Mathematics BSc, MSc
Lecture:
Tuesdays 14:15 - 15:55, H507 (with a 10-minute break)
Practice:
Tuesdays 10:15 - 11:55, E501
Material: The lecture does not follow any (English) book, but different topics can be found in the following books:
Lawrence C. Evans, Partial Differential Equations, AMS, Providence, 2002.Exercises can be found in these books.
1. For the practice part:
During the semester, there are going to be two midterms.
There are also some bonus problems at the end of each practice part, which can be solved at home and then submitted on the next practice session.
Grades at the end of the semester: (the points are subject to modification, but only downwards)
40-59: grade 2
60-79: grade 3
80-99: grade 4
above 100: grade 5
2. For the lecture part:
The course ends with a written exam.
It has two parts: the first part consists of small questions, like stating a definition/theorem, or some easy questions which will be answered during the semester as "remarks" (or they are trivial consequences of some theorems).
In the second part you have to describe a part of the material thoroughly, but you will be guided by some helping questions.
Lecture notes
Last modified: 20 May 2025 (These are being corrected continuously, so please always use the most up-to-date version.)
Schedule for the semester:
| 17 February 2026 | Practice |
Simple equations |
| Lecture | Introduction. Physical examples: heat equation, wave equation. | |
| 24 February 2026 | Practice |
First order linear equations |
| Lecture | Classification of 2nd order linear PDEs. The class of smooth functions with compact support. | |
| 3 March 2026 |
Practice |
First order quasilinear equations, Classification of 2nd order PDEs |
| Lecture | The applications of mollifiers. Smooth partition of unity. Definition of a distribution. | |
| 10 March 2026 |
Practice |
Classification of 2nd order PDEs, Distributions I. |
| Lecture | Distributions: equivalence, support, operations, derivative, direct product. | |
| 17 March 2026 | Practice |
Distributions I. (ending) |
| Lecture | Distributions: convolution. Fundamental solutions. | |
| 24 March 2026 | Practice |
First midterm2025 Midterm, 2024 Midterm, 2024 Mock Midterm , 2020 Midterm |
| Lecture | Cauchy problem of the wave equation. | |
| 31 March 2026 | Practice |
Distributions II. |
| Lecture | Cauchy problem of the heat equation. | |
| 7 April 2026 |
Practice |
Spring break |
| Lecture | ||
| 14 April 2026 |
Practice |
Hyperbolic Cauchy problems (wave equation) |
| Lecture | Maximum principle for the heat equation. | |
| 21 April 2026 |
Practice |
Parabolic Cauchy problems (heat equation) |
| Lecture | Boundary value problems | |
| 28 April 2026 |
Practice |
Elliptic boundary-value problems |
| Lecture | Eigenvalue problems | |
| 5 May 2026 |
Practice |
Eigenvalues, method of Fourier |
| Lecture | Green functions. | |
| 12 May 2026 |
Practice |
Second midterm2025 Midterm, 2024 Midterm, 2024 Mock Midterm , 2020 Midterm |
| Lecture | Sobolev spaces. | |
| 19 May 2026 |
Practice |
Midterm retakes |
| Lecture | Weak solution of boundary value problems. | |
| 26 May 2026 |
Practice |
To be announced... |
| Lecture | To be announced... |
