Computer Algebra Recipes A Gourmet’s Guide to the Mathematical Models of Science

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.

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.