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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：

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