Computer algebra recipes

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.

Contents: From the contents:

• Introduction:
• 0.1. Computer Algebra Systems. 0.2. The Spiral Staircase to Learning. 0.3. How to Climb the Spiral Staircase.-
• I. THE APPETIZERS:
• 1. The Pictures of Science:
• 1.1. Introduction.
• 1.2. Data and Function Plots:
• 1.2.1. Correcting for Inflation; 1.2.2. The Plummeting Badminton Bird; 1.2.3. Minimizing the Travel Time.
• 1.3. Log-log (Power Law) Plots:
• 1.3.1. Chimpanzee Brain Size; 1.3.2. Scaling Arguments and Gulliver's Travels.
• 1.4. Contour and Gradient Plots:
• 1.4.1. The Secret Message; 1.4.2. Designing a Ski Hill.
• 1.5. Animated Plots:
• 1.5.1. Waves are Dynamic; 1.5.2. The Sands of Time.
• 2. Deriving Model Equations:
• 2.1. Introduction.
• 2.2. Linear Correlation:
• 2.2.1. What is Linear Correlation? 2.2.2. The Corn Palace. 2.3. Lease Squares Derivation of Model Equations: 2.3.1. Regression Analysis; 2.3.2. Will You Be Better Off Than Your Parents? 2.3.3. What was the Heart Rate of a Brachiosaurus? 2.3.4. Senate Renewal; 2.3.5. Bikini Sales and the Logistic Curve; 2.3.6 Following the Dow Jones Index; 2.3.7. Variation of "g" with Latitude; 2.3.8. Finding Romeo a Juliet.
• 2.4. Deriving Multiple Regression.