Undergraduate Texts in Contemporary Physics

A Gourmet's Guide to the Mathematical Models of Science

By: Richard Enns, George C. McGuire

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Hardcover | 8 June 2001

At a Glance

Hardcover
796 Pages

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25.4 x 17.78 x 4.29

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Computer algebra systems have the potential to revolutionize the teaching of and learning of science. Not only can students work thorough mathematical models much more efficiently and with fewer errors than with pencil and paper, they can also work with much more complex and computationally intensive models. Thus, for example, in studying the flight of a golf ball, students can begin with the simple parabolic trajectory, but then add the effects of lift and drag, of winds, and of spin. Not only can the program provide analytic solutions in some cases, it can also produce numerical solutions and graphic displays. Aimed at undergraduates in their second or third year, this book is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, physics, chemistry. The text is organized along a spiral, revisiting general topics such as graphics, symbolic computation, and numerical simulation in greater detail and more depth at each turn of the spiral. The heart of the text is a large number of computer algebra recipes. These have been designed not only to provide tools for problem solving, but also to stimulate the reader's imagination. Associated with each recipe is a scientific model or method and a story that leads the reader through steps of the recipe. The recipes are also included on the CD-ROM enclosed with the book. Each section of recipes is followed by a set of problems that readers can use to check their understanding or to develop the topic further.

Industry Reviews

From the reviews:

"In the book, the authors are showing the reader what they can do with Maple 6, and they can do a lot. Simply flipping the pages of the book, the reader might get very inspired by the formulas and pictures. ... Most of the text I covered up to now contains useful and exciting examples ... . the book is definitely very useful for educators ... ." (L. Kocbach, Computer Physics Communications, Vol. 144, 2002)

"This book captures the essence of the CAS approach and it is the best book of its kind that I am aware of. The level of mathematics, the eclectic, abundant and carefully selected problem set, the friendly and expansive text and the clear demonstration of the power of the CAS approach all add up to a first rate book. ... I highly recommend that you get your library to order a copy." (B.I. Henry, The Physicist, Vol. 39 (2), 2002)

"This book is a readable introduction to Maple, a computer algebra system. The authors present real life situations, describe them in the language of mathematics, and then use Maple to find or deduce conclusions, predictions and classifications of each of these situations." (Vaclav Koubek, Zentralblatt MATH, Vol. 976, 2002)

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You Can Find This Book In

Non-Fiction Science Physics Mathematics Algebra Science in General Maths for Scientists Engineering & Technology Technology in General Maths for Engineers Applied Mathematics Computing & I.T.

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Preface	p. vii
Introduction	p. 1
Computer Algebra Systems	p. 1
The Spiral Staircase to Learning	p. 3
How to Climb the Spiral Staircase	p. 7
The Appetizers	p. 9
The Pictures of Science	p. 11
Introduction	p. 11
Data and Function Plots	p. 13
Correcting for Inflation	p. 13
The Plummeting Badminton Bird	p. 20
Minimizing the Travel Time	p. 29
Log-Log (Power Law) Plots	p. 33
Chimpanzee Brain Size	p. 33
Scaling Arguments and Gulliver's Travels	p. 38
Contour and Gradient Plots	p. 43
The Secret Message	p. 43
Designing a Ski Hill	p. 47
Animated Plots	p. 53
Waves Are Dynamic	p. 53
The Sands of Time	p. 56
Deriving Model Equations	p. 59
Introduction	p. 59
Linear Correlation	p. 60
What Is Linear Correlation?	p. 60
The Corn Palace	p. 61
Least Squares Derivations	p. 63
Regression Analysis	p. 63
Will You Be Better Off Than Your Parents?	p. 65
What Was the Heart Rate of a Brachiosaurus?	p. 71
Senate Renewal	p. 78
Bikini Sales and the Logistic Curve	p. 81
Following the Dow Jones Index	p. 86
Variation of "g" with Latitude	p. 93
Finding Romeo a Juliet	p. 97
Multiple Regression Equations	p. 101
Real Estate Appraisals	p. 102
And the Winner Is?	p. 107
Algebraic Models	p. 113
Introduction	p. 113
Algebraic Examples	p. 114
Bombs Versus Schools	p. 114
Kirchhoff Rules the Electrical World	p. 121
The Window Washer's Secret	p. 128
The Science Student's Summer Job Interview	p. 134
Envelope of Safety	p. 140
Rainbow County	p. 144
Integral Examples	p. 150
The Great Pyramid of Cheops	p. 150
Noah's Ark	p. 156
Vector Examples	p. 166
Vectoria's Mathematical Heritage	p. 166
Ain't She Sweet	p. 173
Born Curl Free	p. 181
Of Flux and Circulation and Coordinates Too	p. 186
Monte Carlo Methods	p. 195
Introduction	p. 195
Random Walks	p. 197
The Concept	p. 197
The Soccer Fan's Drunken Walk	p. 200
Blowin' in the Wind	p. 205
Flight of Penelope Jitter Bug	p. 209
That Meandering Perfume Molecule	p. 212
Monte Carlo Integration	p. 215
Standard Numerical Integration Algorithms	p. 215
Monte Carlo Integration	p. 219
Wait and Buy Later!	p. 220
Wait and Buy Later! The Sequel	p. 224
Estimating [pi]	p. 229
Chariot of Fire and Destruction	p. 231
Probability Distributions	p. 236
Of Nuts and Bolts and Hospital Beds Too	p. 236
The Ice Wines of Rainbow County	p. 243
Monte Carlo Statistical Distributions	p. 250
Estimating e	p. 250
Vapor Deposition	p. 255
The Entrees	p. 261
Phase-Plane Portraits	p. 263
Introduction	p. 263
Phase-Plane Portraits	p. 263
Stationary or Singular Points	p. 265
Linear ODE Models	p. 268
Tenure Policy at Erehwon University	p. 268
Vectoria Investigates the RLC Circuit	p. 273
Nonlinear ODE Models	p. 280
Classification of Stationary Points	p. 280
Rabbits and Foxes	p. 284
The Mona Lisa of Nonlinear Science	p. 292
Mike Creates a Higher-Order Singular Point	p. 301
The Gnus and Sung of Erehwon	p. 308
Nonautonomous ODEs	p. 314
Can an Unstable Spring Find Stability?	p. 314
The Period Doubling Route to Chaos	p. 317
Linear ODE Models	p. 325
Introduction	p. 325
Solving Linear ODEs with Maple	p. 326
First-Order ODE Models	p. 332
There Goes Louie's Alibi	p. 332
The Water Skier	p. 341
Second-Order ODE Models	p. 345
Shrinking the Safety Envelope	p. 345
Halley's Comet	p. 350
Frank N. Stein Is Not Heartless	p. 358
Vectoria Feels the Force and Hits the Bottle	p. 362
Bessel and Legendre ODE Models	p. 369
Introduction to Special Functions	p. 369
The Vibrating Bungee Cord	p. 376
Wheel of misFortune	p. 382
The Weedeater	p. 391
Nonlinear ODE Models	p. 397
Introduction	p. 397
First-Order Models	p. 398
The Nonlinear Diode	p. 398
The Bad Bird Equation	p. 402
The Struggle for Existence	p. 407
Second-Order Models	p. 414
Pirates of the Caribbean	p. 414
Oh What Sounds We Hear!	p. 418
Those Lennard-Jones Vibrational Blues	p. 424
Golf Is Such an "Uplifting" Experience	p. 432
This Would Be a Great Amusement Park Ride	p. 438
Limit Cycles	p. 445
The Bizarre World of the Tunnel Diode Oscillator	p. 445
Follow That Rabbit	p. 452
Difference Equation Models	p. 459
Introduction	p. 459
Linear Difference Equation Models	p. 460
First-Order Linear Models	p. 461
Those Dratted Gnats	p. 461
Gone Fishing	p. 464
Second-Order Linear Models	p. 467
Fibonacci's Adam and Eve Rabbit	p. 467
How Red Is Your Blood?	p. 471
Fermi-Pasta-Ulam Is Not a Spaghetti Western	p. 473
Nonlinear Difference Equation Models	p. 484
First-Order Nonlinear Models	p. 484
Competition for Available Resources	p. 484
The Logistic Map and Cobweb Diagrams	p. 492
Second-Order Nonlinear Models	p. 499
The Bouncing Ball Art Gallery	p. 499
Onset of Chaos: A Model for the Outbreak of War	p. 503
Numerically Solving ODEs	p. 513
Finite Difference Approximations to Derivatives	p. 513
Rabbits and Foxes: The Sequel	p. 516
Glycolytic Oscillator	p. 521
Some Analytic Approaches	p. 527
Introduction	p. 527
Checking Solutions	p. 527
The Palace of the Governors	p. 527
Play It, Sam	p. 532
The Three-Piece String	p. 536
Calculus of Variations	p. 541
Dress Design, The Erehwonese Way	p. 541
Queen Dido's Problem	p. 548
The Human Fly Plans His Escape Route	p. 552
Fourier Series	p. 559
Hi C Is Not Always a Drink	p. 562
Play It, Sam: A New Perspective	p. 565
Vectoria Sums a Series	p. 569
Fractal Patterns	p. 573
Introduction	p. 573
Difference Equation Patterns	p. 574
Wallpaper for the Mind	p. 574
Sierpinski's Fractal Gasket	p. 576
Barnsley's Fern	p. 583
Douady's Rabbit and Other Fauna and Flora	p. 588
The Rings of Saturn	p. 592
ODE Patterns	p. 601
The Butterfly Attractor	p. 601
Rossler's Strange Attractor	p. 606
Cellular Automata Patterns	p. 608
A Navaho Rug Design	p. 608
The One Out of Eight Rule	p. 611
The Desserts	p. 615
Diagnostic Tools for Nonlinear Dynamics	p. 617
Introduction	p. 617
The Poincare Section	p. 617
The Concept	p. 617
A Rattler Signals Chaos	p. 618
The Power Spectrum	p. 622
The Concept	p. 622
The Rattler Returns	p. 624
The Bifurcation Diagram	p. 628
The Concept	p. 628
Pitchforks and Other Bifurcations	p. 629
The Lyapunov Exponent	p. 632
The Concept	p. 632
Mr. Lyapunov Agrees	p. 633
Reconstructing an Attractor	p. 635
The Concept	p. 635
Chaos Versus Noise	p. 636
Linear PDE Models	p. 641
Introduction	p. 641
The Linear PDEs of Mathematical Physics	p. 641
Separation of Variables	p. 643
Diffusion and Laplace's Equation Models	p. 647
Freeing Excalibur	p. 647
Aussie Barbecue	p. 651
Erehwon Institute of Technology	p. 655
Hugo and the Atomic Bomb	p. 659
Hugo Prepares for his Job Interview	p. 666
Wave Equation Models	p. 672
Vectoria Encounters Simon Legree	p. 672
Homer's Jiggle Test	p. 676
Vectoria's Second Problem	p. 681
Semi-Infinite and Infinite Domains	p. 685
Vectoria's Third Problem	p. 686
Assignment Complete!	p. 688
Radioactive Contamination	p. 691
"Play It, Sam" Revisited	p. 696
Nonlinear PDE Models: Solition Solutions	p. 701
Introduction	p. 701
Solitary Waves	p. 702
The Graphical Hunt for Solitons	p. 704
Of Kinks and Antikinks	p. 704
In Search of Bright Solitons	p. 708
Can Three Solitary Waves Live Together?	p. 712
Analytic Soliton Solutions	p. 715
Follow That Wave!	p. 715
Looking for a Kinky Solution	p. 719
Simulating PDE Models	p. 723
Introduction	p. 723
Diffusion and Wave Equation Models	p. 724
Freeing Excalibur the Numerical Way	p. 724
Vectoria Secret	p. 728
Enjoy the Klein-Gordon Vibes	p. 730
Soliton Collisions	p. 734
To Be or Not to Be a Soliton	p. 734
Are Diamonds a Kink's Best Friend?	p. 738
Epilogue	p. 745
Bibliography	p. 747
Index	p. 753
Table of Contents provided by Syndetics. All Rights Reserved.

Undergraduate Texts in Contemporary Physics

A Gourmet's Guide to the Mathematical Models of Science

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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