Lectures
Tuesday 10:00-11:00 AM
Wednesday 10:00-10:55 AM
Friday 11:00-11:55 AM
Office hours: Wednesday 5-6 PM
Homework
Weekly homework problems will be uploaded here.
TA
Dr Rajas Sandeep Sompurkar. Office hours: Wednesday 3-4 PM
Contents
The complex plane and elementary functions, The extended complex plane, fractional linear transformations. Holomorphic functions, Cauchy-Riemann equations, harmonic functions. Complex line integrals, Cauchy’s theorem, Cauchy’s integral formula, Mean value property, Liouville’s theorem, Morera’s theorem. Power series expansion, zeros of a holomorphic function. Maximum modulus principle, Schwarz lemma, automorphisms of the disc. Open and local mapping theorems, Inverse function theorem. Isolated singularities, Laurent series expansion, classification of singularities. Residue theorem, evaluation of integrals. The argument principle, Rouche’s theorem, Hurwitz’s theorem. Riemann mapping theorem.
Textbook
S. Kumaresan, A Pathway to Complex Analysis
References
1. T. W. Gamelin, Complex Analysis
2. L. V. Ahlfors, Complex Analysis
2. J. B. Conway, Functions of one complex variable
3. R. Remmert, Theory of complex functions
4. E. M. Stein and Rami Shakarchi, Complex Analysis
Evaluation
End-sem 35%
Mid-sem 35%
Quizzes, Assignment 30%.