Diese Seite auf DE
Modul
Variational Methods [M-MATH-105093]
Credits
8Recurrence
UnregelmäßigDuration
1 SemesterLanguage
Level
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-110302 | Variational Methods | 8 |
Competence Certificate
The module will be completed by an oral exam (ca. 30 min).
Competence Goal
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.
Content
- 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
Recommendation
The contents of the courses Functional Analysis, Classical Methods for Partial Differential Equations, or Boundary and Eigenvalue problems are recommended.
Workload
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