Functional Analysis and Partial Differential Equations
| Course unit title | Functional Analysis and Partial Differential Equations |
| Course unit code | 024613031001 |
| Language of instruction | German, English |
| Type of course unit (compulsory, optional) | Compulsory |
| Teaching hours per week | 30 |
| Year of study | 2026 |
| Number of ECTS credits allocated | 3 |
| Name of lecturer(s) | Thomas STEINBERGER |
| courseEvent.detail.semester | |
| Degree programme | Mechatronics |
| Subject area | Engineering Technology |
| Type of degree | Master full-time |
| Type of course unit (compulsory, optional) | Compulsory |
| Course unit code | 024613031001 |
| Teaching units | 30 |
| Year of study | 2026 |
| Name of lecturer(s) | Thomas STEINBERGER |
Mathematical background at Bachelor level in technical studies.
Linear Algebra and Numerical Optimaziation
- Partial Differential Equations
- Linear Partial Differential Equations, Method of Characteristics
- Laplace, heat conduction and wave equation
- Boundary and initial value problems
- Functional analytical methods
- Hilbert space
- Weak form
- Existence of solutions
- Ritz-Galerkin method for numerical approximation
The students
- can interpret function spaces as vector spaces.
- are able to classify partial differential equations (PDE) (order, linearity, type)
- can create the weak form of simple PDEs with suitable boundary or initial values.
- understand the idea of the Ritz-Garlerkin method for numerical solution.
- can solve simple PDEs numerically using a suitable software tool.
Integrated course: Besides the lectures the participants work on many exercises at home asynchronously and during the course.
Oral Exam
None
- Evans, L. C. (2010). Partial Differential Equations (2nd ed.). AMS.
- Burg, K., Haf, H., Wille, F., & Meister, A. (2010). Partielle Differentialgleichungen und funktionalanalytische Grundlagen (5. Aufl.). Vieweg+Teubner.
Attandance