2) ) (e cos(2) − 2 sin(2) e cos(2) )sin(2 e cos(2) )The evalf command returns a floating-point approximation of theresult.> evalf( % );−0.1388047428The command makes syntactical substitutions, not mathematical substitutions.This means that you can make substitutions for any subexpression.> subs( cos(x)=3, yprime );cos(x e 3 ) (e 3 − x sin(x) e 3 )sin(x e 3 )But you are limited to subexpressions as Maple identifies them.> expr := a * b * c * a^b;expr := a b c a b> subs( a*b=3, expr );a b c a b
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Learning Guidecommand the brillianc
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ii•Waterloo Maple Inc.57 Erb Stre
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iv • ContentsThe numer and denom
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vi • ContentsThe Parts of an Expr
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viii • Contents
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2 • Chapter 1: Introduction to Ma
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4 • Chapter 1: Introduction to Ma
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6 • Chapter 2: Mathematics with M
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8 • Chapter 2: Mathematics with M
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10 • Chapter 2: Mathematics with
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44 • Chapter 3: Finding Solutions
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98 • Chapter 4: Graphics> f := x
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100 • Chapter 4: Graphics> plot(
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102 • Chapter 4: GraphicsFigure 4
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104 • Chapter 4: Graphics0.40.2-1
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106 • Chapter 4: GraphicsIn the p
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108 • Chapter 4: Graphics54321-2
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110 • Chapter 4: Graphics> pointp
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112 • Chapter 4: Graphics3.43.232
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114 • Chapter 4: GraphicsParametr
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116 • Chapter 4: GraphicsPlotting
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118 • Chapter 4: GraphicsCones ar
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120 • Chapter 4: Graphicsthe resu
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122 • Chapter 4: Graphics> animat
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124 • Chapter 4: Graphics> animat
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126 • Chapter 4: Graphics> plot(
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128 • Chapter 4: Graphics> a := p
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130 • Chapter 4: GraphicsP4.6 Spe
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132 • Chapter 4: Graphics1e+141e+
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236 • Chapter 6: Examples from Ca
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270 • Chapter 7: Input and Output
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288 • Chapter 8: Maplets8.2 Termi
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290 • Chapter 8: Maplets8.5 How t
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292 • Chapter 8: Maplets8.10 Conc
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294 • Indexexact, 8finite rings a
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296 • Indexspherical, 114viewing,
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298 • IndexXML, 283ExportMatrix,
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300 • IndexHP LaserJet, 284HTML,
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302 • IndexMatrix, 34, 90matrixpl
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304 • IndexSlode, 81Sockets, 81So
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306 • Indexdecomposition, 64defin
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308 • Indexshell plots, 115side r
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310 • Indexunordered lists (sets)
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