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.

Daniel J. Arrigo, Ph.D., is a Professor in the Department of Mathematics at the University of Central Arkansas. The author of over 35 journal articles and three published books, 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.  In 2006, he was awarded his University’s Research, Scholarship, and Creativity award, and in 2019, the University’s Teaching Excellence award.