Date of Graduation

Spring 2014

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Les Reid

Keywords

distribution, Fourier transform, fundamental solution, convolution, Schwartz space

Subject Categories

Mathematics

Abstract

What can we learn about functions that lack derivatives in the classical sense and how can we work with them accordingly? The answer lies in the theory of distributions. In this paper we examine properties of distributions. We demonstrate the effect of taking the Fourier transform on distributions, and how this aids us in determining fundamental solutions of various equations including Stoke's, Lam\'{e}'s, and Poisson's, as well as the heat and wave equation.

Copyright

© Stephen Clair Dickey

Campus Only

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