Complex numbers and functions. Cauchy theorem and its applications, calculus of residues, expansions of analytic functions, analytic continuation, conformal mapping and Riemann mapping theorem, harmonic functions. Dirichlet principle, Riemann surfaces;
Prerequisites: Undergraduate analysis
Text Book: Functions of One Complex Variable, Second Edition by J. B. Conway
Additional reading: There are a numerous books on complex variable. A classic is Complex Analysis by L. Ahlfors.
QUALIFYING EXAM CONTENT
In Conway: Chapters TBA
1. Starting Mon 1/31, classes will be held in-person in the designated room APM B402A. They will now be recorded by the EVT system and available there. Details about EVT access are TBA.
2. The midterm will be held during the class hour 1-1:50pm on Wed 2/9. It will, however, be remotely given, Zoom proctored, and Gradescope will be used to collect the solutions, as was done in the Fall. Details TBA.
3. This weeks HW deadline will be pushed until after the weekend. Thus, HW3 is due on Mon 1/31.
4. Material for midterm on 2/9: Ch VI, VII.1-3 in Conway.
5. FINAL EXAM on 3/18, 11:30-2:30. Remote via Canvas. Material : Ch VI, VII.1-6, VIII in Conway.