SS 20/21: ** Introduction to PDEs ** (tutorials)

**Lecutre**: Agnieszka Ćwierczewska-Gwiazda (Tuesday, 14:15 - 15:45)

**Tutorial**: Kuba Skrzeczkowski (Thursdays, 12:15 - 13:45)

**USOS**: link

This is an introduction to the wild and diverse area of Partial Differential Equations. The course consists of three parts: (A) classical theory, (B) Sobolev spaces and (C) general theory for elliptic and parabolic operators.

** Grading**:

- (H) homeworks - 11-12 series of 2 problems each week
**submitted in groups of 2**= max 24 points, - (A) active class participation - 13 classes x 1 point per class = max 13 points (this includes turning on your audio, video - 0.5 AND asking questions, answers etc - 0.5),
- (P) mini-project - self-study of a small piece of advanced material, writing it in an understable way and presenting it to others. This year, we will study Schauder estimates for Laplacian and Hille-Yosida Theorem.

** Admission to the final oral exam ** after collecting:

- 60% points from homeworks (H),
- 80% from active class participation (A),
- passed mini-project: oral presentation and report (P).

** COVID related info ** : We gonna meet on Zoom each Thursday. You are expected to turn on your camera and audio (in case you don't have appropriate equipment contact me before 1/03).
I will upload content of the iPad blackboard and videos from the class below. Each week I will offer online office hours on Zoom. To compensate for the social distancing, you are expected
to submit homeworks in groups of 2. You should discuss content of the lecture and the tutorial with your friend.

** Problem Sets ** :

- PS A1. Transport equation: an example of hyperbolic equations.
- PS A2. Laplace and Poisson equation: examples of elliptic equations.
- PS A3. Heat equation: an example of parabolic equations.
- PS B1. Introduction to distributions and differentiation.
- PS B2. Sobolev spaces: examples, calculus and smooth approximation.
- PS B3. Sobolev spaces: important results.
- PS C1. Introduction to weak formulations.
- PS C2. Theory for elliptic equations in Hilbert spaces.

** My notes (maybe helpful?) ** :

- PS A1. Transport equation: an example of hyperbolic equations. (ver: 18.03.2021)
- PS A2. Laplace and Poisson equation: examples of elliptic equations. (ver: 22.04.2021)
- PS A3. Heat equation: an example of parabolic equations. (ver: 22.04.2021)
- PS B1. Introduction to distributions and differentiation. (ver: 29.04.2021)
- PS B2. Sobolev spaces: examples, calculus and smooth approximation. (ver: 13.05.2021)
- PS B3. Sobolev spaces: important results. (ver: 20.05.2021)
- PS C1. Introduction to weak formulations. (ver: 27.05.2021)
- PS C2. Theory for elliptic equations in Hilbert spaces. (ver: 27.05.2021)

** Homeworks ** are listed here

** Special problems ** are listed here

** Zoom blackboards: ** :

- Class 1 (04.03): blackboard is here
- Class 2 (11.03): blackboard is here
- Class 3 (18.03): blackboard is here
- Class 4 (25.03): blackboard is here
- Class 5 (08.04): blackboard is here
- Class 6 (15.04): blackboard is here
- Class 7 (22.04): blackboard is here
- Class 8 (29.04): blackboard is here
- Class 9 (06.05): blackboard is here
- Class 10 (13.05): blackboard is here
- Class 11 (20.05): blackboard is here
- Class 12 (27.05): blackboard is here
- Class 13 (10.06): blackboard is here

** Mini-project topics: ** :

** Class recordings **, ** solutions to homeworks ** and ** class results ** are updated on moodle.