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正版新书]数学物理(美)S.哈桑尼(Sadri Hassani) 著 著978751922
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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
9 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
S.哈桑尼,美国Illinois State大学物理系教授。
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