Mathematics BSc, MSc
Lecture:
Tuesdays 10:15 - 11:55, H405A (with a 10-minute break)
Practice:
Tuesdays 14:05 - 15:35, H406
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: 25 March 2025 (These are being corrected continuously, so please always use the most up-to-date version.)
Schedule for the semester:
11 February 2025 | Lecture |
Introduction. |
Practice | Simple equations | |
18 February 2025 | Lecture |
Physical examples: heat equation, wave equation. Classification of 2nd order linear PDEs (part 1). |
Practice | First order linear equations | |
25 February 2025 | Lecture |
Classification of 2nd order linear PDEs (part 2). The class of smooth functions with compact support. |
Practice | First order quasilinear equations, Classification of 2nd order PDEs | |
4 March 2025 |
Lecture |
The applications of mollifiers. Smooth partition of unity. The D(Omega) convergence. |
Practice | Classification of 2nd order PDEs, Distributions I. | |
11 March 2025 | Lecture |
Distributions: basic concepts, examples, equivalence. |
Practice | Distributions I. (ending) | |
18 March 2025 | Lecture |
Distributions: support, operations, differentiation, Cartesian product. |
Practice | First midterm2025 Midterm, 2024 Midterm, 2024 Mock Midterm , 2020 Midterm |
|
25 March 2025 | Lecture |
Distributions: Convolution. |
Practice | Distributions II. | |
1 April 2025 |
Lecture |
Fundamental solutions. Cauchy problem of the wave equation (part 1). |
Practice | Hyperbolic Cauchy problems (wave equation) | |
8 April 2025 |
Lecture |
Cauchy problem of the wave equation (part 2). Cauchy problem of the heat equation. |
Practice | Parabolic Cauchy problems (heat equation) | |
15 April 2025 |
Lecture |
Boundary value problems. |
Practice | Elliptic boundary-value problems | |
22 April 2025 |
Lecture |
Spring break |
Practice | ||
29 April 2025 |
Lecture |
Eigenvalue problems. |
Practice | Eigenvalues, method of Fourier | |
6 May 2025 |
Lecture |
Sobolev spaces. |
Practice | Second midterm2024 Midterm, 2024 Mock Midterm , 2020 Midterm |
|
13 May 2025 |
Lecture |
Weak solution of boundary value problems. |
Practice | Midterm retakes |
|
20 May 2025 |
Lecture |
??? |
Practice | Midterm re-retakes (?) |