Transformation groups and lie algebras / Nail H. Ibragimov.

Format:

Book

Author/Creator:

Ibragimov, N. Kh. (Nailʹ Khaĭrullovich), author.

Language:

English

Subjects (All):

Lie algebras.

Transformation groups.

Physical Description:

1 online resource (197 p.)

Place of Publication:

Beijing, China : Higher Education Press, 2013.

Summary:

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 the book provide universal and effective method for solving nonlinear differential equations analytically. Introduction to approximate transformation groups also contained in the book helps to develop skills in constructing approximate solutions for differential equations with a small parameter. Read

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed November 22, 2016).

ISBN:

7-89423-644-6