变换群和李代数

本书特色

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　　《非线性物理科学：变换群和李代数（英文版）》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。《非线性物理科学：变换群和李代数（英文版）》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。

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作者简介

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　　伊布拉基莫夫（Ibragimov，N.H.）教授为瑞士科学家，被公认为是在微分方程对称分析方面世界上最具权威的专家之一。他发起并构建了现代群分析理论，并推动了该理论在多方面的应用。

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目录

prefacepart ⅰ local transformation groups1 preliminaries1.1 changes of frames of reference and point transformations1.1.1 translations1.1.2 rotations1.1.3 galilean transformation1.2 introduction of transformation groups1.2.1 definitions and examples1.2.2 different types of groups1.3 some useful groups1.3.1 finite continuous groups on the straight line1.3.2 groups on the plane1.3.3 groups in irnexercises to chapter 12 one-parameter groups and their invariants2.1 local groups of transformations2.1.1 notation and definition2.1.2 groups written in a canonical parameter2.1.3 infinitesimal transformations and generators2.1.4 lie equations2.1.5 exponential map2.1.6 determination of a canonical parameter2.2 invariants2.2.1 definition and infinitesimal test2.2.2 canonical variables2.2.3 construction of groups using canonical variables2.2.4 frequently used groups in the plane2.3 invariant equations2.3.1 definition and infinitesimal test2.3.2 invariant representation ofinvariant manifolds2.3.3 proof of theorem2.3.4 examples on theoremexercises to chapter 23 groups adnutted by differential equations3.1 preliminaries3.1.1 differential variables and functions3.1.2 point transformations3.1.3 frame of differential equations3.2 ptolongation of group transformations3.2.1 0ne-dimensional case3.2.2 prolongation with several differential variables3.2.3 general case3.3 prolongation of group generators3.3.1 0ne-dimensional case3.3.2 several differential variables3.3.3 general case3.4 first definition of symmetry groups3.4.1 definition3.4.2 examples3.5 second definition of symmetry groups3.5.1 definition and determining equations3.5.2 determining equation for second-order odes3.5.3 examples on solution of determining equationsexercises to chapter 34 lie algebras of operators4.1 basic definitions4.1.2 properties of the commutator4.1.3 properties of determining equations4.2 basic properties4.2.1 notation4.2.2 subalgebra and ideal4.2.3 derived algebras4.2.4 solvable lie algebras4.3 isomorphism and similarity4.3.1 isomorphic lie akebras4.3.2 similar lie algebras4.4 low-dimensionallie algebras4.4.1 0ne-dimensional algebras4.4.2 two-dimensional algebras in the plane4.4.3 three-dimensional algebras in the plane4.4.4 three-dimensional algebras in lr34.5 lie algebras and multi-parameter groups4.5.1 definition of multi-parameter groups4.5.2 construction of multi-parameter groups5 galois groups via symmetries5.1 preliminaries5.2 symmetries of algebraic equations5.2.1 determining equation5.2.2 first example5.2.3 second example5.2.4 third example5.3 construction of galois groups5.3.1 first example5.3.2 second example5.3.3 third example5.3.4 concluding remarksassignment to part ipart ii approximate transformation groups6.1 motivation6.2 a sketch on lie transformation groups6.2.1 0ne-parameter transformation groups6.2.2 canonical parameter6.2.3 group generator and lie equations6.3 approximate cauchy problem6.3.1 notation6.3.2 definition of the approximate cauchy problem7 approximate transformations7.1 approximate transformations defined7.2 approximate one-parameter groups7.2.1 introductory remark7.2.2 definition ofone-parameter approximate7.2.3 generator of approximate transformation group7.3 infinitesimal description7.3.1 approximate lie equations7.3.2 approximate exponential mapexercises to chapter 78 approximate symmetries8.1 definition of approximate symmetries8.2 calculation of approximate symmetries8.2.1 determining equations8.2.2 stable symmetries8.2.3 algorithm for calculation8.3.2 approximate commutator and lie algebras9.1 integration of equations with a smallparameter usingapproximatesymmetries9.1.1 equation having no exact point symmetries9.1.2 utilization of stable symmetries9.2 approximately invariant solutions9.2.1 nonlinear wave equation9.2.2 approximate travelling waves of kdv equation9.3 approximate conservation lawsexercises to chapter 9assignment to part iibibliographyindex

封面

书名:变换群和李代数

作者:伊布拉基莫夫

页数:185

定价:¥59.0

出版社:高等教育出版社

出版日期:2013-03-01

ISBN:9787040367416

PDF电子书大小:159MB 高清扫描完整版