Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Each solution of a system of differential equations corresponds to a particular process. Therefore, methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations. The emphasis is on the methods of differential constraints, degenerate hodograph and group analysis. These methods have become a necessary part of applied mathematics and mathematical physics. The book is primarily designed to present both fundamental theoretical and algorithmic aspects of these methods. The description of algorithms contains illustrative examples which are typically taken from continuum mechanics. Some sections of the book introduce new applications and extensions of these methods, such as integro-differential and functional differential equations, a new area of group analysis.

Emphasis is on applications with numerous worked examples to illustrate basic concepts

Equations with One Dependent Function.- Systems of Equations.- Method of the Degenerate Hodograph.- Method of Differential Constraints.- Invariant and Partially Invariant Solutions.- Symmetries of Equations with Nonlocal Operators.- Symbolic Computer Calculations.