Holomorphic functions and the
Cauchy-Riemann equations, Power series, Functions defined by power
series as
holomorphic functions, Complex line integrals and Cauchys theorem,
Cauchys integral formula. Representations of holomorphic functions in
terms of power series. Zeroes of analytic
functions, Liouvilles theorem, The fundamental theorem of algebra, The
maximum modulus principle, Schwarzs lemma, The argument principle, The
open mapping property of holomorphic
functions. The calculus of residues and evaluation of integrals using
contour integration.
Reference Texts:
1. D. Sarason: Notes on Complex Function Theory
2. T. W. Gamelin: Complex Analysis
3. J. B. Conway: Functions of one complex Variable
- Teacher: Mathew Joseph