Symmetry Analysis of Differential Equations: An Introduction (Synthesis Lectures on Mathematics & Statistics)

This Second Edition presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs).Providing comprehensive coverage, the book fills a gap in the literature by discussing elementary symmetry concepts and invariance, including methods for reducing the complexity of ODEs and PDEs in an effort to solve the associated problems.The author presents thoroughly class-tested classical methods in a systematic, logical, and well-balanced manner.As the book progresses, the chapters graduate from elementary symmetries and the invariance of algebraic equations, to ODEs and PDEs, followed by coverage of the nonclassical method and compatibility.This new edition features coverage on equations with multiple symmetries (inherited symmetries), contact symmetries, and second order equations vs. equivalent systems.