Advanced Complex Analysis

MATH14-301(i) Advanced Complex Analysis

A good understanding of MATH101 Complex Analysis is an essential prerequisite.

Syllabus: Hadamard’s three circles theorem, Phragmen-Lindelof theorem. The space of continuous functions C(G,Ω), spaces of analytic functions, Hurwitz’s thorem, Montel’s theorem, spaces of meromorphic functions. Riemann mapping theorem, Weiersirass’ factorization theorem, factorization of the sine function. Runge’s theorem, simply connected regions, Mittag-Leffler’s theorem Harmonic functions, maximum and minimum principles, harmonic functions on a disk, Harnack’s theorem, sub-harmonic and super-harmonic functions, maximum and minimum principles, Dirichlet problem, Green’s function. Entire functions. Jensen’s formula, Bloch’s theorem, Picard theorems, Schottky’s theorem.

• • Text: J B Conway, Functions of one complex variables, 2nd ed, Narosa Publishing House, New Delhi, 2002.

  • References.

    • [1] L.V. Ahlfors, Complex Analysis, Mc. Graw Hill Co., New York, 1988.

    • [2] L. Hahn, B. Epstein, Classical Complex Analysis, Jones and Bartlett,

    • India, New Delhi, 2011.

    • [3] W. Rudin, Real and Complex Analysis, McGraw-Hill, 1987

    • [4] D. Ullrich, Complex Made Simple, AMS, 2008

  • Solution Manual by Andreas Kleefeld for Conway's book is here

  • Notes (based on Conway's book) of the lectures given during 2012-13 session is here

  • Lecture Hours: Tuesday to Friday, 10:00an- 11:00am, R5 @ Satyakam Bhawan,New Social Sciences Extension. Building; Tutorial on Mondays (Tutor: Manisha Saini)