Elementary Lie Group Analysis and Ordinary Differential Equations

ISBN-13: 9780471974307 / Angielski / Twarda / 1999 / 368 str.

Nail H. Ibragimov; N. Kh Ibragimov;Ibragimov

Opis

Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lies striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail.

• This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory
• Includes a concise and self contained introduction to differential equations
• Easy to follow and comprehensive introduction to Lie group analysis
• The methods described in this book have many applications

The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems.

Recenzje

" this is the first self–contained university text on ordinary differential equations " (Zentralblatt Math, Vol.1047, No.22, 2004)

Spis treści

Introduction to Differential Equations.

Transformation Groups.

Lie Group Analysis of Ordinary Differential Equations.

Brief on Lie Algebras.

First Order Differential Equations.

Integration of Second Order Equations.

Basic Theory of Linear Equations.

Nonlinear Second Order Equations.

Integration of Third Order Equations.

Nonlinear Superposition Principle.

Index.