现代数学物理教程

图书信息

分类：科学技术,自然科学,数学

作者简介

作者简介 暂缺《现代数学物理教程》作者简介

内容简介

内容简介 　　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。

目录

图书目录
acknowledgements1 sets and structures1.1 sets and logic1.2 subsets, unions and intersections of sets1.3 cartesian products and relations1.4 mappings1.5 infinite sets1.6 structures1.7 category theory2 groups2.1 elements of group theory2.2 transformation and permutation groups2.3 matrix groups2.4 homomorphisms and isomorphisms2.5 normal subgroups and factor groups2.6 group actions2.7 symmetry groups3 vector spaces3.1 rings and fields3.2 vector spaces3.3 vector space homomorphisms3.4 vector subspaces and quotient spaces3.5 bases ofavector space3.6 summation convention and transformation of bases3.7 dual spaces4 linear operators and matrices4.1 eigenspaces and characteristic equations4.2 jordan canonical form4.3 linear ordinary differential equations4.4 introduction to group representation theory5 inner product spaces5.1 real inner product spaces5.2 complex inner product spaces5.3 representations of finite groups6 algebras6.1 algebras and ideals6.2 complex numbers and complex structures6.3 quaternions and clifford algebras6.4 grassmann algebras6.5 lie algebras and lie groups7 tensors7.1 free vector spaces and tensor spaces7.2 multilinear maps and tensors7.3 basis representation of tensors7.4 operations on tensors8 exterior algebra8.1 r-vectors and r-forms8.2 basis representation of r-vectors8.3 exterior product8.4 interior product8.5 oriented vector spaces8.6 the hodge dual9 special relativity9.1 minkowski space-time9.2 relativistic kinematics9.3 particle dynamics9.4 electrodynamics9.5 conservation laws and energy-stress tensors10 topology10.1 euclidean topology10.2 general topological spaces10.3 metric spaces10.4 induced topologies10.5 hausdorff spaces10.6 compact spaces10.7 connected spaces10.8 topological groups10.9 topological vector spaces11 measure theory and integration11.1 measurable spaces and functions11.2 measure spaces11.3 lebesgue integration12 distributions12.1 test functions and distributions12.2 operations on distributions12.3 fourier transforms12.4 green's functions13 hilbert spaces13.1 definitions and examples13.2 expansion theorems13.3 linear functionals13.4 bounded linear operators13.5 spectral theory13.6 unbounded operators14 quantum mechanics14.1 basic concepts14.2 quantum dynamics14.3 symmetry transformations14.4 quantum statistical mechanics15 differential geometry15.1 differentiable manifolds15.2 differentiable maps and curves15.3 tangent, cotangent and tensor spaces15.4 tangent map and submanifolds15.5 commutators, flows and lie derivatives15.6 distributions and frobenius theorem16 differentiable forms16.1 differential forms and exterior derivative16.2 properties of exterior derivative16.3 frobenius theorem: dual form16.4 thermodynamics16.5 classical mechanics17 integration on manifolds17.1 partitions of unity17.2 integration of n-forms17.3 stokes' theorem17.4 homology and cohomology17.5 the poincare lemma18 connections and curvature18.1 linear connections and geodesics18.2 covariant derivative of tensor fields18.3 curvature and torsion18.4 pseudo-riemannian manifolds18.5 equation of geodesic deviation18.6 the riemann tensor and its symmetries18.7 caftan formalism18.8 general relativity18.9 cosmology18.10 variation principles in space-time19 lie groups and lie algebras19.1 lie groups19.2 the exponential map19.3 lie subgroups19.4 lie groups of transformations19.5 groups of isometricsbibliographyindex