Theory of Functions of a Complex Variable I
Cauchy's theorem and contour integration; the argument principle; maximum modulus principle; Schwarz symmetry principle; analytic continuation; monodromy theorem; applications to the gamma function and Riemann's zeta function; entire and meromorphic functions; conformal mapping; Riemann mapping theorem; univalent functions.
Complex Analysis, Ahlfors, McGraw-Hill.
MATH 766 or concurrent.
- Complex Numbers
- Complex Functions
- Analytic functions as mappings
- Complex Integration
- Series Development
- Additional Topics
(Sheu 2006 )