現代數學物理教程 [A Course in Modern Mathematical Physics] 下載 mobi epub pdf 電子書 2024

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內容簡介

《現代數學物理教程》是一部學習數學物理入門書籍，也是一部教程，讓讀者在物理的背景下建立現代數學概念，重點強調微分幾何。寫作風格上保持瞭作者一貫的特點，清晰，透徹，引人入勝。大量的練習和例子是《現代數學物理教程》的一大亮點，擴展索引對初學者也是十分有用。內容涵蓋瞭張量代數，微分幾何，拓撲，李群和李代數，分布理論，基礎分析和希爾伯特空間。目次:幾何與結構;群；嚮量空間；綫性算子和矩陣；內積空間；代數；張量；外代數；狹義相對論；拓撲學；測度論和積分；分布；希爾伯特空間；量子力學；微分幾何；微分形式；流形上的積分；聯絡和麯率；李群和李代數。

內頁插圖

目錄

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

現代數學物理教程 [A Course in Modern Mathematical Physics] 下載 mobi epub pdf txt 電子書 格式

評分☆☆☆☆☆

從目錄來看，本書很偏重於數學，但這是它的特色，很多內容是講述物理學中所用到是數學，或者是現代數學在物理學中的應用，不同於一般的那些講復變，傅裏葉變換，傅裏葉積分，特殊函數等老套的數理方法圖書，本書更強調，現代數學的物理應用，非常有助於提高讀者的數學知識結構，這對於非數學科技工作者來說是很難得的。此書的排版和印刷質量都不錯，不過字體較小些，當然，京東的價格是一如既往地很優惠。本書是一部學習數學物理入門書籍，也是一部教程，讓讀者在物理的背景下建立現代數學概念，重點強調微分幾何。內容涵蓋瞭張量代數，微分幾何，拓撲，李群和李代數，分布理論，基礎分析和希爾伯特空間。目次：幾何與結構；群；嚮量空間；綫性算子和矩陣；內積空間；代數；張量；外代數；狹義相對論；拓撲學；測度論和積分；分布；希爾伯特空間；量子力學；微分幾何；微分形式；流形上的積分；聯絡和麯率；李群和李代數。作者講述清晰，透徹，引人入勝。大量的練習和例子是《現代數學物理教程》的一大亮點。稍顯不足的是，涵蓋的內容廣泛，深度不足，內容有些淺，但是一般來說，深度和廣度不可兼顧，作為一本入門書籍是相當不錯瞭，鑒於數學的應用越來越廣泛，這部書更會受到非數學的研究生喜歡，對數學學生來說，這本書也是很好的參考書。

評分☆☆☆☆☆

好書要慢慢讀，需要時間去品味

評分☆☆☆☆☆

我國高等教育的物理、化學等理科專業缺失現代數學，很多知識到瞭研究生需要用纔學習，沒有係統性，本科學的《高等代數》都是3、4百年的知識。這是一本很好的現代數學入門書籍。

評分☆☆☆☆☆

還不錯的，齣版時間都是最新的

評分☆☆☆☆☆

不錯

評分☆☆☆☆☆

不錯

評分☆☆☆☆☆

學習起來有點睏難，工作瞭就彆買瞭

評分☆☆☆☆☆

是一部比較深的數學物理教材，主要講述希爾伯特空間、李群李代數以及微分幾何，非常好！

評分☆☆☆☆☆

用來當工具書很好，用到哪裏學哪裏

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