## Computer Algebra Recipes: An Advanced Guide to Scientific ModelingModern computer algebra systems are revolutionizing the teaching and learning of mathematically intensive subjects in science and engineering, enabling students to explore increasingly complex and computationally intensive models that provide analytic solutions, animated numerical solutions, and complex two- and three-dimensional graphic displays. This self-contained text benefits from a spiral structure that regularly revisits the general topics of graphics, symbolic computation, and numerical simulation with increasing intricacy at each turn. The text is built around a large number of computer algebra worksheets or "recipes" that have been designed using MAPLE to provide tools for problem solving and to stimulate critical thinking. No prior knowledge of MAPLE is assumed. All relevant commands are introduced on a need-to-know basis and are indexed for easy reference. Each recipe is associated with a scientific model or method and an interesting or amusing story designed to both entertain and enhance concept comprehension and retention. Aimed at third- and fourth-year undergraduates in science and engineering, the text contains numerous examples in disciplines that will challenge students progressing in mathematics, physics, engineering, game theory, and physical chemistry. |

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### Contents

1 | |

2 | |

3 | |

8 | |

9 | |

11 | |

13 | |

111 Romeo and Juliet | 18 |

Linear PDE Models Part 1 | 207 |

512 Play It Sam | 211 |

513 Three Easy Pieces | 215 |

514 Complex Yet Simple | 220 |

52 Diffusion and Laplaces Equation Models | 223 |

522 Aussie Barbecue | 227 |

523 Bennys Solution | 231 |

524 Hugo and the Atomic Bomb | 236 |

112 Theres No Damping Vectorias Romantic Heart | 23 |

113 Van der Pols Limit Cycle | 28 |

12 ThreeDimensional Autonomous Systems | 32 |

121 The PeriodDoubling Route to Chaos | 33 |

122 The Oregonator | 40 |

123 Rösslers Strange Attractor | 44 |

PhasePlane Analysis | 47 |

211 Foxes Munch Rabbits | 51 |

212 The Mona Lisa of Nonlinear Science | 58 |

213 Mike Creates a HigherOrder Fixed Point | 67 |

214 The Gnus and Sung of Erehwon | 73 |

215 A Plethora of Points | 78 |

22 ThreeDimensional Autonomous Systems | 82 |

23 Numerical Solution of ODEs | 88 |

231 Finite Difference Approximations | 89 |

The Sequel | 91 |

233 Glycolytic Oscillator | 96 |

234 Fox Rabies Epidemic | 101 |

THE ENTREES | 107 |

Linear ODE Models | 109 |

31 FirstOrder Models | 110 |

312 Greg Arious Nerds Problem | 115 |

32 SecondOrder Models | 118 |

322 Meet Mr Laplace | 121 |

323 Jennifers Formidable Series | 126 |

33 Special Function Models | 130 |

331 Jennifer Introduces a Special Family | 131 |

332 The Vibrating Bungee Cord | 137 |

333 Mathieus Spring | 142 |

334 QuantumMechanical Tunneling | 144 |

Nonlinear ODE Models | 149 |

41 FirstOrder Models | 150 |

412 The Struggle for Existence | 152 |

413 The Bad Bird Equation | 161 |

42 SecondOrder Models | 164 |

422 Oh What Sounds We Hear | 168 |

423 Vectoria Feels the Force and Hits the Bottle | 175 |

424 Golf Is Such an Uplifting Experience | 179 |

43 Variational Calculus Models | 185 |

432 Queen Dido Wasnt a Dodo | 191 |

433 The Human Fly Plans His Escape Route | 195 |

434 This Would Be a Great Amusement Park Ride | 201 |

525 Hugo Prepares for His Job Interview | 241 |

Linear PDE Models Part 2 | 247 |

612 Homers Jiggle Test | 251 |

613 Vectorias Second Problem | 254 |

614 Sound of Music? | 257 |

62 Semiinfinite and Infinite Domains | 261 |

622 Assignment Complete | 263 |

623 Radioactive Contamination | 266 |

624 Play It Sam Revisited | 270 |

63 Numerical Simulation of PDEs | 274 |

631 Freeing Excalibur the Numerical Way | 275 |

632 Enjoy the KleinGordon Vibes | 278 |

633 Vectorias Secret | 281 |

THE DESSERTS | 285 |

The Hunt for Solitons | 287 |

71 The Graphical Hunt for Solitons | 290 |

712 In Search of Bright Solitons | 293 |

713 Can Three Solitons Live Together? | 296 |

72 Analytic Soliton Solutions | 299 |

721 Follow That Wave | 300 |

722 Looking for a Kinky Solution | 304 |

723 We Have Solitons | 306 |

73 Simulating Soliton Collisions | 308 |

732 Are Diamonds a Kinks Best Friend? | 312 |

Nonlinear Diagnostic Tools | 319 |

811 A Rattler Signals Chaos | 320 |

812 Hamiltonian Chaos | 323 |

82 The Power Spectrum | 329 |

821 Frank N Steins Heartbeat | 332 |

822 The Rattler Returns | 334 |

83 The Bifurcation Diagram | 337 |

831 Pitchforks and Other Bifurcations | 338 |

84 The Lyapunov Exponent | 342 |

841 Mr Lyapunov Agrees | 343 |

85 Reconstructing an Attractor | 345 |

851 Putting Humpty Dumpty Together Again | 346 |

852 Random Is Random | 349 |

853 Butterfly Reconstruction | 351 |

Epilogue | 354 |

355 | |

361 | |

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Computer Algebra Recipes: An Advanced Guide to Scientific Modeling Richard H. Enns,George C. McGuire No preview available - 2007 |