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Prof. Dr. Jörg Eschmeier

Sebastian Toth

9 ECTS

Monday, 04.05.2020, at 10:15 a.m. via video conference

Monday 10 - 12 a.m., Lecture Hall III, E 2.5 and Thursday, 12 - 14 p.m. , Lecture Hall III, E 2.5

The lecture deals with the general theory of holomorphic funtions in one complex variable. Contents are path integrals, power series, Cauchy's integral theorem, applications of Cauchy's integral theorem, isolated singularities, the residue theorem and conformal maps. As typical applications we will prove the Fundamental Theorem of algebra, see methods how to calculate improper Riemann integrals and prove some results about rational approximation of large classes of holomorphic functions. Complex analysis has important applications in many different areas of mathematics.

Analysis I and II.

Passing of the first or second exam.

Please note that the first and the second exam count as seperate attempts

To be admitted to the exam, you need 50 % of the points achievable in the homework assignments.

Written exam

• Friday, 24.07.2020, 9-12, Lecture Halls I+II+III, E 2.5
• Thursday, 01.10.2020, 9-12, Lecture Halls I+II+III, E 2.5

Until one week before the corresponding exam via LSF.

There are four Tutorial groups. There will be a video conference weekly.

In the tutorial groups, solutions of the homework problems will be presented. You can also ask questions concerning the contents of the lecture as well as past and upcoming exercise sheets.

You can find the lecture notes on the German Homepage.

Every Thursday there will be a new exercise sheet. You can find it on the German Homepage via Material zur Vorlesung -> Übungsblätter. You may submit the solutions for the exercise sheets in groups up to three participants, belonging to the same tutorial group. But, please don't meet in one person. You will submit your solutions every Thursday before the lecture starts in the week after the exercise sheet has been uploaded on the Hompage via E-mail.

• Fischer, Lieb Funktionentheorie, Vieweg
• Lorenz, Funktionentheorie, Spektrum Akademischer Verlag
• Remmert, Funktionentheorie I, II, Springer
• Conway, Functions of one complex variable, Springer
• Fischer, Lieb, A course in complex analysis, Springer