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, residue calculus | 3.1,3.2,3.3 |
| 8 | Apr 19 | Residue calculus | 3.2 |
| 9 | Apr 22, Apr 26 | Argument principle | 3.4-5 |
| 10 | Apr 29, May 3 | Complex logarithm and Basel problem | 3.6 and 5 |
| 11 | May 6, May 10 | Fourier analysis and harmonic functions | 3.7 and 4.2 |
| 12 | May 13, May 17 | Conformal/Moebius maps | 8.1, 8.2 |
| 13 | May 24 | Riemann's mapping theorem | 8.3 |
| 14 | May 27, May 31 | Riemann's mapping theorem and final review | 8.3 |
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