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变换群和李代数(英文版) (Transformation Groups and
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商品名称:变换群和李代数(英文版) (Transformation Groups and
物料号 :36741-00
重量:0.000千克
ISBN:9787040367416
出版社:高等教育出版社
出版年月:2013-03
作者:Nail Ibragimov
定价:59.00
页码:185
装帧:精装
版次:1
字数:210
开本:16开
套装书:否

本书与新加坡世界科技出版社合作出版。 本书为作者在俄罗斯、美国、南非和瑞典多年讲述变换群和李群分析课程的讲义。书中所讨论的局部李群方法提供了求解非线性微分方程解析解通用且非常有效的方法,而近似变换群可以提高构造含少量参数的微分方程的技巧。本书通俗易懂、叙述清晰,并提供丰富的模型,能帮助读者轻松地逐步深入各种主题。

Front Matter
Part I Local Transformation Groups
1 Preliminaries
  1.1 Changes of frames of reference and point transformations
   1.1.1 Translations
   1.1.2 Rotations
   1.1.3 Galilean transformation
  1.2 Introduction of transformation groups
   1.2.1 Definitions and examples
   1.2.2 Different types of groups
  1.3 Some useful groups
   1.3.1 Finite continuous groups on the straight line
   1.3.2 Groups on the plane
   1.3.3 Groups in IRn
  Exercises to Chapter 1
2 One-parameter groups and their invariants
  2.1 Local groups of transformations
   2.1.1 Notation and definition
   2.1.2 Groups written in a canonical parameter
   2.1.3 Infinitesimal transformations and generators
   2.1.4 Lie equations
   2.1.5 Exponential map
   2.1.6 Determination of a canonical parameter
  2.2 Invariants .
   2.2.1 Definition and infinitesimal test
   2.2.2 Canonical variables
   2.2.3 Construction of groups using canonical variables
   2.2.4 Frequently used groups in the plane
  2.3 Invariant equations
   2.3.1 Definition and infinitesimal test
   2.3.2 Invariant representation of invariant manifolds
   2.3.3 Proof of Theorem 2.9
   2.3.4 Examples on Theorem 2.9
  Exercises to Chapter 2
3 Groups admitted by differential equations
  3.1 Preliminaries
   3.1.1 Differential variables and functions
   3.1.2 Point transformations
   3.1.3 Frame of differential equations
  3.2 Prolongation of group transformations
   3.2.1 One-dimensional case
   3.2.2 Prolongation with several differential variables
   3.2.3 General case
  3.3 Prolongation of group generators
   3.3.1 One-dimensional case
   3.3.2 Several differential variables
   3.3.3 General case
  3.4 First definition of symmetry groups
   3.4.1 Definition
   3.4.2 Examples
  3.5 Second definition of symmetry groups
   3.5.1 Definition and determining equations
   3.5.2 Determining equation for second-order ODEs
   3.5.3 Examples on solution of determining equations
  Exercises to Chapter 3
4 Lie algebras of operators
  4.1 Basic definitions
   4.1.1 Commutator
   4.1.2 Properties of the commutator
   4.1.3 Properties of determining equations
   4.1.4 Lie algebras
  4.2 Basic properties
   4.2.1 Notation
   4.2.2 Subalgebra and ideal
   4.2.3 Derived algebras
   4.2.4 Solvable Lie algebras
  4.3 Isomorphism and similarity
   4.3.1 Isomorphic Lie algebras
   4.3.2 Similar Lie algebras
  4.4 Low-dimensional Lie algebras
   4.4.1 One-dimensional algebras
   4.4.2 Two-dimensional algebras in the plane
   4.4.3 Three-dimensional algebras in the plane
   4.4.4 Three-dimensional algebras in IR3
  4.5 Lie algebras and multi-parameter groups
   4.5.1 Definition of multi-parameter groups
   4.5.2 Construction of multi-parameter groups
  Exercises to Chapter 4
5 Galois groups via symmetries
  5.1 Preliminaries
  5.2 Symmetries of algebraic equations
   5.2.1 Determining equation
   5.2.2 First example
   5.2.3 Second example
   5.2.4 Third example
  5.3 Construction of Galois groups
   5.3.1 First example
   5.3.2 Second example
   5.3.3 Third example
   5.3.4 Concluding remarks
Assignment to Part I
Part II Approximate Transformation Groups
6 Preliminaries
  6.1 Motivation
  6.2 A sketch on Lie transformation groups
   6.2.1 One-parameter transformation groups
   6.2.2 Canonical parameter
   6.2.3 Group generator and Lie equations
   6.2.4 Exponential map
  6.3 Approximate Cauchy problem
   6.3.1 Notation
   6.3.2 Definition of the approximate Cauchy problem
7 Approximate transformations
  7.1 Approximate transformations defined
  7.2 Approximate one-parameter groups
   7.2.1 Introductory remark
   7.2.2 Definition of one-parameter approximate transformation groups
   7.2.3 Generator of approximate transformation group
  7.3 Infinitesimal description
   7.3.1 Approximate Lie equations
   7.3.2 Approximate exponential map
  Exercises to Chapter 7
8 Approximate symmetries
  8.1 Definition of approximate symmetries
  8.2 Calculation of approximate symmetries
   8.2.1 Determining equations
   8.2.2 Stable symmetries
   8.2.3 Algorithm for calculation
  8.3 Examples .
   8.3.1 First example
   8.3.2 Approximate commutator and Lie algebras
   8.3.3 Second example
   8.3.4 Third example
  Exercises to Chapter 8
9 Applications
  9.1 Integration of equations with a small parameter using approximate symmetries
   9.1.1 Equation having no exact point symmetries
   9.1.2 Utilization of stable symmetries
  9.2 Approximately invariant solutions
   9.2.1 Nonlinear wave equation
   9.2.2 Approximate travelling waves of KdV equation
  9.3 Approximate conservation laws
  Exercises to Chapter 9
Assignment to Part II
Bibliography
Index

非线性物理科学系列NPS

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