This course gives an introduction to the classical theory of partial differential equations. In particular, the following contents are dealt with:
- Classification and well-posed problems,
- Quasilinear equations: Cauchy problem,
- Wave equation: existence, uniqueness, stability, maximum principle,
- Poisson equation: separation ansatz, fundamental solutions, Green's function, maximum principle, existence and uniqueness,
- Heat equation: separation of variables, Fourier transformation, semigroups, maximum principle, existence and uniqueness.
Notice
Without a proof of successful participation in the exercise classes, only 3 credit points will be awarded for the module.