Computer Algebra Recipes: An Advanced Guide to Scientific Modeling

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Springer Science & Business Media, Dec 31, 2007 - Mathematics - 374 pages
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Modern 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. Computer Algebra Recipes: An Advanced Guide to Mathematical Modeling can serve as an effective computational science text, with a set of problems following each section of recipes to enable readers to apply and confirm their understanding. The book may also be used as a reference, for self-study, or as the basis of an on-line course.

 

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Contents

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
Bibliography
355
Index
361
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