Course No
MA607
Credit
8
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