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 |