250064 VO Advanced complex analysis (2024W)
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Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
- Tuesday 01.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Friday 04.10. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 08.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Tuesday 15.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Friday 18.10. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 22.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Tuesday 29.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Tuesday 05.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Tuesday 12.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Friday 15.11. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 19.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Tuesday 26.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Friday 29.11. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 03.12. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Tuesday 10.12. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Friday 13.12. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 17.12. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Tuesday 07.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Friday 10.01. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 14.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Tuesday 21.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
- Friday 24.01. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 28.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Information
Aims, contents and method of the course
The course is a continuation of the bachelor course on complex analysis and will treat advanced topics that are part of the classical material in complex analysis.Topics: homology, homotopy, winding numbers, characterization of simple connectivity on the plane, the Fourier transform and Paley-Wiener theorems, entire functions and order of growth, Jensen's formula, factorization of analytic functions, theorems of Weierstrass, Hadamard, Mittag-Leffler, approximation theorem of Runge, meromorphic functions, Riemann mapping theorem, extension of conformal equivalences to the boundary, analytic continuation and special functions (Gamma, Theta, Zeta), bounded functions on the unit disk and their zeros, Blaschke products, the prime number theorem.There is an accompanying problem seminar class.Prerequisites: analytic functions and their characterization, line integrals and Cauchy's integral theorem, residue theorem, singularities, Laurent series.
Assessment and permitted materials
The course assessment for the lecture (VO) will be via an oral examination at the end of the course. The course assessment for the tutorials (PS) will be via participation (solving/presenting assigned problems) during the problem seminar.
Minimum requirements and assessment criteria
Satisfactory answer of questions about course’s topics and solution of problems.
To pass, at least half of the questions need to be answered correctly.Theoretical list of grades:
88-100 sehr gut
75-87 gut
62-74 befriedigend
50-61 genuegend
<50 nicht genuegend
To pass, at least half of the questions need to be answered correctly.Theoretical list of grades:
88-100 sehr gut
75-87 gut
62-74 befriedigend
50-61 genuegend
<50 nicht genuegend
Examination topics
Entire course material
Reading list
John B. Conway, Functions of one complex variable I
E. Stein, R. Shakarchi, Princeton Lectures on Analysis, Vol. 2
W. Schlag, A Course in Complex Analysis and Riemann Surfaces, AMS, Providence, 2014.
L. Ahlfors, Complex analysis
B. Simon, Basic complex analysis
W. Rudin, Real and complex analysis
E. Stein, R. Shakarchi, Princeton Lectures on Analysis, Vol. 2
W. Schlag, A Course in Complex Analysis and Riemann Surfaces, AMS, Providence, 2014.
L. Ahlfors, Complex analysis
B. Simon, Basic complex analysis
W. Rudin, Real and complex analysis
Association in the course directory
MANK
Last modified: Sa 22.03.2025 09:46