(Additional )Prerequisite courses for Undergraduates: UM 204
Complex numbers, holomorphic and analytic functions, Cauchy-Riemann equations, Cauchy’s integral formula, Liouville’s theorem and proof of fundamental theorem of algebra, the maximum-modulus principle. Isolated singularities, residue theorem, Argument Principle. Mobius transformations, conformal mappings, Schwarz lemma, automorphisms of the disc and complex plane. Normal families and Montel’s theorem. The Riemann mapping theorem. If time permits - analytic continuation and/or Picard’s theorem.
Suggested books and references:
Ahlfors, L. V., Complex Analysis, McGraw-Hill, 1979.
Conway, J. B., Functions of One Complex Variable, Springer-veriag, 1978.