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.
Competencies / intended learning achievements
Upon completion of this module, the students have studied and understand the extension of ordinary differential equations to partial differential equations. They understand the proofs presented in the lecture and are able to comprehend and explain them.
By completing exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies.
Further literature will be announced in the lecture; Exercise material is provided.