Maple 9 Learning Guide - Maplesoft

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266 • Chapter 7: Solving Calculus Problems> sol1 := dsolve({eq, ini}, {y(t)}, type=numeric);sol1 := proc(x_rkf45 ) . . . end procUse the odeplot command from the plots package to plot the solution.> with(plots):> odeplot( sol1, [t, y(t)], 0..4 );32.52y1.510.50 1 2 3 4tThe Dirac Delta Function You can use the Dirac delta function ina manner similar to the Heaviside function above to produce impulsiveforcing functions.> eq := diff(y(t),t) = -y(t)*Dirac(t-1);eq := d y(t) = −y(t) Dirac(t − 1)dt> ini := y(0) = 3;ini := y(0) = 3> dsolve({eq, ini}, {y(t)});y(t) = 3 e (−Heaviside(t−1))Convert the solution to a function that can be plotted.
f := unapply( rhs( % ), t );7.2 Ordinary Differential Equations • 267f := t → 3 e (−Heaviside(t−1))> plot( f, 0..4 );32.82.62.42.221.81.61.41.20 1 2 3 4However, the numeric solution does not see the nonzero value ofDirac(0).> sol2 := dsolve({eq, ini}, {y(t)}, type=numeric);sol2 := proc(x_rkf45 ) . . . end procUse odeplot from plots to plot the numeric solution.> with(plots, odeplot);[odeplot]> odeplot( sol2, [t,y(t)], 0..4 );
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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||
Page 223 and 224: 7 Solving Calculus ProblemsThis cha
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Page 227 and 228: 7.1 Introductory Calculus • 219In
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Page 249 and 250: 7.2 Ordinary Differential Equations
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Page 253 and 254: Evaluate the result at values for t
Page 261 and 262: odeplot( sol, [t, x(t)], -1..2 );7.
Page 265 and 266: You must evaluate the derivatives a
Page 269 and 270: DEplot( ode, dep-var, range, [ini-c
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Page 273: 7.2 Ordinary Differential Equations
Page 277 and 278: eq := diff(y(t),t) = 1-y(t)*f(t);7.
Page 279 and 280: 7.3 Partial Differential Equations
Page 285 and 286: 8 Input and OutputMaple provides co
Page 287 and 288: 8.1 Reading Files • 279For exampl
Page 289 and 290: 8.2 Writing Data to a File • 281W
Page 291 and 292: ExportVector( "vectordata.txt", V )
Page 293 and 294: 8.2 Writing Data to a File • 285o
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
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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 and 316: Index!, 8I ( √ −1), 14π, 12~,
Page 317 and 318: Index • 309combiningpowers, 37pro
Page 319 and 320: Index • 311integer quotient, 9int
Page 321 and 322: Index • 313partial, 173fsolve, 54
Page 323 and 324: 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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