Preface
Note to the Reader
List of Symbols
0 Mathematical Preliminaries
Ⅰ Finite-Dimensional Vector Spaces
1 Vectiors and Transformations
2 Operator Algebra
3 Matrices:Operator Representations
4 Spectral Decomposition
Ⅱ Infinite-Dimensional Vector Spaces
5 Hilbert Spaces
6 Generalized Functions
7 Classical Orthogonal Polynmials
8 Fourier Analysis
Ⅲ Complex Analysis
9 Complex Calculus
10 Calculus of Residues
11 Complex Analysis:Advamced Topics
Ⅳ Differential Equations
12 Separation of Variables in Spherical oordinates
13 Secpmd-Order Linear Differential Equations
14 Complex Analysis of SOLDEs
15 Integral Transforms and Differential Equations
Ⅴ Operators on Hilbert Spaces
16 An Introduction to Operator Theory
17 Integral Equations
18 Sturm-Liouville Systems:Formalism
19 Sturm-Liouville Systems:Examples
Ⅵ Green's Functions
20 Green's Functions in One Dimension
21 Multidimensional Green's Functions:Formalism
22 Multidimensional Green's Functions:Applications
23 Multidimensional Green's Functions:Applications
24 Group Representation Theory
25 Algebra of Tensors
26 Analysis of Tensors
Ⅶ Lie Groups and Their Applictions
27 Lie Groups and Lie Algebras
28 Differential Geometry
29 Lie Groups and Differential Equations
30 Calculus of Variations,Symmetries,and Conservation Laws
Bibliography
Index
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