Complex Analysis

Code: MA741 | L-T-P-C: 4-0-0-8

MA741 Complex Analysis L-T-P-C [4-0-0-8]

Prerequisites: Nil

Analytic functions, properties of elementary analytic functions. Complex integration, Cauchy's theorem, Liouville's theorem, power series representation, open mapping theorem, calculus of residues. Harmonic functions, Poisson integral, Harnack's theorem, Schwarz reflection principle. Maximum modulus principle, Schwarz lemma, Phragmen-Lindelof method. Runge's theorem, Mittag-Leffler theorem, Weierstrass theorem, Jensen's formula, Hadamard's theorem. Analytic continuation, monodromy theorem. Equicontinuous, Normal families, Arzela's theorem, Riemann mapping theorem and its consequences.

Texts/References:

1. L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1979.
2. J. B. Conway, Functions of One Complex Variable, 2nd Edition, Springer/Narosa, 1978.
3. S. Lang, Complex Analysis, 4th Edition, Springer, 1999.
4. R. Narasimhan and Y. Nievergelt, Complex Analysis in One Variable, Birkhauser, 2001.
5. R. Remmert, Theory of Complex Functions, Springer (India), 2005.
6. T. W. Gamelin, Complex Analysis, UTM, Springer, 2003.