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L. Dresner, "Applications of Lie's Theory of Ordinary and Partial Differential Equations"

Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.

Review

This book gives a simple and direct introduction to the powerful methods of Lie for the solution of ordinary and partial differential equations. The author focuses on a small number of central topics and treats each one in an informal and leisurely manner. The topics covered include: one-parameter transformation groups; Lie's integrating factor for first-order ODE; reduction of second order ODE by one- and two-parameter groups; Noether's theorem; similarity and traveling wave solutions to PDE; and approximate methods. Each chapter contains an excellent selection of problems whose solutions are provided.

Ian Anderson (1-UTS; Logan, UT) -- Mathematical Reviews, Issue 2000e

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