Complex Analysis
Complex numbers, Analytic functions, Cauchy’s integral theorem and integral formula, Power series, Liouville’s theorem, Mean-value and maximum-modulus theorems, Morera’s theorem, Schwarz reflection principle, Isolated singularities, Residue theorem, Contour integration, Moebius transformations, Conformal mappings, the Riemann mapping theorem, Analytic continuation, Schwarz lemma. Recommended books
- Bak, J. and Newman, D. J., Complex Analysis, Springer-Verlag, 1982.
- Ahlfors, L. V., Complex Analysis, McGraw-Hill, 1979.
- Conway, J. B., Functions of a Complex variable, I, Springer-Verlag, 1978.
- Ablowitz, M. J. and Fokas, A. S., Complex Variables, Cambridge Univ. Press, 1998.