MATH 453
Introduction to the Theory of Partial Differential Equations Spring 2017
Division III Quantitative/Formal Reasoning
This is not the current course catalog

The study of Partial Differential Equations (PDE) is a very prominent branch of modern analysis with many real-life applications. Unlike previous courses you may have taken, in this senior seminar we will set the applications-part aside, and instead study PDE from a rigorous point of view, using tools from mathematical analysis. We will start by examining properties of three classical PDE: Laplace’s equation, the heat equation, and the wave equation. Then, we will move on with an introduction to Sobolev spaces and see how to use them to study general second-order elliptic equations. Finally, we will end with first-order PDE and the method of characteristics and, if time permits, we will also cover the theory of Hamilton-Jacobi equations and conservation laws. My hope is that, by the end of the course, you will not only have a deeper understanding of PDE, but also a newfound appreciation of mathematical analysis.