Computer Algebra Recipes: An Introductory Guide to the Mathematical Models of Science

ISBN-13: 9780387257679 / Angielski / Miękka / 2006 / 430 str.

Richard H. Enns; George C. McGuire

Opis

Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models. Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry. The topics are organized into the Appetizers dealing with graphical aspects, the Entrees concentrating on symbolic computation, and the Desserts illustrating numerical simulation. The heart of the text is a large number of computer algebra recipes based on the Maple 10 software system. 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 an interesting or amusing story (accompanied with a thought-provoking quote) that leads the reader through the various 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. This text is the first of two volumes, the advanced guide, aimed at junior/senior/graduate level students, dealing with more advanced differential equation models."

Recenzje

From the reviews:

"Computer Algebra Recipes . . . is an eclectic collection of application stories together with associated Maple computer algebra worksheets or recipes. . . . The authors have designed this book to show how a computer algebra system such as Maple can be a valuable tool for computer modeling. . . . Any student who works through this text will develop a very good sense of what mathematical modeling is about. . . . This text would work well for self-study or as a source of material for projects." (Bill Satzer, MathDL - Online, April, 2006)

"All given algorithms have been designed not only to provide tools for problem solving, but also to stimulate the reader's imagination. .... Moreover, each section of recipes is followed by a set of problems that reader can use to check their understanding. ... Therefore, this handbook is appropriate for any junior/senior level course in Modern Algebra, Abstract Algebra, Algebraic Structures." (Jerzy Martyna, Zentralblatt MATH, Vol. 1106 (8), 2007)

"The authors ... aim is to introduce the reader to what they call 'the 'new' computational science based on the utilization of a CAS [computer algebra system].' ... I ... enjoyed reading this book and I learned a lot of Maple as I went through the worksheets. ... a text in a course that equips undergraduates to analyze and solve problems with a CAS. ... the book might be described as a tutorial on Maple that is based on mathematical models." (L. F. Shampine, SIAM Review, Vol. 49 (1), 2007)

Spis treści

The Appetizers.- The Pictures of Science.- Deriving Model Equations.- The Entrees.- Algebraic Models. Part I.- Algebraic Models. Part II.- Linear ODE Models.- Difference Equation Models.- The Desserts.- Monte Carlo Methods.- Fractal Patterns.

Blurb

Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models.
Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry. The topics are organized into the Appetizers dealing with graphical aspects, the Entrees concentrating on symbolic computation, and the Desserts illustrating numerical simulation.
The heart of the text is a large number of computer algebra recipes based on the Maple 10 software system. 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 an interesting or amusing story (accompanied with a thought-provoking quote) that leads the reader through the various steps of the recipe.
This text is the first of two volumes.  The advanced guide, aimed at junior/senior/graduate level students, deals with more advanced differential equation models.