现代数学物理教程

图书标准信息

• 作者 斯泽克雷斯（Peter Szekeres） 编
• 出版社 世界图书出版公司
• 出版时间 2011-06
• 版次 1
• ISBN 9787510035098
• 定价 99.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 600页
• 正文语种 英语

【内容简介】

《现代数学物理教程》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《现代数学物理教程》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。

【目录】

acknowledgements
1setsandstructures
1.1setsandlogic
1.2subsets,unionsandintersectionsofsets
1.3cartesianproductsandrelations
1.4mappings
1.5infinitesets
1.6structures
1.7categorytheory

2groups
2.1elementsofgrouptheory
2.2transformationandpermutationgroups
2.3matrixgroups
2.4homomorphismsandisomorphisms
2.5normalsubgroupsandfactorgroups
2.6groupactions
2.7symmetrygroups

3vectorspaces
3.1ringsandfields
3.2vectorspaces
3.3vectorspacehomomorphisms
3.4vectorsubspacesandquotientspaces
3.5basesofavectorspace
3.6summationconventionandtransformationofbases
3.7dualspaces

4linearoperatorsandmatrices
4.1eigenspacesandcharacteristicequations
4.2jordancanonicalform
4.3linearordinarydifferentialequations
4.4introductiontogrouprepresentationtheory

5innerproductspaces
5.1realinnerproductspaces
5.2complexinnerproductspaces
5.3representationsoffinitegroups

6algebras
6.1algebrasandideals
6.2complexnumbersandcomplexstructures
6.3quaternionsandcliffordalgebras
6.4grassmannalgebras
6.5liealgebrasandliegroups

7tensors
7.1freevectorspacesandtensorspaces
7.2multilinearmapsandtensors
7.3basisrepresentationoftensors
7.4operationsontensors

8exterioralgebra
8.1r-vectorsandr-forms
8.2basisrepresentationofr-vectors
8.3exteriorproduct
8.4interiorproduct
8.5orientedvectorspaces
8.6thehodgedual

9specialrelativity
9.1minkowskispace-time
9.2relativistickinematics
9.3particledynamics
9.4electrodynamics
9.5conservationlawsandenergy-stresstensors

10topology
10.1euclideantopology
10.2generaltopologicalspaces
10.3metricspaces
10.4inducedtopologies
10.5hausdorffspaces
10.6compactspaces
10.7connectedspaces
10.8topologicalgroups
10.9topologicalvectorspaces

11measuretheoryandintegration
11.1measurablespacesandfunctions
11.2measurespaces
11.3lebesgueintegration

12distributions
12.1testfunctionsanddistributions
12.2operationsondistributions
12.3fouriertransforms
12.4green'sfunctions

13hilbertspaces
13.1definitionsandexamples
13.2expansiontheorems
13.3linearfunctionals
13.4boundedlinearoperators
13.5spectraltheory
13.6unboundedoperators

14quantummechanics
14.1basicconcepts
14.2quantumdynamics
14.3symmetrytransformations
14.4quantumstatisticalmechanics

15differentialgeometry
15.1differentiablemanifolds
15.2differentiablemapsandcurves
15.3tangent,cotangentandtensorspaces
15.4tangentmapandsubmanifolds
15.5commutators,flowsandliederivatives
15.6distributionsandfrobeniustheorem

16differentiableforms
16.1differentialformsandexteriorderivative
16.2propertiesofexteriorderivative
16.3frobeniustheorem:dualform
16.4thermodynamics
16.5classicalmechanics

17integrationonmanifolds
17.1partitionsofunity
17.2integrationofn-forms
17.3stokes'theorem
17.4homologyandcohomology
17.5thepoincarelemma

18connectionsandcurvature
18.1linearconnectionsandgeodesics
18.2covariantderivativeoftensorfields
18.3curvatureandtorsion
18.4pseudo-riemannianmanifolds
18.5equationofgeodesicdeviation
18.6theriemanntensoranditssymmetries
18.7caftanformalism
18.8generalrelativity
18.9cosmology
18.10variationprinciplesinspace-time

19liegroupsandliealgebras
19.1liegroups
19.2theexponentialmap
19.3liesubgroups
19.4liegroupsoftransformations
19.5groupsofisometrics
bibliography
index