Three-Dimensional and Axisymmetric Potential Problems

Abstract

In this lecture we consider briefly the solution of Laplace’s equation in three dimensions:

$$[\frac{{{\partial ^2}\phi }}{{\partial {{\text{x}}^{\text{2}}}}} + \frac{{{\partial ^2}\phi }}{{\partial {{\text{y}}^{\text{2}}}}} + \frac{{{\partial ^2}\phi }}{{\partial {{\text{z}}^{\text{2}}}}} = 0$$

((1))

, by methods analogous to those applied to two-dimensional problems in the preceding lecture. In particular, we discuss the application of the simple-layer Newtonian potential to the Dirichlet problem.