数学物理（第1卷 英文版）

Preface
Note to the Reader
List of Symbols
0 Mathematical Preliminaries
0.1 Sets
0.2 Maps
0.3 Metric Spaces
0.4 Cardinality
0.5 Mathematical Induction
0.6 Problems
I Finite-Dimensional Vector Spaces
1 Vectors and Transformations
　　1.1 Vector Spaces
　　1.2 Inner Product
　　1.3 Linear Transformations
　　1.4 Algebras
　　1.5 Problems
2 Operator Algebra
　　2.1 Algebra of L (V)
　　2.2 Derivatives of Functions of Operators
　　2.3　Conjugation of Operators
　　2.4　Hermitian and Unitary Operators
　　2.5　Projection Operators
　　2.6　Operators in Numerical Analysis
　　2.7　Problems
3 Matrices: Operator Representations
　　3.1　Matrices
　　3.2 Operations on Matrices
　　3.3　Orthonormal Bases
　　3.4 Change of Basis and Similarity Transformation
　　3.5 The Determinant
　　3.6　The Trace
　　3.7 Problems
4 Spectral Decomposition
　　4.1　Direct Sums
　　4.2　Invariant Subspaces
　　4.3　Eigenvalues and Eigenvectors
　　4.4 Spectral Decomposition
　　4.5　Functions of Operators
　　4.6 Polar Decomposition
　　4.7　Real Vector Spaces
　　4.8　Problems
II Infinite-Dimensional Vector Spaces
　5 Hilbert Spaces
　　5.1　The Question of Convergence
　　5.2　The Space of Square-Integrable Functions
　　5.3　Problems
　6 Generalized Functions
　　6.1　Continuous Index
　　6.2 Generalized Functions
　　6.3　Problems
　7 Classical Orthogonal Polynomials
　　7.1　General Properties
　　7.2 Classification
　　7.3　Recurrence Relations
　　7.4 Examples of Classical Orthogonal Polynomials
……
III Complex Analysis
IV Differential Equations
V Operators on Hilbert Spaces
VI Green'S Functions
VII Groups and Manifolds
VIII Lie Croups and Their Applications
Bibvliography
Index