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Transformation groups and Lie algebras / (Record no. 415222)

000 -LEADER
fixed length control field 06213cam a22002415i 4500
001 - CONTROL NUMBER
control field 17871571
003 - CONTROL NUMBER IDENTIFIER
control field ISI Library, Kolkata
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20141216161151.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 130830s2013 si a b 001 0 eng
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9789814460842 (hardback)
040 ## - CATALOGING SOURCE
Original cataloging agency ISI Library
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Edition number 23
Item number Ib14
Classification number 512.55
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Ibragimov, Nail H.
245 10 - TITLE STATEMENT
Title Transformation groups and Lie algebras /
Statement of responsibility, etc Nail H Ibragimov.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc Singapore :
Name of publisher, distributor, etc World Scientific,
Date of publication, distribution, etc c2013.
300 ## - PHYSICAL DESCRIPTION
Extent x, 185 p. :
Other physical details illustrations ;
Dimensions 25 cm.
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references (pages 181-182) and index.
505 ## - FORMATTED CONTENTS NOTE
Formatted contents note Machine generated contents note: pt. I Local Transformation Groups --<br/> 1. Preliminaries --<br/> 1.1. Changes of frames of reference and point transformations --<br/> 1.1.1. Translations --<br/> 1.1.2. Rotations --<br/> 1.1.3. Galilean transformation --<br/> 1.2. Introduction of transformation groups --<br/> 1.2.1. Definitions and examples --<br/> 1.2.2. Different types of groups --<br/> 1.3. Some useful groups --<br/> 1.3.1. Finite continuous groups on the straight line --<br/> 1.3.2. Groups on the plane --<br/> 1.3.3. Groups in IRn --<br/> Exercises to Chapter 1 --<br/> 2. One-parameter groups and their invariants --<br/> 2.1. Local groups of transformations --<br/> 2.1.1. Notation and definition --<br/> 2.1.2. Groups written in a canonical parameter --<br/> 2.1.3. Infinitesimal transformations and generators --<br/> 2.1.4. Lie equations --<br/> 2.1.5. Exponential map --<br/> 2.1.6. Determination of a canonical parameter --<br/> 2.2. Invariants --<br/> 2.2.1. Definition and infinitesimal test --<br/> 2.2.2. Canonical variables 2.2.3. Construction of groups using canonical variables --<br/> 2.2.4. Frequently used groups in the plane --<br/> 2.3. Invariant equations --<br/> 2.3.1. Definition and infinitesimal test --<br/> 2.3.2. Invariant representation of invariant manifolds --<br/> 2.3.3. Proof of Theorem 2.9 --<br/> 2.3.4. Examples on Theorem 2.9 --<br/> Exercises to Chapter 2 --<br/> 3. Groups admitted by differential equations --<br/> 3.1. Preliminaries --<br/> 3.1.1. Differential variables and functions --<br/> 3.1.2. Point transformations --<br/> 3.1.3. Frame of differential equations --<br/> 3.2. Prolongation of group transformations --<br/> 3.2.1. One-dimensional case --<br/> 3.2.2. Prolongation with several differential variables --<br/> 3.2.3. General case --<br/> 3.3. Prolongation of group generators --<br/> 3.3.1. One-dimensional case --<br/> 3.3.2. Several differential variables --<br/> 3.3.3. General case --<br/> 3.4. First definition of symmetry groups --<br/> 3.4.1. Definition --<br/> 3.4.2. Examples --<br/> 3.5. Second definition of symmetry groups --<br/> 3.5.1. Definition and determining equations 3.5.2. Determining equation for second-order ODEs --<br/> 3.5.3. Examples on solution of determining equations --<br/> Exercises to Chapter 3 --<br/> 4. Lie algebras of operators --<br/> 4.1. Basic definitions --<br/> 4.1.1. Commutator --<br/> 4.1.2. Properties of the commutator --<br/> 4.1.3. Properties of determining equations --<br/> 4.1.4. Lie algebras --<br/> 4.2. Basic properties --<br/> 4.2.1. Notation --<br/> 4.2.2. Subalgebra and ideal --<br/> 4.2.3. Derived algebras --<br/> 4.2.4. Solvable Lie algebras --<br/> 4.3. Isomorphism and similarity --<br/> 4.3.1. Isomorphic Lie algebras --<br/> 4.3.2. Similar Lie algebras --<br/> 4.4. Low-dimensional Lie algebras --<br/> 4.4.1. One-dimensional algebras --<br/> 4.4.2. Two-dimensional algebras in the plane --<br/> 4.4.3. Three-dimensional algebras in the plane --<br/> 4.4.4. Three-dimensional algebras in IR3 --<br/> 4.5. Lie algebras and multi-parameter groups --<br/> 4.5.1. Definition of multi-parameter groups' --<br/> 4.5.2. Construction of multi-parameter groups --<br/> Exercises to Chapter 4 --<br/> 5. Galois groups via symmetries 5.1. Preliminaries --<br/> 5.2. Symmetries of algebraic equations --<br/> 5.2.1. Determining equation --<br/> 5.2.2. First example --<br/> 5.2.3. Second example --<br/> 5.2.4. Third example --<br/> 5.3. Construction of Galois groups --<br/> 5.3.1. First example --<br/> 5.3.2. Second example --<br/> 5.3.3. Third example --<br/> 5.3.4. Concluding remarks --<br/> Assignment to Part 1 --<br/> pt. II Approximate Transformation Groups --<br/> 6. Preliminaries --<br/> 6.1. Motivation --<br/> 6.2. A sketch on Lie transformation groups --<br/> 6.2.1. One-parameter transformation groups --<br/> 6.2.2. Canonical parameter --<br/> 6.2.3. Group generator and Lie equations --<br/> 6.2.4. Exponential map --<br/> 6.3. Approximate Cauchy problem --<br/> 6.3.1. Notation --<br/> 6.3.2. Definition of the approximate Cauchy problem --<br/> 7. Approximate transformations --<br/> 7.1. Approximate transformations defined --<br/> 7.2. Approximate one-parameter groups --<br/> 7.2.1. Introductory remark --<br/> 7.2.2. Definition of one-parameter approximate transformation groups --<br/> 7.2.3. Generator of approximate transformation group 7.3. Infinitesimal description --<br/> 7.3.1. Approximate Lie equations --<br/> 7.3.2. Approximate exponential map --<br/> Exercises to Chapter 7 --<br/> 8. Approximate symmetries --<br/> 8.1. Definition of approximate symmetries --<br/> 8.2. Calculation of approximate symmetries --<br/> 8.2.1. Determining equations --<br/> 8.2.2. Stable symmetries --<br/> 8.2.3. Algorithm for calculation --<br/> 8.3. Examples --<br/> 8.3.1. First example --<br/> 8.3.2. Approximate commutator and Lie algebras --<br/> 8.3.3. Second example --<br/> 8.3.4. Third example --<br/> Exercises to Chapter 8 --<br/> 9. Applications --<br/> 9.1. Integration of equations with a small parameter using approximate symmetries --<br/> 9.1.1. Equation haying no exact point symmetries --<br/> 9.1.2. Utilization of stable symmetries --<br/> 9.2. Approximately invariant solutions --<br/> 9.2.1. Nonlinear wave equation --<br/> 9.2.2. Approximate travelling waves of KdV equation --<br/> 9.3. Approximate conservation laws --<br/> Exercises to Chapter 9 --<br/> Assignment to Part II.
520 ## - SUMMARY, ETC.
Summary, etc Part I of these book introduces the reader to the basic concepts of the classical theory of local transformation groups and their Lie algebras. It has been designed for the graduate course on Transformation groups and Lie algebras. <br/>Part II of these book provides an easy to follow introduction to the new topic. It is based on talks about various conferences, in particular on the plenary lecture at the International Workshop.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Transformation groups.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Lie algebras.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Koha item type Books
Holdings
Lost status Not for loan Permanent Location Current Location Date acquired Cost, normal purchase price Full call number Accession Number Koha item type
    ISI Library, Kolkata ISI Library, Kolkata 2014-09-15 2482.75 512.55 Ib14 135300 Books
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