Computer Algebra Recipes for Mathematical Physics - Enns, Richard H.; SpringerLink (Online service) (Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2005)
Over two hundred novel and innovative computer algebra worksheets or "recipes" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn. Key features: * Uses the MAPLE computer algebra system to allow the reader to easily and quickly change the mathematical models and the parameters and then generate new answers * No prior knowledge of MAPLE is assumed; the relevant MAPLE commands are introduced on a need-to-know basis * All MAPLE commands are indexed for easy reference * A classroom-tested story/anecdote format is used, accompanied with amusing or thought-provoking quotations This is a self-contained and standalone text, similar in style and format to Computer Algebra Recipes: A Gourmet's Guide to Mathematical Models of Science (ISBN 0-387-95148-2), Springer New York 2001 and Computer Algebra Recipes for Classical Mechanics (ISBN 0-8176-4291-9), Birkhäuser 2003. Computer Algebra Recipes for Mathematical Physics may be used in the classroom, for self-study, as a reference, or as a text for an online course.
The Appetizers -- Linear ODEs of Physics -- Applications of Series -- Vectors and Matrices -- The Entrees -- Linear PDEs of Physics -- Complex Variables -- Integral Transforms -- Calculus of Variations -- The Desserts -- NLODEs & PDEs of Physics -- Numerical Methods.
Keywords: Mathematical physics; Physics; Computer software; Applied mathematics; Engineering mathematics; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematical Software; Applications of Mathematics; Mathematical and Computational Engineering; Numerical and Computational Physics, Simulation