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

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很棒的图书，印刷精美，用它来好好学习！

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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！

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好书要慢慢读，需要时间去品味

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不错

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wonderful!

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用来当工具书很好，用到哪里学哪里

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this is really a modern book on mathematical physics

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从目录来看，本书很偏重于数学，但这是它的特色，很多内容是讲述物理学中所用到是数学，或者是现代数学在物理学中的应用，不同于一般的那些讲复变，傅里叶变换，傅里叶积分，特殊函数等老套的数理方法图书，本书更强调，现代数学的物理应用，非常有助于提高读者的数学知识结构，这对于非数学科技工作者来说是很难得的。此书的排版和印刷质量都不错，不过字体较小些，当然，京东的价格是一如既往地很优惠。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。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。作者讲述清晰，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。稍显不足的是，涵盖的内容广泛，深度不足，内容有些浅，但是一般来说，深度和广度不可兼顾，作为一本入门书籍是相当不错了，鉴于数学的应用越来越广泛，这部书更会受到非数学的研究生喜欢，对数学学生来说，这本书也是很好的参考书。

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