Transformation Groups and Lie Algebras.
This book is based on the extensive experience of teaching for mathematics, physics and engineering students in Russia, USA, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics. The methods of local Lie groups discussed in t...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
BeiJing :
Higher Education Press Limited Company,
2013.
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| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- Part I Local Transformation Groups; Chapter 1 Preliminaries; 1.1 Changes of frames of reference and point transformations; 1.2 Introduction of transformation groups; 1.3 Some useful groups; Exercises to Chapter 1; Chapter 2 One-parameter groups and their invariants; 2.1 Local groups of transformations; 2.2 Invariants; 2.3 Invariant equations; Exercises to Chapter 2; Chapter 3 Groups admitted by differential equations; 3.1 Preliminaries; 3.2 Prolongation of group transformations; 3.3 Prolongation of group generators; 3.4 First definition of symmetry groups.
- 3.5 Second definition of symmetry groupsExercises to Chapter 3; Chapter 4 Lie algebras of operators; 4.1 Basic definitions; 4.2 Basic properties; 4.3 Isomorphism and similarity; 4.4 Low-dimensional Lie algebras; 4.5 Lie algebras and multi-parameter groups; Exercises to Chapter 4; Chapter 5 Galois groups via symmetries; 5.1 Preliminaries; 5.2 Symmetries of algebraic equations; 5.3 Construction of Galois groups; Assignment to Part I; Part II Approximate Transformation Groups; 36741-00_chapter06; Chapter 6 Preliminaries; 6.1 Motivation; 6.2 A sketch on Lie transformation groups.
- 6.3 Approximate Cauchy problemChapter 7 Approximate transformations; 7.1 Approximate transformations defined; 7.2 Approximate one-parameter groups; 7.3 Infinitesimal description; Exercises to Chapter 7; Chapter 8 Approximate symmetries; 8.1 Definition of approximate symmetries; 8.2 Calculation of approximate symmetries; 8.3 Examples; Exercises to Chapter 8; Chapter 9 Applications; 9.1 Integration of equations with a small parameter usingapproximate symmetries; 9.2 Approximately invariant solutions; 9.3 Approximate conservation laws; Assignment to Part II; Bibliography; Index.
