Physical Sciences and Mathematics Commons^™

Partial Differential Equations, Nathaniel James Onnen

Honors Theses

This paper will discuss methods for solving many different partial differential equations, as well as real world applications in physics. We are interested in finding solutions to the wave and heat equations in one dimension, the wave equation in two dimensions, as well as a solution to Schrodinger’s equation. In order to do this, we will study different methods including Fourier series, Bessel functions, and Hermite polynomials. I will use these methods to derive solutions for the mentioned problems, as well as to produce visualizations for many of them.