现代数学物理教程

出版时间:2011-6  出版社:世界图书出版公司  作者:斯泽克雷斯 编  页数:600  
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内容概要

  本书是一部学习数学物理入门书籍,也是一部教程,让读者在物理的背景下建立现代数学概念,重点强调微分几何。写作风格上保持了作者一贯的特点,清晰,透彻,引人入胜。大量的练习和例子是本书的一大亮点,扩展索引对初学者也是十分有用。内容涵盖了张量代数,微分几何,拓扑,李群和李代数,分布理论,基础分析和希尔伯特空间。目次:几何与结构;群;向量空间;线性算子和矩阵;内积空间;代数;张量;外代数;狭义相对论;拓扑学;测度论和积分;分布;希尔伯特空间;量子力学;微分几何;微分形式;流形上的积分;联络和曲率;李群和李代数。
  读者对象:数学、物理专业的本科生,研究生和相关的科研人员。

作者简介

编者:(澳大利亚)斯泽克雷斯 (Peter Szekeres)

书籍目录

acknowledgements
1 sets and structures
 1.1 sets and logic
 1.2 subsets, unions and intersections of sets
 1.3 cartesian products and relations
 1.4 mappings
 1.5 infinite sets
 1.6 structures
 1.7 category theory
2 groups
 2.1 elements of group theory
 2.2 transformation and permutation groups
 2.3 matrix groups
 2.4 homomorphisms and isomorphisms
 2.5 normal subgroups and factor groups
 2.6 group actions
 2.7 symmetry groups
3 vector spaces
 3.1 rings and fields
 3.2 vector spaces
 3.3 vector space homomorphisms
 3.4 vector subspaces and quotient spaces
 3.5 bases ofavector space
 3.6 summation convention and transformation of bases
 3.7 dual spaces
4 linear operators and matrices
 4.1 eigenspaces and characteristic equations
 4.2 jordan canonical form
 4.3 linear ordinary differential equations
 4.4 introduction to group representation theory
5 inner product spaces
 5.1 real inner product spaces
 5.2 complex inner product spaces
 5.3 representations of finite groups
6 algebras
 6.1 algebras and ideals
 6.2 complex numbers and complex structures
 6.3 quaternions and clifford algebras
 6.4 grassmann algebras
 6.5 lie algebras and lie groups
7 tensors
 7.1 free vector spaces and tensor spaces
 7.2 multilinear maps and tensors
 7.3 basis representation of tensors
 7.4 operations on tensors
8 exterior algebra
 8.1 r-vectors and r-forms
 8.2 basis representation of r-vectors
 8.3 exterior product
 8.4 interior product
 8.5 oriented vector spaces
 8.6 the hodge dual
9 special relativity
 9.1 minkowski space-time
 9.2 relativistic kinematics
 9.3 particle dynamics
 9.4 electrodynamics
 9.5 conservation laws and energy-stress tensors
10 topology
 10.1 euclidean topology
 10.2 general topological spaces
 10.3 metric spaces
 10.4 induced topologies
 10.5 hausdorff spaces
 10.6 compact spaces
 10.7 connected spaces
 10.8 topological groups
 10.9 topological vector spaces
11 measure theory and integration
 11.1 measurable spaces and functions
 11.2 measure spaces
 11.3 lebesgue integration
12 distributions
 12.1 test functions and distributions
 12.2 operations on distributions
 12.3 fourier transforms
 12.4 green's functions
13 hilbert spaces
 13.1 definitions and examples
 13.2 expansion theorems
 13.3 linear functionals
 13.4 bounded linear operators
 13.5 spectral theory
 13.6 unbounded operators
14 quantum mechanics
 14.1 basic concepts
 14.2 quantum dynamics
 14.3 symmetry transformations
 14.4 quantum statistical mechanics
15 differential geometry
 15.1 differentiable manifolds
 15.2 differentiable maps and curves
 15.3 tangent, cotangent and tensor spaces
 15.4 tangent map and submanifolds
 15.5 commutators, flows and lie derivatives
 15.6 distributions and frobenius theorem
16 differentiable forms
 16.1 differential forms and exterior derivative
 16.2 properties of exterior derivative
 16.3 frobenius theorem: dual form
 16.4 thermodynamics
 16.5 classical mechanics
17 integration on manifolds
 17.1 partitions of unity
 17.2 integration of n-forms
 17.3 stokes' theorem
 17.4 homology and cohomology
 17.5 the poincare lemma
18 connections and curvature
 18.1 linear connections and geodesics
 18.2 covariant derivative of tensor fields
 18.3 curvature and torsion
 18.4 pseudo-riemannian manifolds
 18.5 equation of geodesic deviation
 18.6 the riemann tensor and its symmetries
 18.7 caftan formalism
 18.8 general relativity
 18.9 cosmology
 18.10 variation principles in space-time
19 lie groups and lie algebras
 19.1 lie groups
 19.2 the exponential map
 19.3 lie subgroups
 19.4 lie groups of transformations
 19.5 groups of isometrics
bibliography
index

章节摘录

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用户评论 (总计6条)

 
 

  •   这是影印本,印刷质量还不错。是一部学习数学物理入门书籍,也是一部教程,适合老师和学生看
  •   相对这么大的体积来说,其实内容不是很多...
  •   后面就像仍在水泥地面上摩擦过一样,脏脏的,一本好书瞬间被搞得没有看的欲望!
  •   介绍了群论,微分几何,测度论等很现代的数学工具,很适合从事理论物理和数学物理方面的同学看,是很好的Arfken的后继数目。
  •   教材内容很全,印刷质量基本看不出是影印,很真,不错
  •   只是大体浏览了下,感觉内容和Hassini差不多。就是叙述更简练了些。作为入门教材还行吧。。。
 

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