Applications of the residue theorem, Montel's theorem, Cauchy-estimates, solutions to d-bar, Runge's theorem, Cousin I and II, Ahlfors-Schwarz-Pick Lemma, Riemann Mapping Theorem, Möbius ...

Central themes in the course are analytic and harmonic functions and their properties, power series and Laurent series, isolated singularities, Cauchy´s integral theorem and residue calculus, the ...

Sequences of real numbers, the notion of convergence of a sequence, completeness, the Bolzano-Weierstrass theorem, limits of series of non-negative reals and convergence tests. Analytical definition ...