Complex Analysis Math 5821



Holomorphic functions, definitions and proprieties…     Uniqueness theorems, maximum principle, Schwarz’s lemma… Automorphism groups,  open  mapping  theorem, Integrals along paths and singularities…General Cauchy's formula and Residue theorem…Laurent's series… Conformal mappingsHurwitz’s theorem, Montel’s theorem, Simply connected domains and Riemann’s theorem, Harmonic functions and the Dirichlet problem, Infinite product of holomorphic functions, Analytic continuation