# Appendix 7A: Two- and Three-Dimensional Green’s Functions

## 7A.1Introduction

We discussed Green’s function briefly (Section 7.2). The one-dimensional Green’s function of the Laplace equation, with Dirichlet boundary conditions, is the solution of the differential equation

subject to the boundary conditions

and is shown to be

For an arbitrary input *f*(*x*), the response *y*(*x*) can be obtained from a superposition integral

The differential equation for *y* is

and the boundary conditions are

Equation 7A.3 for *y* is the solution to Equation 7A.4, where ...

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