Introduction to Complex Analysis and its applications. Here's the official Course Catalogue page.
| Day | Content | Notes | Chapters |
|---|---|---|---|
| 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 | |
| 3.12.24, 4.12.24 | The Homotopy Theorem, symply connectedness, primitives, Complex Logarithm, Principal branch, Winding numbers. | N 21 N 22 | |
| 10.12.24, 11.12.24 | Conformal maps, conformal equivalence, Riemann Mapping Theorem, Schwarz Lemma | N 23 N 24 | Stein_9 |
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 | Solutions 10 | 06.12.24 | |
| Serie 11 | Solutions 11 | 13.12.24 | In 11.3, \(4\pi\) instead of \(3\pi\) |
| Serie 12 |
| Time | Room | Assistant |
|---|---|---|
| Tu 14-16 | ETZ G 91 | S. Hartung |
| Tu 14-16 | GLC E 24 | C. Tulej |
| Tu 14-16 | HG E 33.1 | S. Huber |
| Tu 14-16 | LEE D 101 | K. Leuppi |
| Tu 14-16 | LEE D 105 (ENG) | I. Quarch |
| Tu 14-16 | LFW C 11 (ENG) | R. Celori |
| Tu 14-16 | GLC E 34.1 (ENG) | E. Quistad |
| Tu 14-16 | ML J 34.3 (ENG) | V. Hoffmann |
| Tu 14-16 | NO C 6 | S. de Meyer |