Computer Algebra Recipes

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BIBLIOGRAPHY 359 [Str94] S. H. Strogatz. Nonlinear Dynamics and Chaos. Addison-Wesley, Reading, MA, 1994. [SWS82] R. H. Simoyi, A. Wolf, and H. L. Swinney. One-dimensional dynamics in a multi-component chemical reaction. Physical Review Letters, 49:245, 1982. [Tys76] J. J. Tyson. The Belousov{Zhabotinskii reaction. In Lecture Notes in Biomathematics, Vol. 10. Springer-Verlag, New York, 1976. [ZK65] N. J. Zabusky and M. D. Kruskal. Interaction of \solitons" in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett., 15:240, 1965.
Index acoustical waveguide, 261 adenosine diphosphate, 98 aliasing, 330 Andromeda Strain, 152 anharmonic force, 34 annulus, 231 aorta, 110 arms race, 105 arrhythmias, 28 arrow notation, 52 arrowheads full, 19 half, 19 attractor butter°y, 83, 351 chaotic, 345 Lorenz, 83 normal, 45 RÄossler, 353 reconstruction, 345 strange, 44 autonomous system, 32 baleen whale, 95 band matrix, 276 bandwidth limited, 330 bandwidth theorem, 273 basketball, falling, 152 Belousov{Zhabotinski, 40 Bernoulli equation, 155 Bernoulli, Daniel, 138 Bessel functions, 132, 254 Bessel recurrence relations, 136 Bessel zeros, 133 bifurcation, 337 diagram, 337 361 pitchfork, 340 tangent, 340 Bloch wall, 292 blood pressure diastolic, 110 systolic, 110 blue whale, 160 boundary condition, 228 bounded orbit, 325 Boussinesq's equation, 296, 303 brachistochrone, 190 bungee cord, 138 Burgers' equation, 296, 306 butter°y reconstruction, 351 butter°y, Lorenz's, 83 candle °ame, 287 capacitor, 29 Casablanca, 211 catenary, 194 Cauchy{Riemann conditions, 220 CDA, 274 center, 17 central di®erence approximation, 90 chain reaction, 236 Chandrasekhar, S., 95 chaos, 33, 38, 336 characteristic directions, 312 chemical oscillator, 40 chemical reaction, 100 empirical rule, 41 Oregonator, 41 classic Maple, 1 coalescence of roots, 68 column vector, 85, 277 competition
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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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