Maple 9 Learning Guide - Maplesoft

More documents

Recommendations

Info

84 • Chapter 4: Maple Organizationliesymm commands for characterizing the contact symmetries of systemsof partial differential equations.LinearAlgebra enhanced linear algebra commands for creating specialtypes of Matrices, calculating with large numeric Matrices, and performingMatrix algebra.LinearFunctionalSystems commands that solve linear functional systemswith polynomial coefficients, find the universal denominator ofa rational solution, and transform a matrix recurrence system into anequivalent system with a nonsingular leading or trailing matrix.ListTools commands that manipulate lists.LREtools commands for manipulating, plotting, and solving linear recurrenceequations.Maplets package commands for creating windows, dialogs, and other visualinterfaces that interact with a user to provide the power of Maple.MathML commands that import and export Maple expressions to and fromMathML text.Matlab commands to use several MATLAB numerical matrix functions,including eigenvalues and eigenvectors, determinants, and LUdecomposition.(Only accessible if MATLAB is installed on your system.)MatrixPolynomialAlgebra set of tools for the algebraic manipulation ofmatrix polynomials.networks tools for constructing, drawing, and analyzing combinatorialnetworks. Facilities for handling directed graphs, and arbitrary expressionsfor edge and vertex weights.numapprox commands for calculating polynomial approximations to functionson a given interval.numtheory commands for classic number theory, primality testing, findingthe nth prime, factoring integers, generating cyclotomic polynomials.This package also contains commands for handling convergents.Ore_algebra routines for basic computations in algebras of linear operators.
4.2 The Maple Packages • 85OrthogonalSeries commands for manipulating series of classical orthogonalpolynomials or, more generally, hypergeometric polynomials.orthopoly commands for generating various types of orthogonal polynomials;useful in differential equation solving.padic commands for computing p-adic approximations to real numbers.PDEtools tools for manipulating, solving and plotting partial differentialequations.plots commands for different types of specialized plots, including contourplots, two- and three-dimensional implicit plotting, plotting text, andplots in different coordinate systems.plottools commands for generating and manipulating graphical objects.PolynomialTools commands for manipulating polynomial objects.powseries commands to create and manipulate formal power series representedin general form.process the commands in this package allow you to write multi-processMaple programs under UNIX r○ .RandomTools commands for working with random objects.RationalNormalForms commands that construct the polynomial normalform or rational canonical forms of a rational function, or minimalrepresentation of a hypergeometric term.RealDomain provides an environment in which the assumed underlyingnumber system is the real number system not the complex numbersystem.ScientificConstants commands that provide access to the values ofvarious constant physical quantities that occur in fields such as chemistryand physics.ScientificErrorAnalysis commands that provide representation andconstruction of numerical quantitites that have a central value andassociated uncertainty or error. This allows users to determine theuncertainty in, for example, the product of quantities-with-error.simplex commands for linear optimization using the simplex algorithm.
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 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: CurveFitting commands that support
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 and 150:
5.6 Special Types of Plots • 141A
Page 151 and 152:
5.6 Special Types of Plots • 1431
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 169 and 170:
Page 171 and 172:
factor( poly, RootOf(x^2-2) );6.1 M
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
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 191 and 192:
Page 193 and 194:
Page 195 and 196:
f := (x, y) → is(x < y)6.3 Struct
Page 197 and 198:
Page 199 and 200:
term3 := 2 cos(x) 2 sin(x)6.3 Struc
Page 201 and 202:
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?