COMPLEX ANALYSIS
Complex numbers, complex-analytic functions, Cauchy’s integral formula, power series, Liouville’s theorem. The maximum-modulus theorem. Isolated singularities, residue theorem, the Argument Principle, real integrals via contour integration. Mobius transformations, conformal mappings. The Schwarz lemma, automorphisms of the dis. Normal families and Montel’s theorem. The Riemann mapping theorem.
Books
- Ahlfors, L. V., Complex Analysis, McGraw-Hill, 1979.
- Conway, J. B., Functions of One Complex Variable, Springer-veriag, 1978.
- Gamelin, T.W., Complex Analysis, UTM, Springer, 2001.