# TMA 4175 - Kompleks analyse - Vår 2009

### Beskjeder

Solution to EXAM PROBLEMS 20/06:exam_soltma_4175_v09.pdf. I think you had done a good job, and it was a pleasure to grade the papers. The grades are submitted to the office. (They are for 00:B, for 01:A, for 04:C, for 05:B, for 07:A, for 08:C, for 11:B, for 19:B, for 21:A.) Have a nice Summer!

• Øvingssett 1. Ch.I: 5.2,7.1,7.4,10.3,11.4,11.5. Ch.II: 3.1(iii), 8.1cd,8.2,16.2,16.3, 16.7.
• Øvingssett 2. Ch.I: 9.1, 14.1. ChII: 6.3. Ch.III: 5.2, 8.1, 8.2, 9.4.
• Øvingssett 3. *problems in Chapters IV and V.
• Øvingssett 4: From Ch.V.16: example 2, problems 1,2,3 and from Ch.VI, problems 7.2 and 12.2.
• Øvingssett 5: 12.2 from last time and from Ch. VII: 5.1,6.1,8.2,11.2,13.1.
• Øvingssett 6(to be discussed 26.03): From Ch.VII: 14.2,16.1,17.2,17.3,18.1,18.2
• Øvingssett 7(to be discussed 05.03): From Ch.VIII:7.1-7.6,(8.3),12.1-12.3
• Øvingssett 8(to be discussed 12.03): 12.1-12.3 from last time, Ch.IX: 5.2-5.3,10.1-10.2
• Øvingssett 9(to be discussed 19.03): 10.1-10.2 from last time, Ch.X: 2.3,4.1,5.1-5.2
• Øvingssett 10(to be discussed 26.03): Ch.X: 10.3,10.5,10.7,11.2,12.2,12.5
• Øvingssett 11(to be discussed 02.04 and NB!16.04): Ch.X: 16.1-16.5,17.2-17.3,19.1-19.2,19.4
• Øvingssett 12 (to be discussed 23.04): 19.1-19.2,19.4 from last time,Ex.problem 5,Aug2007
• Øvingssett 13 (to be discussed 30.04): Gamelin ChX.III:3.3,3.4,3.16,Sarason Ch.IX:17.1-17.3

### Kursbeskrivelse:

"Emnet gir en innføring i grunnleggende teori for kompleks integrasjon, konforme avbildninger og harmoniske funksjoner. Utvalgte videregående emner som f.eks. analytisk fortsettelse, analytisk tallteori, harmoniske funksjoner, interpolasjon og approksimasjon, og anvendelser innen fluid-dynamikk." (Fra studiehandboken)

### Foreleser:

Kari Hag - kari [at] math [dot] ntnu [dot] no, Rom 929 Sentralbygg II.

 Treffetid: Mandag 14-15
Forelesninger: Tirsdag 10-12 i R10, fredag 8-10 i F4
Øving: Torsdag 15-16 i F6 

### Lærebok/Støttelitteratur:

Donald Sarason: "Complex Function Theory".

Theodore W. Gamelin: "Complex Analysis"

Rolf Nevanlinna, Veikko Paatero: "Introduction to Complex Analysis".

Elias M. Stein & Rami Shakarchi: "Complex Analysis"

### Pensum:

Donald Sarason: "Complex Function Theory" (entire book). Here are some class notes on our big theorem, The Riemann Mapping Theorem: Class Notes.

In addition some pages from Fisher and Gamelin: tilleggspensum.pdf. OOPS the Fisher pages didn't come out right. A new version: schwarz-christoffel.pdf

For some general background material see here, and for some pages on connectedness see here.

And don't forget the exercises!

### Evaluering:

Eksamen er fire timer skriftlig og avholdes onsdag den 20. mai. Hjelpemiddelkode D NB! You are allowed to bring notes on an A5-size sheet ("yellow sheet") that has the department stamp on it.