Funktionentheorie/Complex Analysis Autumn 2024

$$f(z)=\frac{1}{2\pi i}\int_{\gamma}\frac{f(w)}{w-z}\,dw$$
Lecturer
Özlem Imamoglu
Coordinator
Riccardo Plati
Lectures
Tuesdays, 10 to 12, in HG F 7.
Wednesdays, 8 to 9 in ML D 28.

Content

Introduction to Complex Analysis and its applications. Here's the official Course Catalogue page.

Summary of the lectures

Streaming under password protection will be available HERE.
DayContentNotesChapters
17.09.24, 18.09.24 Introduction, examples, holomorphicity, properties of holomorphic functions. Cauchy-Riemann equations. N 1, N 2 Stein_1, Stein_2
24.09.24, 25.09.24 Power Series, line integrals. N 3, N 4 Stein_3, Paper
01.10.24, 02.10.24 Goursat and Cauchy Theorems. N 5, N 6 Stein_4
8.10.24, 9.10.24 Cauchy Theorem and Cauchy integral Formula, Liouville Theorem. N 7, N 8 Stein_5
15.10.24, 16.10.24 Analytic continuation, limit points, order of zeros. N 9 N 10
22.10.24, 23.10.24 Analytic continuation, sequences of holomorphic functions, zeta function, Morera's Theorem. N 11 N 12 Stein_6
29.10.24, 30.10.24 Holomorphic functions by integration, singularities, Riemann's Theorem of removable singularities, poles. N 13 N 14 Stein_7
05.11.24, 06.11.24 Mock exam. Solutions to the mock exam. Mock Exam Solutions
12.11.24, 13.11.24 Residue Theorem, Laurent series for poles with finite order, Applications to real integrals, Meromorphic functions, essential singularities, Casorati-Weierstrass. N 15 N 16
19.11.24, 20.11.24 Stereographic projection, Argument Principle, Rouche' Theorem, example of application for the Fundamental Theorem of Algebra. N 17 N 18 Stein_8
26.11.24, 27.11.24 open mapping Theorem, Maximum modulus Principle, Homotopy and simply connected domains. Homotopy Theorem. N 19 N 20

Exercises

Upload your solutions before the corresponding deadline using the SAM-up tool. In each problem set there will be two starred exercises, each of which can provide up to 1 point. Points will be awarded by the TAs in case of correct solutions or of significant work. At the end of the semester, students who gained a sufficient amount of points will be eligible for a bonus on the final grade of the exam, up to 0.25.

Problem Set Solutions (uploaded on Mondays) Due Date (2:00 PM) Comments
Serie 1 Solutions 1 27.09.24 Corrected typo in 1.6 (b)
Serie 2 Solutions 2 4.10.24
Serie 3 Solutions 3 11.10.24
Serie 4 Solutions 4 18.10.24 Corrected MC (b) and typo in 4.3
Serie 5 Solutions 5 25.10.24
Serie 6 Solutions 6 01.11.24
Serie 7 Solutions 7 08.11.24
Serie 8 Solutions 8 22.11.24 8.4 (b) modified
Serie 9 Solutions 9 30.11.24
Serie 10 06.12.24

Exercise classes

TimeRoomAssistant
Tu 14-16ETZ G 91S. Hartung
Tu 14-16GLC E 24C. Tulej
Tu 14-16HG E 33.1S. Huber
Tu 14-16LEE D 101K. Leuppi
Tu 14-16LEE D 105 (ENG)I. Quarch
Tu 14-16LFW C 11 (ENG)R. Celori
Tu 14-16GLC E 34.1 (ENG)E. Quistad
Tu 14-16ML J 34.3 (ENG)V. Hoffmann
Tu 14-16NO C 6S. de Meyer

Literature