MA6120 Advanced Complex Analysis (modified)

Course Details

Unit I: Analytic Continuation, Monodromy theorem, Hurwitz' theorem, Inverse function theorem, Winding number, Simply connected domains. (15 Lectures)

Unit II: Automorphisms of the upper half plane, the unit disc, Schwarz-Pick Lemma, Montel’s theorem, Riemann mapping theorem. (10 Lectures)

Unit III: The Poisson Integral formula, Characterization of harmonic functions, Schwarz Reflection principle, Runge’s theorem, Mittag-Lefler theorem, Infinite products, Weierstrass’ product theorem, Gamma and Zeta functions – a brief introduction. (15 Lectures)

Course References:

Text Books:
1. T.W. Gamelin, Complex Analysis, Springer-Verlag, 2001.
2. S. Ponnusamy and H. Silverman, Complex Variables with Applications, 2006, 524 pp, Birkhaeuser, Boston.

Reference Books:
1. L. Ahlfors: Complex Analysis, 2nd ed., McGraw-Hill,New York, 1966.
2. J.B. Conway, Functions of One Complex Variable, 2nd ed., Springer, 2002.