COMPLEX ANALYSIS II
Harmonic and subharmonic functions, Green’s function, and the Dirichlet problem for the Laplacian; the Riemann mapping theorem (revisited) and characterizing simple connectedness in the plane; Picard’s theorem; the inhomogeneous Cauchy–Riemann equations and applications; covering spaces and the monodromy theorem.
Books
- Narasimhan, R., Complex Analysis in One Variable, 1st ed. or 2nd ed. (with Y. Nievergelt), Birkhauser (2nd ed. is available in Indian reprint, 2004)
- Greene, R.E. and Krantz, S.G., Functions Theory of One Complex Variable, 2nd ed., AMS 2002 (available in Indian reprint, 2009, 2011)