Spring 24

Lectures

We
Timeslot:
15:00 - 17:00
Room:
Y27H28 Seats: 50

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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