Computer Algebra Recipes

by Enns, Richard H.; McGuire, George C.

• ISBN13: 9780387257679
• ISBN10: 0387257675
• Edition: CD
• Format: Paperback
• Copyright: 2006-04-30
• Publisher: Springer-Nature New York Inc

Summary

Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models.Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry. The topics are organized into the Appetizers dealing with graphical aspects, the Entrees concentrating on symbolic computation, and the Desserts illustrating numerical simulation.The heart of the text is a large number of computer algebra recipes based on the Maple 10 software system. 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 an interesting or amusing story (accompanied with a thought-provoking quote) that leads the reader through the various 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.This text is the first of two volumes, the advanced guide, aimed at junior/senior/graduate level students, dealing with more advanced differential equation models.

Table of Contents

Preface	v
Introduction	1	(1)
Computer Algebra Systems	1	(2)
Computer Algebra Recipes	3	(2)
Introductory Recipe: Bridge Design 101	5	(4)
Maple Help	9	(1)
How to Use This Text	10	(1)
I. THE APPETIZERS	11	(108)
The Pictures of Science	13	(52)
Data and Function Plots	13	(23)
Correcting for Inflation	15	(7)
The Plummeting Badminton Bird	22	(9)
Minimizing the Travel Time	31	(5)
Log-Log (Power Law) Plots	36	(10)
Chimpanzee Brain Size	36	(4)
Scaling Arguments and Gulliver's Travels	40	(6)
Contour and Gradient Plots	46	(10)
The Secret Message	46	(3)
Designing a Ski Hill	49	(7)
Animated Plots	56	(9)
Waves Are Dynamic	56	(3)
The Sands of Time	59	(2)
These Arrows Are Useful	61	(4)
Deriving Model Equations	65	(54)
Linear Correlation	66	(3)
The Corn Palace	67	(2)
Least Squares Derivations	69	(37)
Will You Be Better Off Than Your Parents?	71	(5)
What Was the Heart Rate of a Brachiosaur?	76	(8)
Senate Renewal	84	(3)
Bikini Sales and the Logistic Curve	87	(4)
Following the Dow Jones Index	91	(7)
Variation of ``g'' with Latitude	98	(5)
Finding Romeo a Juliet	103	(3)
Multiple Regression Equations	106	(13)
Real Estate Appraisals	107	(6)
And the Winner Is?	113	(6)
II. THE ENTREES	119	(198)
Algebraic Models. Part I	121	(52)
Scalar Models	121	(35)
Bombs Versus Schools	122	(7)
Kirchhoff Rules the Electrical World	129	(7)
The Window Washer's Secret	136	(6)
The Science Student's Summer Job Interview	142	(6)
Envelope of Safety	148	(4)
Rainbow County	152	(4)
Integral Examples	156	(17)
The Great Pyramid of Cheops	156	(6)
Noah's Ark	162	(11)
Algebraic Models. Part II	173	(40)
Vector Models	173	(29)
Victoria's Mathematical Heritage	174	(5)
Vectoria and Fowles's Fly	179	(4)
Ain't She Sweet	183	(5)
Born Curl-Free	188	(6)
Of Coordinates and Circulation Too	194	(5)
All Is Flux	199	(3)
Matrix Models	202	(11)
Secret Message Revisited	202	(3)
A Fishy Tale	205	(3)
Population Waves	208	(5)
Linear ODE Models	213	(58)
Phase-Plane Portraits	214	(15)
Tenure Policy at Erehwon University	216	(5)
Vectoria Investigates the RLC Circuit	221	(8)
First-Order ODE Models	229	(16)
There Goes Louie's Alibi	229	(9)
The Water Skier	238	(4)
Ready to Charge	242	(3)
Second-Order ODE Models	245	(26)
Shrinking the Safety Envelope	245	(6)
Frank N. Stein Is Not Heartless	251	(4)
Halley's Comet	255	(5)
Wheel of misFortune	260	(6)
The Weedeater	266	(3)
Can an Unstable Spring Find Stability?	269	(2)
Difference Equation Models	271	(46)
Linear Models	272	(20)
Those Dratted Gnats	272	(4)
Gone Fishing	276	(3)
Fibonacci's Adam and Eve Rabbit	279	(4)
How Red Is Your Blood?	283	(2)
Fermi-Pasta-Ulam Is Not a Spaghetti Western	285	(7)
Nonlinear Models	292	(25)
Competition for Available Resources	292	(7)
The Logistic Map and Cobweb Diagrams	299	(7)
The Bouncing Ball Art Gallery	306	(4)
Onset of Chaos: A Model for the Outbreak of War	310	(7)
III. THE DESSERTS	317	(100)
Monte Carlo Methods	319	(62)
Random Walks	321	(17)
The Soccer Fan's Drunken Walk	324	(5)
Blowin' in the Wind	329	(4)
Flight of Penelope Jitter Bug	333	(2)
That Meandering Perfume Molecule	335	(3)
Monte Carlo Integration	338	(23)
Numerical Integration Methods	339	(5)
Wait and Buy Later!	344	(4)
Wait and Buy Later! The Sequel	348	(5)
Estimating π	353	(2)
Chariot of Fire and Destruction	355	(6)
Probability Distributions	361	(11)
Of Nuts and Bolts and Hospital Beds Too	361	(6)
The Ice Wines of Rainbow County	367	(5)
Monte Carlo Statistical Distributions	372	(9)
Estimating e	372	(4)
Vapor Deposition	376	(5)
Fractal Patterns	381	(36)
Difference Equations	384	(24)
Wallpaper for the Mind	384	(2)
Sierpinski's Fractal Gasket	386	(5)
Barnsley's Fern	391	(5)
Douady's Rabbit and Other Fauna and Flora	396	(4)
The Rings of Saturn	400	(8)
Cellular Automata	408	(6)
A Navaho Rug Design	408	(3)
The One out of Eight Rule	411	(3)
Strange Attractors	414	(3)
Lorenz's Butterfly	414	(2)
Epilogue	416	(1)
Bibliography	417	(4)
Index	421