Ebook: Computer Algebra Recipes: A Gourmet’s Guide to the Mathematical Models of Science
- Genre: Computers // Software: Systems: scientific computing
- Tags: Symbolic and Algebraic Manipulation, Physics general, Computational Intelligence
- Series: Undergraduate Texts in Contemporary Physics
- Year: 2001
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-8
Front Matter....Pages 9-9
The Pictures of Science....Pages 11-58
Deriving Model Equations....Pages 59-112
Algebraic Models....Pages 113-194
Monte Carlo Methods....Pages 195-260
Front Matter....Pages 261-261
Phase-Plane Portraits....Pages 263-324
Linear ODE Models....Pages 325-396
Nonlinear ODE Models....Pages 397-458
Difference Equation Models....Pages 459-526
Some Analytic Approaches....Pages 527-572
Fractal Patterns....Pages 573-614
Front Matter....Pages 615-615
Diagnostic Tools for Nonlinear Dynamics....Pages 617-639
Linear PDE Models....Pages 641-700
Nonlinear PDE Models: Soliton Solutions....Pages 701-722
Simulating PDE Models....Pages 723-743
Epilogue....Pages 745-745
Back Matter....Pages 747-778
Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-8
Front Matter....Pages 9-9
The Pictures of Science....Pages 11-58
Deriving Model Equations....Pages 59-112
Algebraic Models....Pages 113-194
Monte Carlo Methods....Pages 195-260
Front Matter....Pages 261-261
Phase-Plane Portraits....Pages 263-324
Linear ODE Models....Pages 325-396
Nonlinear ODE Models....Pages 397-458
Difference Equation Models....Pages 459-526
Some Analytic Approaches....Pages 527-572
Fractal Patterns....Pages 573-614
Front Matter....Pages 615-615
Diagnostic Tools for Nonlinear Dynamics....Pages 617-639
Linear PDE Models....Pages 641-700
Nonlinear PDE Models: Soliton Solutions....Pages 701-722
Simulating PDE Models....Pages 723-743
Epilogue....Pages 745-745
Back Matter....Pages 747-778
....