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401-2303-00L 6 Credits BSC D-CHAB , D-MATH , D-PHYS

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Complex Analysis

Funktionentheorie

Lecturers & Examiners: Prof. Dr. Thomas Hans Willwacher

VVZ CR n/a

Last Updated: 2026-02-05 15:47:58

Abstract

Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, special functions, conformal mappings, Riemann mapping theorem.

Objective

Working knowledge of functions of one complex variables; in particular applications of the residue theorem.

Resources

Literature

B. Palka: "An introduction to complex function theory." Undergraduate Texts in Mathematics. Springer-Verlag, 1991. E.M. Stein, R. Shakarchi: Complex Analysis. Princeton University Press, 2010 Th. Gamelin: Complex Analysis. Springer 2001 E. Titchmarsh: The Theory of Functions. Oxford University Press D. Salamon: "Funktionentheorie". Birkhauser, 2011. (In German) L. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co. K.Jaenich: Funktionentheorie. Springer Verlag R.Remmert: Funktionentheorie I. Springer Verlag E.Hille: Analytic Function Theory. AMS Chelsea Publications

General Information

Language: German
Levels: BSC
Frequency: Yearly recurring

Examination

Type: session examination
Mode: written 120 minutes
Aids: Wörterbuch Muttersprache – Deutsch

Die während des Semesters angebotenen Lernelemente messen die aktive Teilnahme am Übungsbetrieb, was in mehreren Teilschritten mit bis zu 0.25 Notenpunkten benotet wird. Dieser Bonus von 0 bis 0.25 wird ungerundet zu der ungerundeten Note aus der Prüfung addiert; das Resultat wird zur Endnote gerundet.Im Prüfungsfach Funktionentheorie wird die Mitarbeit durch je 1 Punkt pro gelöste Übungsaufgabe bewertet. Die im Semester erreichten Punkte werden in einen Notenbonus von maximal 0.25 Notenpunkten umgerechnet.0 bis p Punkte: Notenbonus 0; ab q Punkten: maximaler Notenbonus 0.25; dazwischen: affin linear.Die Punktzahlen p < q werden vom Dozenten festgelegt.

Course Components

Type	Title	Time & Place	Hours
lecture	Funktionentheorie	Tue 10:15-12:00 (NO C 60) Fri 11:15-12:00 (NO C 60)	3 h weekly
exercise	Funktionentheorie Groups are selected in myStudies.	Tue 14:15-16:00 (ETZ E 6) Tue 14:15-16:00 (HG E 33.1) Tue 14:15-16:00 (HG G 26.3) Tue 14:15-16:00 (IFW A 32.1) Tue 14:15-16:00 (LEE C 104) Tue 14:15-16:00 (LEE D 101) Tue 14:15-16:00 (LEE D 105) Tue 14:15-16:00 (LFW C 11) Tue 14:15-16:00 (ML F 38) Tue 14:15-16:00 (ML J 34.3) Tue 14:15-16:00 (NO C 44) Tue 14:15-16:00 (NO C 6)	2 h weekly

Offered In

Mathematics Bachelor
- Bachelor Studies (Programme Regulations 2016)
  - Compulsory Courses
    - Examination Block I (In Examination Block I either the course unit 402-2883-00L Physics III or the course unit 402-2203-01L Classical Mechanics must be chosen and registered for an examination. (Students may also enrol for the other of the two course units; within the ETH Bachelor's programme in mathematics, this other course unit cannot be registered in myStudies for an examination nor can it be recognised for the Bachelor's degree.))
Physics Bachelor
- Bachelor Studies (Programme Regulations 2016)
  - Second and Third Year Compulsory Courses
    - Examination Block I
Interdisciplinary Sciences Bachelor
- Physical-Chemical Direction
  - 3. Semester (Physical-Chemical Direction)
    - Electives (The Bachelor's programme in Interdisciplinary Sciences allows students to choose from any subject taught at a Bachelor level at ETH Zurich. In consultation with the Director of Studies of Interdisciplinary Sciences, every student must establish his/her own individual study programme at the beginning of the 2nd year. See the Programme Regulations 2018 for further details.)