Mathematics BSc
Lecture:
Tuesdays 10:15 - 11:45, Building T, Room T603
Practice:
Tuesdays 14:15 - 15:45, Building T, Room T603
Materials: 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 at the end of each above-mentioned book.
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 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: 15 March 2023 (These are being corrected continuously, so please always use the most up-to-date version.)
Schedule for the semester:
28 February 2023 | Lecture |
Introduction. Physical examples: heat equation |
Practice | Simple equations | |
7 March 2023 | Lecture |
Physical examples: wave equation. Classification of 2nd order linear PDEs. |
Practice | First order linear and quasilinear equations | |
14 March 2023 | Lecture |
The class of smooth functions with compact support. The applications of mollifiers. |
Practice | Classification of 2nd order PDEs | |
21 March 2023 | Lecture |
Smooth partition of unity. Distributions: basic concepts. |
Practice | Break (issued by the dean) | |
28 March 2023 | Lecture |
Distributions: examples, equivalence, support, operations. |
Practice | Distributions I. | |
4 April 2023 | Lecture |
Distributions: differentiation, Cartesian product. |
Practice | Distributions II. | |
11 April 2023 | Lecture |
Spring break |
Practice | ||
18 April 2023 | Lecture |
Distributions: Convolution. |
Practice | First midtermSolutions, 2020 Midterm |
|
25 April 2023 | Lecture |
Fundamental solutions. Cauchy problem of the wave equation (part 1). |
Practice | Parabolic fundamental solutions | |
2 May 2023 | Lecture |
Cauchy problem of the wave equation (part 2). Cauchy problem of the heat equation. |
Practice | Parabolic Cauchy problems | |
9 May 2023 | Lecture |
Maximum principle of the heat equation. |
Practice | Hyperbolic Cauchy problems | |
16 May 2023 | Lecture |
Boundary value problems. |
Practice | Elliptic boundary-value problems | |
23 May 2023 | Lecture |
Sobolev spaces. |
Practice | Eigenvalues, parabolic problems | |
30 May 2023 | Lecture |
Weak solution of boundary value problems. |
Practice | Second midtermSolutions, 2020 Midterm |