Modul

The module will be completed by an oral exam (approx. 30 min).

Graduates will be able to

• assess the significance of boundary value and eigenvalue problems within mathematics and/or physics and illustrate them using examples,
• describe qualitative properties of solutions,
• prove the existence of solutions to boundary value problems using functional analysis methods,
• make statements about the existence of eigenvalues and eigenfunctions of elliptic differential operators and describe their properties.

None

• Examples of boundary and eigenvalue problems
• Maximum principles for 2nd order equations
• Function spaces, e.g. Sobolev spaces
• Weak formulation of 2nd order linear elliptic equations
• Existence and regularity theory for elliptic equations
• Eigenvalue theory for weakly formulated elliptic eigenvalue problems

Total workload: 240 hours

Attendance: 90 hours

• lectures, problem classes, and examination 

Self-studies: 150 hours

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research relating to the course content,
• preparation for the module examination