COURSE DESCRIPTION
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
RECENT UPDATES
- 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.