Maple 9 Learning Guide - Maplesoft

More documents

Recommendations

Info

142 • Chapter 5: PlottingHere <strong>Maple</strong> inflates the previous spacecurve to form a tube.> tubeplot( [cos(t),sin(t),t], t=0..4*Pi, radius=0.5 );The matrixplot command plots the values of a object of type Matrix.> A := LinearAlgebra[HilbertMatrix](8):> B := LinearAlgebra[ToeplitzMatrix]([1,2,3,4,-4,-3,-2,-1],> symmetric):> matrixplot( A+B, heights=histogram, axes=frame,> gap=0.25, style=patch);420–2–424column68864row2The following is a demonstration of a root locus plot.> rootlocus( (s^5-1)/(s^2+1), s, -5..5, style=point,> adaptive=false );
5.6 Special Types of Plots • 14310.50–0.5–1–1.5 –1 –0.5 0 0.5 1 1.5The arrow command plots arrows or vectors in two or three dimensions.> plots[arrow]( [, ], [, ], difference,> scaling=constrained );543211 1.5 2 2.5 3For a listing of other available plot types, enter ?plots at the <strong>Maple</strong>prompt.Visualization Component of the Student PackageThe Student package is a collection of subpackages designed to assistwith the teaching and learning of standard undergraduate mathematics.There are many routines for displaying functions, computations,and theorems. For example, in the Student[Calculus1] subpackage,the visualization routines are designed to assist in the understandingof basic calculus concepts. The following is an example of theStudent[Calculus1][DerivativePlot] command.The DerivatePlot(f(x),x=a..b) command plots an expression andits derivatives.> with(Student[Calculus1]):> f := proc() evalf(sqrt(rand()/10^12)) end proc:> colors := proc() COLOR(RGB, f(), f(), f()) end proc:
Page 1 and 2:
Maple 9Learning GuideBased in part
Page 3 and 4:
ContentsPreface 1Audience . . . . .
Page 5 and 6:
Contents • vRoot Finding and Fact
Page 7:
Contents • viiLast-Name Evaluatio
Page 11 and 12:
1 Introduction to MapleMaple is a S
Page 13 and 14:
2 Mathematics with Maple:The Basics
Page 15 and 16:
2.2 Numerical Computations • 7are
Page 17 and 18:
2.2 Numerical Computations • 9Tab
Page 19 and 20:
2.2 Numerical Computations • 11Im
Page 21 and 22:
2.2 Numerical Computations • 13Th
Page 23 and 24:
2.2 Numerical Computations • 15Ma
Page 25 and 26:
2.3 Basic Symbolic Computations •
Page 27 and 28:
2.4 Assigning Expressions to Names
Page 29 and 30:
2.5 Basic Types of Maple Objects2.5
Page 31 and 32:
2.5 Basic Types of Maple Objects
Page 33 and 34:
{1,2,3,a,b,c} intersect {0,1,y,a};2
Page 35 and 36:
third_set := old_set minus {2, 5};2
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
2.6 Expression Manipulation • 333
Page 43 and 44:
x 2 + x y + y 2(y + x) (x 2 + y 2 )
Page 45 and 46:
2.6 Expression Manipulation • 37T
Page 47 and 48:
2.6 Expression Manipulation • 39>
Page 49 and 50:
2.6 Expression Manipulation • 41C
Page 51 and 52:
3 Finding SolutionsThis chapter int
Page 53 and 54:
3.1 The Maple solve Command • 45s
Page 55 and 56:
3.1 The Maple solve Command • 47A
Page 57 and 58:
3.1 The Maple solve Command • 49>
Page 59 and 60:
3.1 The Maple solve Command • 51>
Page 61 and 62:
3.1 The Maple solve Command • 53f
Page 63 and 64:
3.2 Solving Numerically Using the f
Page 65 and 66:
3.2 Solving Numerically Using the f
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 81 and 82:
Page 83 and 84:
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 and 98:
4.2 The Maple Packages • 89To vie
Page 99 and 100: 4.2 The Maple Packages • 91> Limi
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
Page 149: 5.6 Special Types of Plots • 141A
Page 153 and 154: 5.7 Manipulating Graphical Objects
Page 155 and 156: 5.7 Manipulating Graphical Objects
Page 157 and 158: hedgehog := [s1, s2, c3, stelhs]:>
Page 159 and 160: 5.8 Code for Color Plates • 151>
Page 161 and 162: 5.10 Conclusion5.10 Conclusion •
Page 163 and 164: 6 Evaluation andSimplificationExpre
Page 165 and 166: expand( (x+1)*(y^2-2*y+1) / z / (y-
Page 167 and 168: 6.1 Mathematical Manipulations •
Page 171 and 172: factor( poly, RootOf(x^2-2) );6.1 M
Page 183 and 184: 6.2 Assumptions • 175> assume( a
Page 185 and 186: 6.2 Assumptions • 177∞Logarithm
Page 187 and 188: 6.2 Assumptions • 179a:nothing kn
Page 189 and 190: 6.3 Structural Manipulations • 18
Page 195 and 196: f := (x, y) → is(x < y)6.3 Struct
Page 199 and 200: term3 := 2 cos(x) 2 sin(x)6.3 Struc
Page 201 and 202:
6.3 Structural Manipulations • 19
Page 203 and 204:
Page 205 and 206:
y := ln( sin( x * exp(cos(x)) ) );y
Page 207 and 208:
√ z sin(z) + w6.3 Structural Mani
Page 209 and 210:
Page 211 and 212:
6.4 Evaluation Rules • 203> eval(
Page 213 and 214:
6.4 Evaluation Rules • 205proc(x:
Page 215 and 216:
6.4 Evaluation Rules • 207The seq
Page 217 and 218:
6.4 Evaluation Rules • 2091Import
Page 219 and 220:
6.4 Evaluation Rules • 211> q :=
Page 221 and 222:
6.5 Conclusion • 213> sum( ’a||
Page 223 and 224:
7 Solving Calculus ProblemsThis cha
Page 225 and 226:
7.1 Introductory Calculus • 217>
Page 227 and 228:
7.1 Introductory Calculus • 219In
Page 229 and 230:
⎡⎧ ⎛1 √⎞1⎨5 − ⎩⎢a
Page 231 and 232:
7.1 Introductory Calculus • 223en
Page 233 and 234:
sol := solve( {err_x=0, err_xi=0},
Page 235 and 236:
7.1 Introductory Calculus • 227If
Page 237 and 238:
7.1 Introductory Calculus • 229>
Page 239 and 240:
7.1 Introductory Calculus • 231{0
Page 241 and 242:
7.1 Introductory Calculus • 233An
Page 243 and 244:
∫ 1+ sin(x) dx27.1 Introductory C
Page 245 and 246:
7.1 Introductory Calculus • 237r
Page 247 and 248:
7.1 Introductory Calculus • 239fy
Page 249 and 250:
7.2 Ordinary Differential Equations
Page 251 and 252:
{y(x) = _C1 },7.2 Ordinary Differen
Page 253 and 254:
Evaluate the result at values for t
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
odeplot( sol, [t, x(t)], -1..2 );7.
Page 263 and 264:
Page 265 and 266:
You must evaluate the derivatives a
Page 267 and 268:
Page 269 and 270:
DEplot( ode, dep-var, range, [ini-c
Page 271 and 272:
DEplot( {eq1, eq2}, [x(t), y(t)], -
Page 273 and 274:
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
Page 281 and 282:
Page 283 and 284:
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
show all

Maple 9 Learning Guide - Maplesoft

Create successful ePaper yourself

Delete template?

Save as template?