Partielle Differentialgleichungen

What it is about

In this module you will learn fundamental methods for the treatment of partial differential equations (PDEs). You will deal with classical representations of solutions for transport, Laplace, heat and wave equations, with conservation laws, Sobolev spaces, and with weak (variational) solutions of elliptic equations and their properties such as existence, uniqueness and regularity.

What you will be able to do

• Distinguishing different types of partial differential equations
• Understanding classical representations of solutions for transport, Laplace, heat and wave equations
• Familiarity with Sobolev spaces
• Formulation and analysis of weak (variational) solutions of elliptic PDEs
• Knowledge of existence, uniqueness and well-posedness questions
• Application of structural properties such as maximum principles

What the module consists of

• VorlesungTransmission of the theoretical foundations and presentation of examples
• ÜbungDeepening through problem sets, solutions and supervised work; will progress to independent work

Teaching method

• Vortrag mit Beispielenfor introduction to theory and illustration through demonstrations
• Diskussion mit Studierendenpromotes independent thinking and understanding of the topics
• Übungssitzungen mit Übungsblätternfacilitate deepening, self-check and group work; initially supervised, later increasingly independent