Computer Algebra Recipes

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368 INDEX with(plots), 7,59 with(plottools, 138 Mathieu equation, 143 Mathieu functions, 142 Mathieu, Emile, 142 MathieuC, 143 MathieuS, 143 matrix, 85 band, 276 multiplication, 276 square, 276 tridiagonal, 276 May, Robert, 149 mean daily temperature, 209 measles, 353 membrane circular, 254 free edges, 253 rectangular, 251 square, 253 mesh diamond-shaped, 312 point, 274 rectangular, 275 method of characteristics, 312 Michaelis{Menton equation, 161 microbiology, 152 Mike, 23 mirage, 190 model KdV soliton, 300 modi¯ed Euler algorithm, 96 modi¯ed KdV equation, 303 Mona Lisa, 58 multiplication factor, 236 musical notes, 257 myxamatosis, 160 National Bureau of Standards, 131 negative damping, 29 neutron density, 236 neutron di®usion, 236 Newton's drag law, 161 Newton's second law, 59, 115 nodal lines, 256 nodal point, 16 nonlinear diode, 159 nonlinear drag, 164 nonlinear rate equations, 41 nonlinear SchrÄodinger equation, 287 nonlinear spring, 72 normal modes, 257, 259 Noyes, R. M., 40 nuclear explosion, 240 nuclear ¯ssion, 236 numerical instability, 96, 277 numerical mesh, 274 Nyquist frequency, 330 Nyquist, H., 330 ODE nth-order, 110 Airy, 23 analytic solution, 22 arms race, 105 autonomous, 13 baleen whale, 95 Bernoulli, 155 Bertalan®y, 161 Bessel, 131 blood pressure model, 110 blue whale, 160 brachistochrone, 190 bungee cord, 138 catenary, 194 chemical oscillator, 44 chemical reaction, 100 competing armies, 57 con°uent hypergeometric, 23 dimensionless, 30 dot notation, 13 Du±ng, 149, 320 eardrum, 168 Euler algorithm, 92 Euler{Lagrange, 185 falling basketball, 152 falling raindrop, 120 ¯nite di®erence approximation, 89 ¯rst integral, 116
INDEX 369 ¯sh harvesting, 100 ¯xed points, 14 °u epidemic, 160 forced sti®, 106 fox rabies, 102 Frobenius series, 132 geodesic, 191 glycolytic, 96 gnus and sung, 74 golf ball, 182 Gompertz, 160 growing pendulum, 141 hard spring, 174 Hermite, 23 homogeneous, 110 inhomogeneous, 110 integrating factor, 115 Lagrange, 202 Laplace transform method, 121 laser beam, 159 learning curve, 114 Legendre, 134 light ray path, 191 linear, 14, 110 logistic, 154 Lorenz, 83 Malthus, 153 Maple odeadvisor, 115 Mathieu, 142 Michaelis{Menton, 161 modi¯ed Euler algorithm, 96 nonautonomous, 13 nonlinear, 14 nonlinear diode, 159 numerical instability, 96 numerical solution, 42 onset of bending, 141 Oregonator, 40 oscillating pivot, 206 p-q diagram, 50 parametric excitation, 206 pendulum, 23 phase-plane analysis, 47 phase-plane portrait, 13 piecewise, 111 plotting numerical solution, 42 population growth, 114 prime notation, 13 pursuit, 164 RÄossler, 45, 88 rabbits and foxes, 14, 51 Rayleigh, 23 Riccati, 162 RK4 algorithm, 96 rkf45 method, 42 RL circuit, 114 Romeo and Juliet, 18 rotating circular loop, 206 SchrÄodinger, 219 second-order, 14, 118 Sel'kov, 97 semi-implicit algorithm, 102 separable, 150 series solution, 126 simple harmonic oscillator, 14 SIR model, 66 soft spring, 23 spherical pendulum, 203 squid and herring, 82 standard form, 14 stationary points, 14 steady-state solution, 124 sti®, 105 sti®ening spring, 141 Sturm{Liouville, 130 trajectory, 14 transient solution, 124 Van der Pol, 28 Verhulst, 72 white dwarf, 95 yeast model, 154 optical pulse, 288 ordinary functions, 130 ordinary point, 15, 47 Oregonator, 40 orthogonality, 136, 226 oscillator forced glycolytic, 337 glycolytic, 96 tunnel diode, 28
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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 317 and 318: 316 CHAPTER 7. THE HUNT FOR SOLITON
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Page 367: INDEX 367 laplace, 121,267,268 lhs,
Page 371 and 372: INDEX 371 quartic map, 345 Queen Di
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Computer Algebra Recipes

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