MMA150 V20 Komplexanalys i flera variabler
This page contains the program of the course: lectures, homework assignments and recommended exercises. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.
As all other courses at the university during the last period of the semester, this course will be given as an online course. Our preliminary plan is as follows:
We will try to have online lectures in Zoom at the same time as the lectures were planned, i.e., a typical week at Mondays 8-10, Tue 13-15 and Thu 13-15. At the end of the lectures, we plan to stay in Zoom a while afterwards so you can ask questions. For information about how to enter Zoom, see the link among the information about the lectures in the course homepage. We encourage you to check this out before the first lecture on Monday morning.
In addition to this, we have activated the discussion forum in Canvas, where you should all be able to create new posts, to ask questions or discuss different matters.
Since this is a completely new situation for all of us, and since it is not unlikely that capacity problems occur when so many go over to online communication, it is quite probably that not everything will go according to the plan, but we just have to do our best and adapt to the situation.
Preliminary program
The schedule of the course is in TimeEdit.
Note that the course will be given online. Information about how the lectures will be done can be found in the Zoom information.
Lectures
| Week | Days (Who) | Sections | Content |
|---|---|---|---|
| 1 | L 1.1-1.4 | Basic definitions and properties of holomorphic functions. Inequivalence of ball and polydisc |
|
| 2 |
30/3 (RL) 31/3 (RL) 2/4 (RL) |
L 1.6, 2.1 KW 2.3-2.4, 2.6 |
Riemann extension theorem Reinhardt domains and power series Domains of holomorphy |
| 3 |
20/4 (EW) 21/4 (EW) 23/4 (EW) |
L 2.2-2.3 KW 2.2-2.3 |
Convexity Levi pseudoconvexity |
| 4 |
27/4 (RL) 28/4 (RL) |
L 2.4 KW 8.1-8.3 |
Subharmonicity |
| 5 |
4/5 (RL) 5/5 (EW) 7/5 (EW) |
L 2.4-2.5 | Plurisubharmonicity Hulls Hartogs pseudoconvexity |
| 6 |
11/5 (RL) 12/5 (RL) 14/5 (RL) |
L 2.6, 4.1 | Holomorphic convexity Levi problem for Reinhardt domains The dbar-equation, the Cauchy-Pompeiu formula |
| 7 |
18/5 (EW) 19/5 (EW) |
L 4.2-4.3 KW 7.1, 7.3-5 |
Solvability of dbar for (0,1)-forms with compact support Hartogs phenomenon Cousin I problem |
| 8 |
25/5 (RL) 26/5 (RL) |
KW 7.5-7.6 (supplementary material: GH, H) |
The local dbar-equation The dbar-equation on polydiscs and pseudoconvex domains |
Homework assignments
| Deadline | |
|---|---|
| Assignment 1 | 21/4 |
| Assignment 2 | 4/5 |
| Assignment 3 | 14/5 |
| Assignment 4 | 26/5 |
You hand in the assignment by uploading your solutions under "Assignments" here in Canvas.
Note: The homework assignments are supposed to be handed in individually. You are free to cooperate with other students and to read whatever literature you can find about the subject. However, you are expected to formulate your solutions independently and it is neither allowed to copy from other students nor to copy solutions form any other source.
Recommended exercises
Course summary:
| Date | Details | Due |
|---|---|---|