Modul

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

Graduates will be able to

• assess the significance of variational problems in relation to their applications in the natural sciences, engineering or geometry and illustrate them using examples,
• formulate variational problems independently,
• recognize the specific difficulties within the calculus of variations,
• analyze and solve concrete, prototypical problems,
• use techniques to prove the existence of solutions to certain classes of variational problems and calculate these solutions in special cases.

• one-dimensional variational problems
• Euler-Lagrange equation
• necessary and sufficient criteria
• multidimensional variational problems
• direct methods of the calculus of variations
• existence of critical points of functionals

The contents of the courses Functional Analysis, Classical Methods for Partial Differential Equations, or Boundary and Eigenvalue problems are recommended.

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