After successful completion of the course, students are able to explain and apply the basic concepts of complex analysis. In particular, they are able

• to describe the notion of holomorphy in different ways,
• to define what conformal and biholomorphic maps are,
• to explain the notion of homotopy,
• to state and apply different versions of the Cauchy theorem,
• to exlain the notion of analytic continuation, the monodromy theorem and the concept of a Riemann surface,
• to explain and prove the Riemann mapping theorem.

Complex differentiation, Cauchy's theorem, isolated singularities, calculus of residues with applications, conformal mappings, Riemannian mapping theorem.

Mathematical definitions and proofs

Written exam with problems similar to the problems in the recitation class and questions on definitions, theorems and proofs. Oral exam with questions on definitions, theorems and proofs.

Basic knowlegde of analysis