Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. Group-Theoretic Methods in Mechanics and Applied Mathematics systematizes the group analysis of the main postulates of classical and relativistic mechanics. Exact solutions are given for the following equations: dynamics of rigid body, heat transfer, wave, hydrodynamics, Thomas-Fermi, and more. The author pays particular attention to the application of group analysis to developing asymptotic methods for problems with small parameters. This book is designed for a broad audience of scientists, engineers, and students in the fields of applied mathematics, mechanics and physics.

chapter Chapter 1|45 pages

Basic Notions of Lie Group Theory

chapter Chapter 3|59 pages

Application of Group Methods to Problems of Mechanics

chapter Chapter 4|26 pages

Finite-Dimensional Hamiltonian Systems

chapter Chapter 5|67 pages

Asymptotic Methods of Applied Mathematics