Maple 9 Learning Guide - Maplesoft

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274 • Chapter 7: Solving Calculus Problems• ini is a parametric curve in three-dimensional space with parameter s• range is the range of sConsider this partial differential equation.> pde := diff(u(x,y), x) + cos(2*x) * diff(u(x,y), y) = -sin(y);pde := ( ∂∂x u(x, y)) + cos(2 x) ( ∂ u(x, y)) = −sin(y)∂yUse the curve given by z = 1 + y 2 as an initial condition, that is,x = 0, y = s, and z = 1 + s 2 .> ini := [0, s, 1+s^2];ini := [0, s, 1 + s 2 ]PDEplot draws the initial-condition curve and the solution surface.> PDEplot( pde, u(x,y), ini, s=-2..2 );u(x,y)71–2–2y22xTo draw the surface, <strong>Maple</strong> calculates these base characteristic curves.The initial-condition curve is easier to see here than in the previous plot.> PDEplot( pde, u(x,y), ini, s=-2..2, basechar=only );
7.3 Partial Differential Equations • 2755u(x,y)1–2–2y22xWith the basechar=true option, PDEplot draws both the characteristiccurves and the surface, as well as the initial-condition curve which isalways present.> PDEplot( pde, u(x,y), ini, s=-2..2, basechar=true );u(x,y)71–2–2y22xMany plot3d options are available. Refer to the ?plot3d,optionshelp page. The initcolor option sets the color of the initial value curve.> PDEplot( pde, u(x,y), ini, s=-2..2,> basechar=true, initcolor=white,> style=patchcontour, contours=20,> orientation=[-43,45] );
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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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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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Page 233 and 234: sol := solve( {err_x=0, err_xi=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
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Page 275 and 276: f := unapply( rhs( % ), t );7.2 Ord
Page 277 and 278: eq := diff(y(t),t) = 1-y(t)*f(t);7.
Page 279 and 280: 7.3 Partial Differential Equations
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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,
Page 327 and 328: Index • 319lighting schemes, 126l
Page 329 and 330: Index • 321refining 2-D plots, 11
Page 331 and 332: Index • 323by total order, 60spac
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Maple 9 Learning Guide - Maplesoft

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