Subject Code: MA7L003 Subject Name:  Advanced Complex Analysis L-T-P: 3-1-0 Credit:4
Pre-requisite(s):  Complex Analysis (MA5L007)
Series and product developments: Power series expansions, Partial fractions and factorizations; Entire functions: The Hadamard’s theorem, Jensen’s formula, The Riemann zeta function; Normal families: Equicontinuity, Normality and compactness, Arzela’s theore; Analytic  continuation and Riemann surfaces: Germs and sheaves, Analytic continuations along arcs, Homotopic curves, The monodromy theorem, Branch points, Algebraic functions; Picard’s theorem: Lacunary values;  The  Reimann mapping theorem;The Dirichlet problem; Canonical mappings of multiply connected regions;  Elliptic functions and Weierstrass Theory; Basic results on univalent functions; The range of analytic functions: Bloch’s theorem, Schottky’s theorem;
Text Books:
  1. Ahlfors L. Complex Analysis, McGraw-Hill
  2. Peter L Duren, Univalent Functions, Springer-Verlag
Reference Books:
  1. Conway J. B.  Functions of One Complex variable-II,  Springer-Verlag
  2. Pommerenke C. Boundary Behaviour of Conformal Maps, Springer
  3. Rudin W. Real and Complex Analysis, TataMcGraw-Hill