# Course

## M652 - Complex Analysis

Course No:
M652
Credit:
4
Approval:
2011
PG-Elective
Syllabus:

Cauchy-Riemann equations, Cauchy's theorem and estimates, Zeros, Poles and Singularities, The open mapping theorem, The argument principle, Maximum modulus principle, Schwarz lemma, Residues and the residue calculus.Normal families, Arzela's theorem, Product developments, functions with prescribed zeroes and poles, Hadamard's theorem, Conformal mappings, Riemann mapping theorem, the linear fractional transformations.

Reference Books:
1. L. V. Ahlfors: Complex analysis (McGraw-Hill), 1978.
2. J. B. Conway: Functions of one complex variable II (Springer), 1995.
3. W. Rudin: Real and Complex Analysis (McGraw-Hill), 1987.
4. R. Remmert: Theory of Complex Functions, Springer 1998.
5. R. V. Churchill and J. W. Brown: Complex Variables and Applications (McGraw-Hill).