MA607- Complex Analysis

Submitted by jsjagajit on 19 December, 2019 - 15:51

Course No:

MA607

Credit:

Approval:

2018

PG-Core

Syllabus:

Review of basic Complex Analysis: Cauchy-Riemann equations, Cauchy's theoremand estimates, power series expansions, maximum modulus principle, Classication ofsingularities and calculus of residues; Normal families, Arzela-Ascoli theorem, Riemann mappingtheorem; Weierstrass factorization theorem, Runges theorem, Mittag-Leers theorem;Hadamard factorization theorem, Analytic Continuation, Gamma and Zeta functions

Reference Books:

L. V. Ahlfors, Complex Analysis, Tata McGraw-Hill, 2013.
J. B. Conway, \Functions of one complex variable", Second edition. Graduate Texts in Mathematics, 11. Springer-Verlag, New York-Berlin, 1978.
R. Narasimhan and Y. Nievergelt, \Complex analysis in one variable", Second edition. Birkhuser Boston,Inc., Boston, MA, 2001.
W. Rudin, Real and Complex Analysis, Tata McGraw-Hill, 2013.
Wolfgang Fischer, Ingo Lieb, A Course in Complex Analysis: From Basic Results to Advanced Topics,Springer, 2012
Eberhard Freitag, Rolf Busam, Complex Analysis, Springer, 2005
Stein and Shakarchi, Complex Analysis, Princeton University Press, 2003
Gamelin, Complex Analysis, Springer, 2000

School of Mathematical Sciences

Course