Computer Algebra Recipes

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   1. Introduction

      • Richard H. Enns, George C. McGuire

      Pages 1-8

3. The Appetizers

   1. Front Matter

      Pages 9-9

      PDF

   2. The Pictures of Science

      • Richard H. Enns, George C. McGuire

      Pages 11-58

   3. Deriving Model Equations

      • Richard H. Enns, George C. McGuire

      Pages 59-112

   4. Algebraic Models

      • Richard H. Enns, George C. McGuire

      Pages 113-194

   5. Monte Carlo Methods

      • Richard H. Enns, George C. McGuire

      Pages 195-260

4. The Entrees

   1. Front Matter

      Pages 261-261

      PDF

   2. Phase-Plane Portraits

      • Richard H. Enns, George C. McGuire

      Pages 263-324

   3. Linear ODE Models

      • Richard H. Enns, George C. McGuire

      Pages 325-396

   4. Nonlinear ODE Models

      • Richard H. Enns, George C. McGuire

      Pages 397-458

   5. Difference Equation Models

      • Richard H. Enns, George C. McGuire

      Pages 459-526

   6. Some Analytic Approaches

      • Richard H. Enns, George C. McGuire

      Pages 527-572

   7. Fractal Patterns

      • Richard H. Enns, George C. McGuire

      Pages 573-614

5. The Desserts

   1. Front Matter

      Pages 615-615

      PDF

   2. Diagnostic Tools for Nonlinear Dynamics

      • Richard H. Enns, George C. McGuire

      Pages 617-639

   3. Linear PDE Models

      • Richard H. Enns, George C. McGuire

      Pages 641-700

   4. Nonlinear PDE Models: Soliton Solutions

      • Richard H. Enns, George C. McGuire

      Pages 701-722

   5. Simulating PDE Models

      • Richard H. Enns, George C. McGuire

      Pages 723-743

6. Epilogue

   1. Epilogue

      • Richard H. Enns, George C. McGuire

      Pages 745-745

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. 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.

• Analysis
• Regression
• algebra
• computer
• computer algebra
• game theory
• model
• simulation

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." (Václav Koubek, Zentralblatt MATH, Vol. 976, 2002)

• Department of Physics, Simon Fraser University, Burnaby, Canada

  Richard H. Enns

• Department of Physics, University College of the Fraser Valley, Abbotsford, Canada

  George C. McGuire

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