Symmetry Analysis Of Differential Equations: An Introduction

Symmetry analysis has played a crucial role in the construction of exact solutions to differential equations. In fact, all the standard techniques for solving first order ordinary differential equations (ODEs) can be explained by symmetry analysis. The usefulness of symmetry analysis is readily evident, and the beauty of the method is that it is both fairly easy to learn and is very algorithmic, making it amenable to a variety of computer algebra packages such as Maple? or MathematicaR.Symmetry Analysis of Differential Equations: An Introductionfills a gap in the literature by providing introductory coverage of both ODEs and partial differential equations (PDEs), explores select advanced topics, and contains platiful problems with complete solutions. Chapter coverages includes: ordinary differential equations with Lie's invariance condition, standard integration techniques, infinitesimal operator and higher order equations, second order questions, and ODE systems; partial differential equations with first and second order equations, systems of PDEs, higher dimensional PDEs, and nonclassical symmetries; and compatibility with nonclassical symmetry analysis and first order compatibility.

DANIEL J. ARRIGO, PhD, is Professor in the Department of Mathematics at the University of Central Arkansas. The author of over 30 journal articles, his research interests include the construction of exact solutions of PDEs; symmetry analysis of nonlinear PDEs; and solutions to physically important equations, such as nonlinear heat equations and governing equations modeling of granular materials and nonlinear elasticity. In 2008, Dr. Arrigo received the Oklahoma-Arkansas Section of the Mathematical Association of America’s Award for Distinguished Teaching of College or University Mathematics.