| The purpose of this thesis is to provide a background in harmonic function theory, including the primary theorems along with their proofs. Graphs of harmonic functions are shown, as well as examples of harmonics functions and their sources. Harmonic functions are critical to mathematical physics as the solution to Laplace's equation. Harmonic functions can represent electric potential, gravitational potential, steady-state temperature, or fluid potential. The theory of conformal mapping is introduced and application problems are solved using harmonic function theory. A search of the current literature yields an article that gives a theorem that enables the author, Axler, to simplify many proofs in the complex analysis. Axler's primary theorem, the Logarithmic Conjugation Theorem, is proven as are a number of theorems associated with various applications. |
