Content: The theory of partial differential equations (PDE) is important in both pure and applied mathematics. This module will deal with the basic concepts of the modern functional-analytic approach to the study of PDE: the notions of PDE and boundary value problems; questions of existence, uniqueness and properties of the solution for general domains and data. To address these questions, modern tools like Sobolev spaces will be introduced. They allow us to give a precise meaning to these questions and answer them for many examples.
Aims: To introduce the rigorous, abstract theory of partial differential equations.