Solution of Ordinary Differential Equations by Continuous Groups / Edition 1

by George Emanuel

Overview

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.

Product Details

ISBN-13:	9780367397876
Publisher:	Taylor & Francis
Publication date:	09/19/2019
Pages:	232
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Emanuel, George

Table of Contents

Preface v

I Background 1

1 Introduction 3

2 Continuous One-Parameter Groups-I 7

2.1 Group Concept 7

2.2 Infinitesimal Transformation 10

2.3 Global Group Equations 13

2.4 Problems 17

3 Method of Characteristics 19

3.1 Theory 19

3.2 Examples 22

3.3 Problems 25

4 Continuous One-Parameter Groups-II 27

4.1 Invariance 27

4.2 The Once-Extended Group 33

4.3 Higher-Order Extended Groups 34

4.4 Problems 35

II Ordinary Differential Equations 37

5 First-Order ODEs 39

5.1 Invariance Under a One-Parameter Group 40

5.2 Canonical Coordinates 48

5.3 Special Procedures 53

5.4 Compendium 65

5.5 Examples 69

5.6 Problems 77

6 Higher-Order ODEs 81

6.1 Invariant Equations 82

6.2 Finding the Groups 88

6.3 System of First-Order ODEs 90

6.4 Compendium 94

6.5 Examples 95

6.6 Problems 105

7 Second-Order ODEs 109

7.1 Classification of Two-Parameter Groups 109

7.2 Invariance and Canonical Coordinates 113

7.3 Compendium 122

7.4 Examples 132

7.5 Problems 140

III Appendices 143

A Bibliography and References 145

B The Rotation Group 147

C Basic Relations 149

D Tables 153

E Answers to Selected Problems 213

Editorial Reviews

Focusing on practice, this book explores the application of Lies groups to solving ordinary differential equations (ODEs). Although the mathematical proofs and derivations are de-emphasized in favor of problem solving, the conceptual basis of continuous groups is retained and related to the theory of problems in engineering and the sciences. New techniques are featured, including the enlargement procedure. The book offers a self-contained treatment that presumes only a rudimentary exposure to ordinary differential equations. Emanuel teaches mathematics and aerospace engineering at the University of Texas, Arlington. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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