 Complex numbers, open sets in the plane.
 Continuity of functions of a complex variable
 Derivative at a point and Cauchy–Riemann equations
 Analytic functions; example of power series and elementary functions
 Cauchy’s theorem and applications.
 Cauchy’s formula and power series expansions
 Morera’s theorem
 Existence of a logarithm and of a square root
 Liouville’s theorem and the fundamental theorem of algebra
 Laurent series and classification of isolated singular points. The residue theorem
 Harmonic functions
 Schwarz’ lemma and applications
 Some ideas on conformal mappings
 Computations of integrals
University course catalogue: 201.1.0071

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