Sequences and series of functions: uniform convergence, power series. Analytic functions: power series, Cauchy’s integral formula. Taylor and Laurent series. Singularities. Residue theorem and applications. Conformal applications. Riemann’s conformal representation theorem. Harmonic functions in the plane. Curvilinear integrals (homotopy).

References:
AHLFORS, L. – Complex Analysis. New York, McGraw-Will, 1966.
CARTAN, H. – Theórie Élementaire des Fonctions Analytiques d’une ou Plusieurs Variables Complexes. Paris, Hermann, 1961.
CONWAY, J. B. – Functions of One Complex Variable, Berlin, Springer-Verlag, 1978.
KNOPP, K. – Theory of Functions, Vol.2, New York, Dover, 1945.
LIMA, E. L. – Curso de Análise. Vol. 2. Rio de Janeiro, IMPA, Projeto Euclides, 1989.

* Basic syllabus. The teacher has the autonomy to make any changes.