Linear operators:
compact operators, spectral theory, unbounded operators and their adjoints, spectral theorem for self adjoint operators.Continuation of the topology of vector spaces: locally convex spaces, weak topologies, compactness, reflexivity.
Function spaces: LP spaces, distributions, Sobolev spaces and embedding theorems.
As mentioned above, you declare which problems you solved and are ready to present, in particular, you need not solve all problems but at least half, however, the more you solve the more points for the grade are gained. More precisely, one receives for the percentage of solved problems a Problem-Factor (POF) according to piecewise linear interpolated between (50%,0), (90%,1) and (100,1.15), meaning you get between 0 and 1 POF for between 50% and 90% solved, and a bonus can be obtained for surpassing 90%).
For every problem, a student will be chosen at random (from all students who solved said problem) who presents his solution on the blackboard. Aside from the mathematical correctness of the solution, high importance is also attached to giving a good presentation and possessing knowledge of the general context of the problem. The presentation will be awarded 2, 1, or 0 points, the full number if the solution is correct and a good presentation is given, 1 point if the presentation style is poor, or a significant part of the solution is incorrect, but still a not negligible part correct. The average of all points gained through presentation divided by 2 constitutes the Presentation-Factor.
Finally, at the end of the semester, there will be an exam that impacts the grading. The Exam-Factor corresponds to the ratio of points achieved in the exam to totally possible points.
Each of the three factors Problem-Factor (POF), Presentation-Factor (PEF) and Exam-Factor (EXF) is between 0 and 1 and contributes one third to the grade, more precisely you get total points P=100/3*(POF+PEF+EXF) and
Grade: | Very good | Good | Satisfactory | Adequate | Unsatisfactory |
P: | >87.5 | 87.5 -75.0 | 75.0-62.5 | 62.5-50.0 | <50.0 |
Moreover, POF must be non-negative and PEF and EXF must be greater equal 0.5, meaning at least half the number of problems must be solved, the average presentations must be 1 or greater and half of the points must be achieved in the exam.
In the case of orange or red Covid traffic light, the exercise classes take place virtually, otherwise in-person, where the basic process and grading remain the same (you can use the uploaded solution for visual reference in your presentation).
Date | Problem-Sheet | Subject | Remarks |
13.10.2021 | 1. Exercise Sheet | Basics of Sobolev spaces | |
27.10.2021 | 2. Exercise Sheet | Approximation via convolution | |
10.11.2021 | 3. Exercise Sheet | Lipschitz domain and trace | |
24.11.2021 | 4. Exercise Sheet | Locally convex vector spaces | |
06-10.12.2021 | 5. Exercise Sheet | Weak topologies | Virtual replacement for holyday on 08.th |
12.01.2022 | 6. Exercise Sheet | Distributions | |
26.01.2022 | 7. Exercise Sheet | Spectral theory | |
TBD | Exam |