Date of Award

4-23-1998

Document Type

Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

First Advisor

Prof. William T. Ross

Abstract

Harmonic Function Theory is a field of differential mathematics that has both many theoretical constructs and physical connections, as well as its store of classical problems.

One such problem is the Dirichlet Problem. While the proof of the existence of a solution is well-founded on basic theory, and general methods for polynomial solutions have been well studied, much ground is still yet to be overturned. In this paper we focus on the examination, properties and computation methods and limitations, of solutions for rational boundary functions.

Another area that we shall study is the properties and generalizations of the zero sets of harmonic functions. Our study in this area has shown that these zero sets satisfy many strict criteria. Many familiar or simple curves do not satisfy such criteria themselves. In this paper we will present the criteria and how it is so restrictive.

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