Review of basic Complex Analysis: Cauchy-Riemann equations, Cauchy’s theorem and estimates, power series expansions, maximum modulus principle, Classification of singularities and calculus of residues. Space of continuous functions, Arzela’s theorem, Spaces of analytic functions, Spaces of meromorphic functions, Riemann mapping theorem, Weierstrass Factorization theorem, Runge’s theorem, Simple connectedness, Mittag-Leffler’s theorem, Analytic continuation, Schwarz reflection principle, Mondromy theorem, Jensen’s formula, Genus and order of an entire function, Hadamard factorization theorem, Little Picard theorem, Great Picard theorem, Harmonic functions.
- L. V. Ahlfors, “Complex Analysis”, Tata McGraw-Hill, 2013.
- J. B. Conway, “Functions of One Complex Variable II”, Graduate Texts in Mathematics 159, Springer-Verlag, 1996.
- W. Rudin, “Real and Complex Analysis”, Tata McGraw-Hill, 2013.
- R. Remmert, “Theory of Complex Functions”, Graduate Texts in Mathematics 122, Springer, 2008.