Maple 9 Learning Guide - Maplesoft

More documents

Recommendations

Info

258 • Chapter 7: Solving Calculus Problemsp := 100 − 8 t + 2 5 t2 − 175 t3 + 1 13000 t4 −150000 t5You can now plot the response.> plot(p, t=0..30);100806040200–205 10 15 20 25 30tThis particular example has the following analytic solution.> dsolve( {eq(t), ini}, {theta(t)} );(−1/10 t)θ(t) = 20 + 80 e> q := rhs(%);(−1/10 t)q := 20 + 80 eThus, you can compare the series solution with the actual solution.> plot( [p, q], t=0..30 );100806040200–205 10 15 20 25 30tInstead of finding the Taylor series by hand, you can use the seriesoption of the dsolve command.
7.2 Ordinary Differential Equations • 259> dsolve( {eq(t), ini}, {theta(t)}, ’series’ );θ(t) =100 − 8 t + 2 5 t2 − 175 t3 + 1 13000 t4 −150000 t5 + O(t 6 )When You Cannot Find a Closed Form SolutionIn some instances, you cannot express the solution to a linear ODE inclosed form. In such cases, dsolve may return solutions containing thedata structure DESol. DESol is a place holder representing the solutionof a differential equation without explicitly computing it. Thus, DESolis similar to RootOf, which represents the roots of an expression. Thisallows you to manipulate the resulting expression symbolically prior toattempting another approach.> de := (x^7+x^3-3)*diff(y(x),x,x) + x^4*diff(y(x),x)> + (23*x-17)*y(x);de :=(x 7 + x 3 − 3) ( d2 y(x)) + x 4 ( ddx 2 dxy(x)) + (23 x − 17) y(x)The dsolve command cannot find a closed form solution to de.> dsolve( de, y(x) );y(x) = DESol{( d2(_Y(x)) + x4 ( ddx _Y(x))}(23 x − 17) _Y(x)dx 2 x 7 + x 3 +− 3 x 7 + x 3 ,− 3){_Y(x)}You can now try another method on the DESol itself. For example, finda series approximation.> series(rhs(%), x);
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 115 and 116:
Page 117 and 118:
polarplot( r-expr, angle=range )5.1
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
5.2 Graphing in Three Dimensions
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
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 261 and 262: odeplot( sol, [t, x(t)], -1..2 );7.
Page 265: 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 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 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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?