Complex Analysis 2023 jyvaskyla

I will be in the usual room during the usual time on Thursday 18/05 to answer questions. Later that day I will be in Ratkomo 1.30-whatever!

Here are the updated lecture notes with chapters on Laurent Series and Residue Theorem added: Download.

The lectures on April 13 and 14 will be run by Carlos because I will be away for a conference. A DEMO session on Friday 14.

Please read lecture notes as they contain more details and sometimes pictures.

Francesco and Emanuele's Demo 1 on 31.03: Download. I will not upload their future ones here, see their website.

Regarding Demo sessions (on Fridays).

1) You must attend them. Maybe missing one session for legitimate reasons is Ok but no more, please.

2) Future Homework will consist of about 10 questions. Of them, 6 (plus/minus 1) will be marked by a *. You will submit them as HW, in written form, to me, on Thursdays. 

3) The rest of questions, the ones without *, will be done in Demo. When you enter the Demo session, there will be a sheet of paper with the list of none-HW question numbers on them. You will mark which questions you (think) you have solved successfully.

4) Demo teacher will call people to illustrate their solutions.

What else to expect in Demo sessions?

5) When you meet on Friday, you have submitted previous HW already the day before. The next HW is due next Thursday. So, you can ask your Demo teacher for hints for that HW as well

6) On 14/4, you and your Demo teacher will solve HW1 questions (as if they were the none-* questions). Again, you can ask for hints on HW 2 if you want.

7) HW 3 will soon be on website and is due 27.04.

8) It is a good time to be planning for how you want to pass the course. More details about course exam later.

Please do not hesitate to email me with questions.

Yours,

Behnam

The latest updated lecture notes. Section on Möbius maps was edited. Download.

A visual guide to Möbius transformations -- uses Riemann sphere too. 

Riemann Mapping Theorem in action: See how mainland Finland deforms into the unit disk while keeping (locally) angles preserved. Tiny squares are kept (almost) squares throughout the deformation. Master's Thesis of Tommi Pettinen at University of Turku. 

18.3.2023 The first five chapters of notes: downlod here.

The weekly schedule. Download.

Lecture notes for CA2 (in English) coming soon here: I have consulted notes by Kilpeläinen (in Finnish) in preparing these, but there are many new topics. Consult the beautifully written complex analysis 1 notes (in English) by Orponen if you need a brush-up on that material. Specially important notions from CA1 for our purposes will be: Cauchy's integral formula, winding number, Morera's theorem and removability of one singularity, and Schwarz lemma.

Link to Complex Analysis course material by T. Orponen: https://sites.google.com/view/tuomaths/teaching/complex-analysis-i

You must complete a minimum of 30% of homework to be able to take the course exam.

The course exam will have 5 problems for a total of 30 points.

If you get a minimum of 14 then you are eligible for a bonus of 1-5 points based on your homework.

Instead of all of the above, you may decide to take a (much) harder Final exam.

Thursday and Friday meetings are 10.15am-12 at MaD 381. 

There will be exercise sessions on Fridays run alternatingly by two other staff. The first lecture is on March 23 and the last on May 12.

There will be Homework.

In CA2, we continue the study of analytic/holomorphic (complex differentiable) functions. In first part we focus on geometric properties of these functions (open mapping theorem, conformality, the identity theorem, etc.) In second half we go back to Cauchy's theorem and integral formulas and use them to prove that analytic functions have power series representations. From the latter even deeper facts about analytic functions are deduced. All in all it will be filled with elegant theorems and elegant proofs.