Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface to the English Edition
Preface to the First Edition
Chapter 1: Linear Operators
1.1: Finite Dimensional Space
1.2: Functionals and Generalized Functions
1.3: Hilbert Space and Completeness
1.4: Self-Adjoint Operators
1.5: Ket- and Bra- Vectors
Chapter 2: Method of Characteristics
2.1: Linear First-Order PDE
2.2: Quasilinear Equation
2.3: System of Equations
Chapter 3: Second-Order Linear Equations
3.1: Canonical Form
3.2: Curvilinear Coordinates
3.3: Separation of Variables
3.4: Fourier Method
Chapter 4: Self-Similarity and Nonlinear Equations
4.1: Symmetry of Equations
4.2: Nonlinear Equations
Chapter 5: Special Functions
5.1: Singular Points
5.2: Hypergeometric Functions
5.3: Orthogonal Polynomials
Chapter 6: Asymptotic Methods
6.1: Asymptotic Power Series
6.2: A Laplace Integral
6.3: Method of Stationary Phase
6.4: Method of Steepest Descents
6.5: The Averaging Method
Chapter 7: Greenβs Functions Method
7.1: Greenβs Functions
7.2: Continuous Spectrum
7.3: Resolvent
Chapter 8: Integral Equations
8.1: Fredholm Equations
8.2: Degenerate Kernel
8.3: Symmetric Kernel
8.4: Inverse Problem for Schr¨odinger Operator
Chapter 9: Groups and Representations
9.1: Groups
9.2: Representations
Chapter 10: Continuous Groups
10.1: Lie Groups and Algebras
10.2: Representations of the Rotation Group
Chapter 11: Group Theory in Physics
11.1: Molecular Oscillations
11.2: Level Splitting
11.3: Selection Rules
11.4: Invariant Tensors
Appendix
Bibliography
Index