ABSTRACT
Diffusion of a drug from a small patch into the skin is an example of a multidimensional mass transfer analog. Laplace's equation arises in many different areas: heat transfer, mass transfer, fluid flow, electromagnetic fields, and mechanics. The solution to Laplace's equation is a potential field that describes how the concentration, temperature, voltage, or charge distribution behaves throughout space. The general set of partial differential equations, including generation, are examples of Poisson's equation. A more limited range of problems can be solved using a technique we considered for ordinary differential equations, namely the method of undetermined coefficients. One of the more common and important examples of a Poisson's-type equation occurs when the generation term is a function of the dependent variable. The equations we will derive were all first considered by the great, French mathematician, P. S. Laplace and since they are all of the same general form, are called Laplace's equation.
