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

Language: Anglais
Cover of the book Computer Algebra Recipes

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Computer algebra systems allow students to work on mathematical models more efficiently than in the case of pencil and paper. The use of such systems also leads to fewer errors and enables students to work on complex and computationally intensive models. 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, and chemistry. The text includes a large number of Maple(R) recipes.
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.