内容简介
This book is devoted to explaining a wide range of applications of continuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems.
目录
Preface to First Edition
Preface to Second Edition
Acknowledgments
Introduction
Notes to the Reader
CHAPTER 1 Introduction to Lie Groups
1.1 Manifolds
Change ofCoordinates
Maps Between Manifolds
The Maximal Rank Condition
Submanifolds
Reaular Submanifolds
Implicit Submanifolds
Curves and Connectedness
1.2 Lie Groups
Lie Subgroups
Local Lie Groups
Local Transformation Groups
Orbits
1.3. Vector Fields
Flows
Action on Functions
Differentials
Lie Brackets
Tangent Spaces and Vectors Fields on Submanifolds
Frobenius' Theorem
1.4 LieAlgebras
One-Parameter Subgroups
Subalgebras
The Exponential Map
Lie Algebras of Local Lie Groups
Structure Constants
Commutator Tables
Infinitesimal Group Actions
1.5. Differential Forms
PuIl-Back and Change ofCoordinates
Interior Products
The Differential
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