Computer Algebra Recipes

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364 INDEX implicit solution, 169 incompressible °uid, 241 inductor, 30 infectious disease, 66 in¯nite domain, 261 initial conditions, 20 initialization, 310 Internet, 260 inverted spring, 34 ion acoustic soliton, 303 iron core inductor, 57 iron sphere temperature, 245 irreversible reaction, 150 isoperimetric problem, 191 Jacobi elliptic function, 173 Josephson junction, 288 K}orÄos, E., 40 KAM torus, 327 Kaup, David, 299 KdV equation, 287, 300 KdV soliton collision, 308 Kerr medium, 288 kink, 304 Kirchho®'s current rule, 29 Kirchho®'s potential rule, 57 Klein{Gordon equation, 278 Korteweg, Diederik, 301 Kruskal, Martin, 309 Lagrange's equations, 202 laminar °ow, 161 Laplace transform, 121, 267 Laplace's equation, 220 Laplace, Pierre-Simon, 121 laser beam competition, 159 laser beams, 318 learning curve, 114 Legendre polynomials, 243 limit cycle, 28 logistic equation, 154 logistic map, 338 Lorentz force, 175 Lorenz equations, 83 Lorenz's butter°y, 351 love a®air, 18 low-pass ¯lter, 330 Lyapunov exponent, 342, 343 Lyapunov, Aleksandr M., 342 magnetic bottle, 175 magnetic spin, 288, 292 magnetohydrodynamic waves, 288 Malthus's equation, 153 Malthus's law, 152 Malthus, Thomas, 153 map cubic, 341 Humpty Dumpty, 346 logistic, 338 one-dimensional, 346 quartic, 341, 345 sine,341,345 tent, 341, 345 Maple active derivative, 19 addition, 4 aliasing symbols, 122 animation, 7 arrow operator, 52 assignment operator, 4 assume vs. assuming, 112 automatic substitution, 19 classic interface, 1 clearing internal memory, 4 colon, 4 command information, 110 comment, 5 conditional statement, 80 constrained scaling, 6 copying examples, 8 CPU time, 91 curly brackets, 15 default accuracy, 4 di®erential operator, 26 digits control, 103 ditto operator, 30 division, 4 functional operator, 52
INDEX 365 Help, Full Text Search, 8 Help, Topic Search, 8 Help, using, 8 inert derivative, 19 inserting comments, 5 library packages, 7 list, 6 list of lists, 6 list procedure, 127 menu index ¯le, 2 multiplication, 4 placeholder, 280 plot options, 6 powers, 4 prime notation, 126 procedure, 52 prompt symbol, 4 recipe, 1 rotating viewing box, 31 semicolon, 4 set, 15 square brackets, 6 standard interface, 1 string, 6 superimposing ¯gures, 53 suppressing output, 4 text on plot, 42 toolbar, 6 type match, 226 unassignment, 54 unprotect Maple symbol, 59 user manuals, 1 variable change, 29 warnings, 7 worksheet, 2 Maple Command ^, 4 ¡ >, 52 *, 4 +, 4 -, 4 ., 180 /, 4 ::, 226 :=, 4 :, 4 ;, 4 >, 277 < >,176 ?coords, 231 ?inifcns, 132 ?, 8 Array, 333 BandMatrix, 276,280 BesselJZeros, 133, 255 BesselJ, 132 BesselY, 133, 237 CrossProduct, 176 DEplot3d, 31,45 DEplot, 24 DEtools[expsols], 267 Determinant, 85 Diff, 19 Digits, 98 Dirac, 264 DotProduct, 180 D, 26 Eigenvalues, 85 EulerLagrange, 188 FourierTransform, 333 Gamma, 59 GenerateMatrix, 85 Gradient, 222 HINT, 225 Hamilton eqs, 325 INTEGRATE, 225 Int, 34 I, 216 Laplacian('cylindrical'), 258 Laplacian, 232 LegendreP, 134 LegendreQ, 134,242 Omega, 203 Order, 128 Phi, 5 Pi, 209 Sum, 226 SurfaceOfRevolution, 189 Tangent, 167 Theta, 60, 203
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Richard H. Enns George C. McGuire C
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PREFACE A computer algebra system (
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viii CONTENTS 2.3.1 Finite Di®eren
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x CONTENTS 8.3 The Bifurcation Diag
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2 INTRODUCTION B. Computer Algebra
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4 INTRODUCTION (a) At what angle Á
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6 INTRODUCTION The negative answer
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8 INTRODUCTION D. Maple Help We tea
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Part I THE APPETIZERS A man ceases
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14 CHAPTER 1. PHASE-PLANE PORTRAITS
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48 CHAPTER 2. PHASE-PLANE ANALYSIS
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Chapter 3 Linear ODE Models Among a
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3.1. FIRST-ORDER MODELS 111 Therate
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3.1. FIRST-ORDER MODELS 113 Pressur
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3.1. FIRST-ORDER MODELS 115 3.1.2 G
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3.1. FIRST-ORDER MODELS 117 Evil Kn
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3.2. SECOND-ORDER MODELS 119 > tf:=
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3.2. SECOND-ORDER MODELS 121 3.2.2
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3.2. SECOND-ORDER MODELS 123 Loadin
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3.2. SECOND-ORDER MODELS 125 0.4 0.
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3.2. SECOND-ORDER MODELS 127 On ent
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3.2. SECOND-ORDER MODELS 129 Using
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3.3. SPECIAL FUNCTION MODELS 131 3.
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3.3. SPECIAL FUNCTION MODELS 133 1
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3.3. SPECIAL FUNCTION MODELS 135 Th
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3.3. SPECIAL FUNCTION MODELS 137 3.
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3.3. SPECIAL FUNCTION MODELS 139 th
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3.3. SPECIAL FUNCTION MODELS 141 PR
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3.3. SPECIAL FUNCTION MODELS 143 ¡
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3.3. SPECIAL FUNCTION MODELS 145 μ
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3.3. SPECIAL FUNCTION MODELS 147 >
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150 CHAPTER 4. NONLINEAR ODE MODELS
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208 CHAPTER 5. LINEAR PDE MODELS. P
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Chapter 6 Linear PDE Models. Part 2
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6.1. WAVE EQUATION MODELS 249 > sol
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6.1. WAVE EQUATION MODELS 251 6.1.2
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6.1. WAVE EQUATION MODELS 253 The p
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6.1. WAVE EQUATION MODELS 255 Recog
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6.1. WAVE EQUATION MODELS 257 PROBL
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6.1. WAVE EQUATION MODELS 259 Then
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6.2. SEMI-INFINITE AND INFINITE DOM
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6.3. NUMERICAL SIMULATION OF PDES 2
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Part III THE DESSERTS The way a chi
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288 CHAPTER 7. THE HUNT FOR SOLITON
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Page 369 and 370: INDEX 369 ¯sh harvesting, 100 ¯xe
Page 371 and 372: INDEX 371 quartic map, 345 Queen Di
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Computer Algebra Recipes

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