# Solution of Ordinary Differential Equations by Continuous Groups

## 1st Edition

Chapman and Hall/CRC

232 pages | 4 B/W Illus.

Hardback: 9781584882435
pub: 2000-11-29
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### Description

Written by an engineer and sharply focused on practical matters, this text explores the application of Lie groups to solving ordinary differential equations (ODEs). Although the mathematical proofs and derivations in are de-emphasized in favor of problem solving, the author retains the conceptual basis of continuous groups and relates the theory to problems in engineering and the sciences.

The author has developed a number of new techniques that are published here for the first time, including the important and useful enlargement procedure. The author also introduces a new way of organizing tables reminiscent of that used for integral tables. These new methods and the unique organizational scheme allow a significant increase in the number of ODEs amenable to group-theory solution.

Solution of Ordinary Differential Equations by Continuous Groups offers a self-contained treatment that presumes only a rudimentary exposure to ordinary differential equations. Replete with fully worked examples, it is the ideal self-study vehicle for upper division and graduate students and professionals in applied mathematics, engineering, and the sciences.

BACKGROUND

Introduction

Continuous One-Parameter Group-I

Group Concept

Infinitesimal Transformation

Global Group Equations

Problems

Method of Characteristics

Theory

Examples

Problems

Continuous One-Parameter Group-II

Invariance

The Once-Extended Group

Higher-Order Extended Groups

Problems

ORDINARY DIFFERENTIAL EQUATIONS

First-Order ODEs

Invariance Under a One-Paramter Group

Canonical Coordinates

Special Procedures

Compendium

Examples

Problems

Higher-Order ODEs

Invariant Equations

Finding the Groups

System of First-Order ODEs

Compendium

Examples

Problems

Second-Order ODEs

Classification of Two-Parameter Groups

Invariance and Canonical Coordinates

Compendium

Examples

Problems

APPENDICES

Bibilography and References

The Rotation Group

Basic Relations

Tables'