Algorithmic Lie Theory for Solving Ordinary Differential Eqautions

Thanks to advancements in computer algebra programs, the massive number of calculations necessary to work through nonlinear ordinary differential equations through the systematic method developed by Sophus Lie is no longer an impediment. Schwarz (mathematics, Fraunhofer Institute) gives students and researchers a solid survey of the mathematical foundations along with advice on using of software systems designed to aid in solving concrete algebraic problems as he works through linear differential equations, Lie transformation groups, equivalence and invariants of differential equations, symmetries of differential equations, transformation to canonical form, and solution algorithms. He provides several interesting appendices (including those covering Loewy decompositions of Kamke's collection and symmetries of Kamke's collection) and a range of useful formulas. Thanks to the large number of exercises (with answers for selected problems), this works as both a classroom text and a self-study guide. Annotation c2008 Book News, Inc., Portland, OR (booknews.com)