TMA 4175 - Complex Analysis - Spring 2017
Yurii Lyubarskii - yura [at] math [dot] ntnu [dot] no, Room 954 Sentralbygg II
- Lectures: Mondays 08:15-10:00, S24, Wednesdays 12:15-14:00 room 734 SB2
- Exercise sessions: Tuesday 17:15-18:00, R50
- Office hours: Monday 10:15-11:00, or by appointment
- Exam: May, 31.
07.06.2017 EXAM TEXT
31.05.2017 EXAM SOLUTIONS (updated)
14.05.2017. TRAINING SET FOR RESIDUES AND INTEGRALS TRAINING SET 1
15.05.2017. TRAINING SET FOR CONFORMAL MAPPINGS TRAINING SET 2 (more to follow)
15.05.2017. PREEXAM MEETINGS (all meetings in my office, SB2, room 954, all start at 13:00 )
19.05, 29.05, 30.05
17.05.2017 TEST EXAM TEST EXAM is on the web. No solutions will be published. You are welcome to come during preexam meetings or by appointment. Have good 17th Mai !
09.01. Mention new lecture schedule!
17.01. I was asked to put information regarding IEASTE jobs on the course webpage. Here is the link: www.facebook.com/INTrondheim
01.02. Additional lecture on Wednesday, 08.02 14:15-16:00. Room 922 SB2
20.02. Additional hour lecture on Wednesday 22.02. 1415-15:00. Room 922 SB2
06.03. Additional hour lecture on Wednesday 08.03. 1415-15:00. Room 922 SB2
What you are expected to know from Matte4K
This is a short list of preliminary knowledge, the most of stuff will be reminded briefly
Lars V. Ahlfors. Complex Analysis, 3rd edition. The book can be found on amazon.co.uk
Theodore W. Gamelin: "Complex Analysis".
On lecture 7 we covered only first 5 pages of notes. This is mainly reminder with some more details of what you had
We will continue on the next lecture.
01.02. Lecture 08. Todays lecture includes the second part of lecture notes prepared for lecture 7. The material can be found in sections 3.3, 3.4 Ch.4 of Ahlfors book.
Lecture 18, 08.03: Hyperbolic metric - handouts
Lecture 19, 13.03: Normal families, we follow Ahlfors book Chapter 5, 4.1-4.4
Lecture 20, 15.03: Hurwitz theorem, Univalent functions, handouts (Gamelin Ch.VIII, Sec. 3,4)
Lectures 21 and 22, 20.03 and 22.03: Riemann mapping theorem, proof. Ahlfors Ch. 6, Sec.1.1 or Gamelin Ch. XI, Sec. 6.
(We did follow proof in Gamelin, but the proofs are not very different)
Dirichlet problem, Mapping of concentric annuli
Short notes: univalent functions, proof of Riemannmapping theorem
Lecture 23, 27.03. Meromorphic functions, Mittag-Leffler theorem (for the plane), handouts, Gamelin Ch. XIII, Sec.2
Lecture 24, 29.03. Entire functions, Infinite products, Weierstrass theorem (handouts), Gamelin Ch. XIII, Sec, 3,4
Lecture 25, 03.04: Plane stationary flow of ideal fluid. (handouts), Gamelin, Ch. XI, Sec. 4
Lecture 26, 05.04: Fluid dynamic continuation. calculating the lifting force (handouts) Lectures 25,26 notes
* 11.01. Ahlfors, Ch.3: Sec 1.2 # 4, 7; Sec. 1.3: 1-4; Sec. 1.4: 2-5
* 25.01. Ahlfors, Ch.4: Sec.3.2 # 1 - 5
* 08.02 Gamelin, Ch. 2 (Printout distributed on the lecture) Sec. 6: # 4,5,6(this one may be difficult), Sec.7: 1a,g, 2,3,5,9
* 22.02 Gamelin, Ch.7 (Printouts distributed on the lecture) Sec.1: # 1g, 2b, 3d; Sec.2: # 4,7; Sec.3: # 3; Sec.4: #2
* 01.03 Gamelin, Ch.7 (Printouts distributed on the lecture) Sec.4: # 4, 5, 8; Sec. 5 # 1, 4; Sec. 6: 3, 4; Sec. 7: # 1,4; Sec. 8: #1 a,e,f; 3.
* 08.03 Exercise set
This set (as well as most of those to follow) is a bit more demanding. You are welcome to ask questions (problem hour or whatever)
Content of the course (This section is under construction)
Below I describe the content of the lectures and refer to the corresponding sections in
the books of Ahlfors and Gamelin,
where the corresponding material can be found. Typically we cover just parts of the corresponding sections. Please check
with yours notes or lecture notes on the web.
It is assumed that you know Complex analysis part from Matte4K (see what to know list)
Elementary point set topology:
Ahlfors, Ch. 3, Sections 1.2-1.5
Refreshing analytic functions (with a bit of new material):
Ahlfors: Ch.2: 2.1 - 2.3 and 3.1 -3.4; Ch.3: 2.1 -2.3; Ch.4: 2.1 -2.3 and 3.1 - 3.4; Ch.5: 1.2 -1.3
Gamelin: Ch.2, 1-3; Ch.3 1-2; Ch.4 1-4; Ch.5, 1-5
Gamelin, Ch.7 or Ahlfors Ch.4, Section 5.3,
see also lecture notes regarding Lagrange interpolation.
Gamelin, Ch3, 1-5, Ch10, 1-2; Ahlfors Ch.4, Sec. 6.1-6.4
Schwarz lemma and hyperbolic geometry.
Gamelin, Ch 9.
Ahlfors, Ch 5, Sec.4