Preface to the First Edition |
Preface to the Second Edition |
The Concept of a Green's Function / Chapter 1: |
Vector Spaces and Linear Transformations / Chapter 2: |
Vector Spaces / 2.1: |
Linearly Independent Vectors / 2.2: |
Orthonormal Vectors / 2.3: |
Linear Transformations / 2.4: |
Systems of Finite Dimension / Chapter 3: |
Matrices and Linear Transformations / 3.1: |
Change of Basis / 3.2: |
Eigenvalues and Eigenvectors / 3.3: |
Symmetric Operators / 3.4: |
Bounded Operators / 3.5: |
Positive Definite Operators / 3.6: |
Continuous Functions / Chapter 4: |
Limiting Processes / 4.1: |
Integral Operators / 4.2: |
The Kernel of an Integral Operator / 5.1: |
Symmetric Integral Transformations / 5.2: |
Separable Kernels / 5.3: |
Eigenvalues of a Symmetric Integral Operator / 5.4: |
Expansion Theorems for Integral Transformations / 5.5: |
Generalized Fourier Series and Complete Vector Spaces / Chapter 6: |
Generalized Fourier Series / 6.1: |
Approximation Theorem / 6.2: |
Complete Vector Spaces / 6.3: |
Differential Operators / Chapter 7: |
Introduction / 7.1: |
Inverse Operators and the [delta]-function / 7.2: |
The Domain of a Linear Differential Operator / 7.3: |
Adjoint Differential Operators / 7.4: |
Self-Adjoint Second-Order Differential Operators / 7.5: |
Non-Homogeneous Problems and Symbolic Operators / 7.6: |
Green's Functions and Second-Order Differential Operators / 7.7: |
The Problem of Eigenfunctions / 7.8: |
Green's Functions and the Adjoint Operator / 7.9: |
Spectral Representation and Green's Functions / 7.10: |
Integral Equations / Chapter 8: |
Classification of Integral Equations / 8.1: |
Method of Successive Approximations / 8.2: |
The Fredholm Alternative / 8.3: |
Symmetric Integral Equations / 8.4: |
Equivalence of Integral and Differential Equations / 8.5: |
Green's Functions in Higher-Dimensional Spaces / Chapter 9: |
Partial Differential Operators and [delta]-functions / 9.1: |
Green's Identities / 9.3: |
Fundamental Solutions / 9.4: |
Self-Adjoint Elliptic Equations (The Dirichlet Problem) / 9.5: |
Self-Adjoint Elliptic Equations (The Neumann Problem) / 9.6: |
Parabolic Equations / 9.7: |
Hyperbolic Equations / 9.8: |
Worked Examples / 9.9: |
Calculation of Particular Green's Functions / Chapter 10: |
Method of Images / 10.1: |
Generalized Green's Functions / 10.2: |
Mixed Problems / 10.3: |
Approximate Green's Functions / Chapter 11: |
Generalized Potentials / 11.1: |
A Representation Theorem / 11.4: |
Choice of Approximate Kernal / 11.5: |
Summary of the Green's Function Method / Appendix A: |
Green's Function Method for Ordinary Differential Equations / A1: |
Green's Function Method for Partial Differential Equations / A2: |
Operators and Expressions / Appendix B: |
The Lebesgue Integral / Appendix C: |
Distributions / Appendix D: |
Bibliography |
Chapter References |
Index |
Preface to the First Edition |
Preface to the Second Edition |
The Concept of a Green's Function / Chapter 1: |