The course gives an overview of the theory of partial differential equations (PDEs).
The course can be divided into two main parts. The first part treats the Laplace-, heat- and wave- equation whichrepresent model examples of linear elliptic, parabolic and hyperbolic PDEs. Furthermore, first-order non-linear problemsand explicit solution techniques (e.g. transform methods, fundamental solutions, Green's function, scale invariance) areconsidered. The second part of the course covers weak solutions for second-order equations. Sobolev spaces areintroduced and studied. The existence, uniqueness and regularity in these spaces is discussed and the properties ofsolutions is studied.
