作者：哈桑尼
页数：698
出版社：世界图书出版公司
出版日期：2017
ISBN：9787519226091
电子书格式：pdf/epub/txt
内容简介
S.哈桑尼著的《数学物理（上第2版）（英文版）》是为学习物理学的读者编写的数学基础教材，书中除了用较现代的方法处理经典的数学物理问题外，还引入了很多有较强物理应用意义的现代数学方法和思想，从涵盖的知识面来看，已远远超出通常数学物理方法教程的范围，因此可以供更大范围的读者参考选用。与第1版相比，第2版重写了许多章节，新增的章节包括代数、克里福代数的表示、纤维丛等内容。
作者简介
S. Hassani（S.哈桑尼）是美国Illinois State 大学物理系教授,本书第1版出版后受到好评,第2版重写了许多章节，新增的章节包括代数、克里福代数的表示、纤维丛和规范场等内容。
本书特色
本书是为学习物理学的读者编写的数学基础教材，书中除了用较现代的方法处理经典的数学物理问题外，还引入了很多有较强物理应用意义的现代数学方法和思想，从涵盖的知识面来看，已远远超出通常数学物理方法教程的范围，因此可以供更大范围的读者参考选用。与第1版相比，第2版重写了许多章节，新增的章节包括代数、克里福代数的表示、纤维丛等内容.
目录
1 Mathematical Preliminaries
Part I Finite-Dimensional Vector Spaces
2 Vectors and Linear Maps
3 Algebras
4 Operator Algebra
5 Matrices
6 Spectral Decomposition
Part II Infinite-Dimensional Vector Spaces
7 Hilbert Spaces
8 Classical Orthogonal Polynomials
Fourier Analysis
Part III Complex Analysis
10 Complex Calculus
11 Calculus of Residues
12 Advanced Topics
Part IV Differential Equations
13 Separation of Variables in Spherical Coordinates
14 Second-Order Linear Differential Equations
15 Complex Analysis of SOLDEs
16 Integral Transforms and Differential Equations
Part V Operators on Hilbert Spaces
17 Introductory Operator Theory
18 Integral Equations
19 Sturm-Liouville Systems
Part VI Green’s Functions
20 Green’s Functions in One Dimension
21 Multidimensional Green’s Functions: Formalism
22 Multidimensional Green’s Functions: Applications
Part VII Groups and Their Representations
23 Group Theory
24 Representation of Groups
25 Representations of the Symmetric Group
Part VIII Tensors and Manifolds
26 Tensors
27 Clifford Algebras
28 Analysis of Tensors
Part IX Lie Groups and Their Applications
29 Lie Groups and Lie Algebras
30 Representation of Lie Groups and Lie Algebras
31 Representation of Clifford Algebras
32 Lie Groups and Differential Equations
33 Calculus of Variations, Symmetries, and Conservation Laws
Part X Fiber Bundles
34 Fiber Bundles and Connections
35 Gauge Theories
36 Differential Geometry
37 Riemannian Geometry
References
Index
Part I Finite-Dimensional Vector Spaces
2 Vectors and Linear Maps
3 Algebras
4 Operator Algebra
5 Matrices
6 Spectral Decomposition
Part II Infinite-Dimensional Vector Spaces
7 Hilbert Spaces
8 Classical Orthogonal Polynomials
Fourier Analysis
Part III Complex Analysis
10 Complex Calculus
11 Calculus of Residues
12 Advanced Topics
Part IV Differential Equations
13 Separation of Variables in Spherical Coordinates
14 Second-Order Linear Differential Equations
15 Complex Analysis of SOLDEs
16 Integral Transforms and Differential Equations
Part V Operators on Hilbert Spaces
17 Introductory Operator Theory
18 Integral Equations
19 Sturm-Liouville Systems
Part VI Green’s Functions
20 Green’s Functions in One Dimension
21 Multidimensional Green’s Functions: Formalism
22 Multidimensional Green’s Functions: Applications
Part VII Groups and Their Representations
23 Group Theory
24 Representation of Groups
25 Representations of the Symmetric Group
Part VIII Tensors and Manifolds
26 Tensors
27 Clifford Algebras
28 Analysis of Tensors
Part IX Lie Groups and Their Applications
29 Lie Groups and Lie Algebras
30 Representation of Lie Groups and Lie Algebras
31 Representation of Clifford Algebras
32 Lie Groups and Differential Equations
33 Calculus of Variations, Symmetries, and Conservation Laws
Part X Fiber Bundles
34 Fiber Bundles and Connections
35 Gauge Theories
36 Differential Geometry
37 Riemannian Geometry
References
Index
