Introduction to Complex Analysis and its applications. Here the official Course Catalogue page.
| Day | Content | Notes | Chapters |
|---|---|---|---|
| 19.09.23, 20.09.23 | Introduction, examples, holomorphicity, properties of holomorphic functions. Cauchy-Riemann equations. | N 1, N 2 | Stein_1 Stein_2 |
| 26.09.23, 27.09.23 | Power Series, line integrals. | N 3, N 4 | Stein_3 |
| 03.10.23, 04.10.23 | Goursat and Cauchy Theorems. | N 5, N 6 | Stein_4 |
| 10.10.23, 11.10.23 | Cauchy Theorem and Cauchy integral Formula, Liouville Theorem. | N 7, N 8 | Stein_5 |
| 17.10.23, 18.10.23 | Analytic continuation, limit points, order of zeros. | N 9 N 10 | |
| 24.10.23, 25.10.23 | Analytic continuation, sequences of holomorphic functions, zeta function, Morera's Theorem. | N 11 N 12 | Stein_6 |
| 31.10.23, 01.11.23 | Holomorphic functions by integration, singularities, Riemann's Theorem of removable singularities, poles. | N 13 N 14 | Stein_7 |
| 07.11.23, 08.11.23 | Residue Theorem, Laurent series for poles with finite order, Applications to real integrals. | N 15 N 16 | |
| 14.11.23, 15.11.23 | Meromorphic functions, essential singularities, Casorati-Weierstrass, stereographic projection, Argument Principle. | N 17 N 18 | |
| 21.11.23, 22.11.23 | Rouche' Theorem, example of application for the Fundamental Theorem of Algebra, open mapping Theorem, Maximum modulus Principle, Homotopy and simply connected domains. Homotopy Theorem. | N 19 N 20 | Stein_8 |
| 28.11.23, 29.11.23 | The Homotopy Theorem, symply connectedness, primitives, Complex Logarithm, Principal branch. | N 21 N 22 | |
| 05.12.23, 06.12.23 | Winding numbers, conformal maps, conformal equivalences. | N 23 N 24 Update for N 24: continuity of \(f^{-1}\) (p. 244) | Stein_9 |
| 12.12.23, 13.12.23 | Riemann Mapping Theorem | N 25 N 26 | |
| 19.12.23, 20.12.23 | Riemann Mapping Theorem, Montel Theorem | N 27 N 28 Zeta function |
Upload your solutions before the corresponding deadline using the SAM-up tool. Only the exercises marked with a star will be graded and are eligible (in case of significant work on them) for bonus points.
| exercise sheet | solutions | deadline (2pm of) | comments |
|---|---|---|---|
| Serie 1 | Solutions 1 | 26.09.23 | |
| Serie 2 | Solutions 2 | 10.10.23 | |
| Serie 3 | Solutions 3 | 17.10.23 | Small typo in 3.3, rescaled contour in the diagonal. |
| Serie 4 | Solutions 4 | 24.10.23 | |
| Serie 5 | Solutions 5 | 31.10.23 | |
| Serie 6 | Solutions 6 | 07.11.23 | Corrected typo in 6.3: the domain has to be connected |
| Serie 7 | Solutions 7 | 14.11.23 | |
| Serie 8 | Solutions 8 | 21.11.23 | |
| Serie 9 | Solutions 9 | 28.11.23 | |
| Serie 10 | Solutions 10 | 05.12.23 | |
| Serie 11 | Solutions 11 | 12.12.23 | |
| Serie 12 | Solutions 12 | 19.12.23 | |
| Mock Exam | Solutions |
| time | room | assistant |
|---|---|---|
| Tu 14-16 | ETZ G 91 | U. Faure |
| Tu 14-16 | HG E 33.1 | J. Meng |
| Tu 14-16 | LEE D 101 | L. Renkin |
| Tu 14-16 | LEE D 105 | D. Schwenkreis |
| Tu 14-16 | LFW C 11 | J. Adolff |
| Tu 14-16 | ML F 38 | K. Stössel |
| Tu 14-16 | ML J 34.3 | V. Hoffmann |
| Tu 14-16 | NO C 44 | M. Vassilev |
| Tu 14-16 | NO C 6 | J. Collombon |