现代数学物理教程 [A Course in Modern Mathematical Physics] 下载 mobi epub pdf 电子书 2024

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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。

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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

前言/序言

现代数学物理教程 [A Course in Modern Mathematical Physics] 下载 mobi epub pdf txt 电子书 格式

评分☆☆☆☆☆

不错

评分☆☆☆☆☆

挺厚的，还没仔细看，以后再评价

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this is really a modern book on mathematical physics

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是一部比较深的数学物理教材，主要讲述希尔伯特空间、李群李代数以及微分几何，非常好！

评分☆☆☆☆☆

还不错的，出版时间都是最新的

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评分☆☆☆☆☆

我国高等教育的物理、化学等理科专业缺失现代数学，很多知识到了研究生需要用才学习，没有系统性，本科学的《高等代数》都是3、4百年的知识。这是一本很好的现代数学入门书籍。

评分☆☆☆☆☆

包装还行，活动时买的。还没看，先收藏。

评分☆☆☆☆☆

书内容No.1好，书的外表负no.1，很旧，很失望。两星

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