1R3. Computer Algebra Recipes for Classical Mechanics. - RH Enns (Dept of Phys, Simon Fraser Univ, Burnaby, BC, V5A 1S6, Canada). and GC McGuire (Dept of Phys, Univ Col of Fraser Valley, Abbotsford, BC, V2S 7M9, Canada). Birkhauser Boston, Cambridge MA. 2003. 264 pp. Softcover, CD-Rom included. ISBN 0-8176-4291-9. $54.95.
Reviewed by WE Clausen (7521 Heffley Court, Canal Winchester OH 43110-8749).
Computer Algebra Recipes for Classical Mechanics is a guide to problem solving in classical mechanics using the Maple 8 computer algebra system. Computer algebra systems allow one not only to carry out the numerical computations of standard programming languages, but also to perform complicated symbolic manipulations. A computer algebra system can perform a wide variety of mathematical operations, including analytic differentiation and analytic/numerical integration, analytic/numerical solution of ordinary/partial differential equations, Taylor series expansions of functions to arbitrary order, analytic/numerical solution and manipulation of algebraic equations, production of two and three-dimensional vector field and contour plots, and animation of analytic and numerical solutions
The book is designed to complement traditional textbooks by showing how computer algebra can be used to solve standard physical models efficiently and to explore more complex physical systems. The heart of this book consists of a set of more than one hundred computer algebra worksheets (the “recipes”), which are systematically organized to correlate with the topics covered in standard undergraduate mechanics texts. A reader desiring to use an alternate computer algebra system or a different release of Maple may have little difficulty in modifying the recipes.
No prior knowledge of Maple is assumed, the relevant command structures being systematically introduced on a need-to-know basis. Each recipe takes the reader from the analytic formulation of a representative type of mechanics problem to its solution (analytical or numerical) to a graphical visualization of the solution. The graphical representations vary from static two-dimensional pictures, to contour and vector field plots, to three-dimensional graphs, which can be rotated, to animations in time. All the recipes are included on the CD that accompanies the book.
The authors have designed each recipe so that by altering the parameter values, or the initial conditions, or the very nature of the model itself, additional mechanics problems can be studied.
The recipes are organized into three levels:
• In the Appetizers, the recipes assume a familiarity with the fundamental concepts of mechanics (eg, kinematics, Newton’s laws with constant forces, conservation of energy and momentum etc) and a mathematical knowledge of vectors, ordinary derivatives, integrals, and linear algebra.
• The Entrees deal with examples from intermediate mechanics (eg, Newtonian dynamics with variable forces and accelerated frames of reference) and make use of partial derivatives, vector calculus, curvilinear coordinates, and linear and nonlinear ordinary differential equations.
• In the advanced mechanics recipes, which form the Desserts, the focus is on examples from Lagrangian and Hamiltonian mechanics.
• The text contains forty-seven problems that have full solutions with the Maple code provided and explained. The problem statements for sixty-six supplementary problems are also included in the text. The CD, which accompanies the book, includes the Maple code for all 113 problems with extensive comments provided for the supplementary problems. The problems are appropriate and imaginative and the solutions take full advantage of the latest revisions in the Maple 8 computer algebra system so that few problems can be solved using earlier Maple releases.