Symmetry Analysis of Differential Equations: An Introduction

286 Pages·2015·3.7 MB·English

by  Arrigo, Daniel

Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
References
Acknowledgments
Chapter 1: An Introduction
1.1 What Is a Symmetry?
1.2 Lie Groups
1.3 Invariance of Differential Equations
1.4 Some Ordinary Differential
Equations
Chapter 2: Ordinary Differential Equations
2.1 Infinitesimal Transformations
2.2 Lie's Invariance Condition
2.3 Standard Integration Techniques
2.4 Infinitesimal Operator and Higher
Order Equations
2.5 Second-Order Equations
Exercises
2.6 Higher Order Equations
2.7 ODE Systems
Chapter 3: Partial Differential Equations
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3.1 First-Order Equations
3.2 Second-Order PDEs
3.3 Higher Order PDEs
3.4 Systems of PDEs
3.5 Higher Dimensional PDEs
Chapter 4: Nonclassical Symmetries and
Compatibility
4.1 Nonclassical Symmetries
4.2 Nonclassical Symmetry Analysis and
Compatibility
4.3 Beyond Symmetries
Analysis—General Compatibility
4.4 Concluding Remarks
Solutions
Section 1.5
Section 2.2.1
Section 2.3.6
Section 2.5.1
Section 2.6.1
Section 2.7.3
Section 3.1.4
Section 3.2.5
Section 3.3.1
Section 3.4.3
Section 3.5.1
Section 4.4
References
3
Index
End User License Agreement
List of Illustrations
Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 1.5
Figure 1.6
Figure 1.7
List of Tables
Table 1.1
Table 2.1
Table 3.1
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Symmetry Analysis of
Differential Equations
An Introduction
Daniel J. Arrigo
Department of Mathematics University of
Central Arkansas Conway, AR
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Library of Congress
Cataloging-in-Publication Data:
Arrigo, Daniel J. (Daniel Joseph), 1960-
Symmetry analysis of differential equations : an
introduction / Daniel J. Arrigo, Department of
Mathematics, University of Central
Arkansas, Conway, AR.
pages cm
Includes bibliographical references and index.
ISBN 978-1-118-72140-7 (cloth)
1. Lie groups–Textbooks. 2. Lie groups–Study and
teaching (Higher) 3. Lie groups–Study and teaching
(Graduate) 4. Differential
equations, Partial–Textbooks. I. Title.
7
QA387.A77 2014
515′.353–dc23
2014007305
Printed in the United States of America.
10 9 8 7 6 5 4
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To the late Bill Ames,
my teacher, my mentor, my friend.
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