SUBJECT

Title

Complex functions

Type of instruction

lecture + practical

Level

master

Part of degree program
Credits

3+3

Recommended in

Semesters 1-4

Typically offered in

Autumn/Spring semester

Course description

Complex differentiation. Power series. Elementary functions. Cauchy’s integral theorem and integral formula. Power series representation of regular functions. Laurent expansion. Isolated singularities. Maximum principle. Schwarz lemma and its applications. Residue theorem. Argument principle and its applications. Sequences of regular functions. Linear fractional transformations. Riemann’s conformal mapping theorem. Extension to the boundary. Reflection principle. Picard’s theorem. Mappings of polygons. Functions with prescribed singularities. Integral functions with prescribed zeros. Functions of finite order. Borel exceptional values. Harmonic functions. Dirichlet problem for a disc.

Readings

L. Ahlfors: Complex Analysis, McGraw-Hill Book Company, 1979.