Maple 9 Learning Guide - Maplesoft

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268 • Chapter 7: Solving Calculus Problems43.5y32.520 1 2 3 4tPiecewise Functions The piecewise command allows you to constructcomplicated forcing functions by approximating sections of it with analyticfunctions, and then taking the approximations together to representthe whole function. First, look at the behavior of piecewise.> f:= x -> piecewise(1 plot(f, 0..3);10.80.60.40.200.5 1 1.5 2 2.5 3Thus, you can use this piecewise function as a forcing function.
eq := diff(y(t),t) = 1-y(t)*f(t);7.2 Ordinary Differential Equations • 269eq := d ({ )1, if 1 − t ≤ 0 and t − 2 < 0;dt y(t) = 1 − y(t) 0, otherwise.> ini := y(0)=3;ini := y(0) = 3> sol3 := dsolve({eq, ini}, {y(t)}, type=numeric);sol3 := proc(x_rkf45 ) . . . end procUse the odeplot command in the plots package to plot the result.> with(plots, odeplot):> odeplot( sol3, [t, y(t)], 0..4 );76y 5430 1 2 3 4tThe DEtools package contains commands that can help you investigate,manipulate, plot, and solve differential equations. For details, referto the ?DEtools help page.Interactive ODE AnalyzerThe dsolve[interactive](odesys,options) command launches a graphicaluser interface for the investigation and solution of ODE and ODEsystems.
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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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Page 227 and 228: 7.1 Introductory Calculus • 219In
Page 229 and 230: ⎡⎧ ⎛1 √⎞1⎨5 − ⎩⎢a
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Page 233 and 234: sol := solve( {err_x=0, err_xi=0},
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Page 239 and 240: 7.1 Introductory Calculus • 231{0
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Page 243 and 244: ∫ 1+ sin(x) dx27.1 Introductory C
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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
Page 271 and 272: DEplot( {eq1, eq2}, [x(t), y(t)], -
Page 275: f := unapply( rhs( % ), t );7.2 Ord
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
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 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
Page 325 and 326: 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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