Lecture courses/details
Lectures
Syllabus
This is an indicative syllabus, which will be adapted as we move along. References are given to Stein and Shakarchi's Complex Analysis, Princeton University Press. These references are indicative; we will sometimes deviate from the text. Nonetheless, reading the text and doing the exercises is strongly recommended!
| Week | Dates | Topics | Chapters in [SS] |
| 1 | Feb 19, 23 | Complex numbers/plane/functions | 1.1-2 |
| 2 | Feb 26, Mar 1 | Holomorphic functions, power series | 1.2 |
| 3 | Mar 4, Mar 8 | Path integrals | 1.3 |
| 4 | Mar 11, Mar 15 | Goursat and Cauchy theorems | 2.1-3 |
| 5 | Mar 18, Mar 22 | Cauchy integral formulas, identity theorem | 2.4 |
| 6 | Mar 25 | Singularities | 3.1 |
| 7 | Apr 8, Apr 12 | Singularities | 3.1,3.3 |
| 8 | Apr 19 | Midterm review | |
| 9 | Apr 22, Apr 26 | Residue calculus | 3.2 |
| 10 | Apr 29, May 3 | Further applications | 3.4 |
| 11 | May 6, May 10 | Conformal mappings | 8.1 |
| 12 | May 13, May 17 | Moebius transformations | 8.2 |
| 13 | May 24 | Riemann's mapping theorem | 8.3 |
| 14 | May 27, May 31 | Thurston's conjecture and final review |
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