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
- Midterm via Canvas on Wednesday Nov 3 during class hour. Material Ch I-III in Conway.
- Excluded material: In Ch. III.3: Symmetry and Orientation Principles. In Ch. IV.1: Bounded variation, rectifiable curves.