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 |
| 17.12.24, 18.12.24 | Riemann Mapping Theorem, Montel Theorem | N 25 N 26 |
The following notes are based on this course's lectures but haven't be proofread by the professor. Should you find any mistakes, you're invited to contact the corresponding author.
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 | Solutions 12 | ||
| Mock Exam | Solutions |
| 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 |