Date of Graduation
Spring 2014
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Les Reid
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.
Keywords
distribution, Fourier transform, fundamental solution, convolution, Schwartz space
Subject Categories
Mathematics
Copyright
© Stephen Clair Dickey
Recommended Citation
Dickey, Stephen Clair, "Distributions and Applications to Partial Differential Equations" (2014). MSU Graduate Theses/Dissertations. 1654.
https://bearworks.missouristate.edu/theses/1654
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