Partial Differential Equations I: Math 784

In this course a graduate introduction to the vast field of Partial Differential Equations (PDE for short) will be given. The first part of the course will be about classical approaches to construct explicit solutions to basic PDE. In particular, we will look at transport, wave, heat, and Laplace equations and basic properties of their solutions. In the second part of the course a more abstract approach to the existence of solutions of some PDE will be presented. In particular, we will discuss the so-called generalized functions and introduce the notions of weak solutions and Sobolev spaces. If time permits, a spectral problem for the Laplace operator will be discussed.

Spring 2022:
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