Course description: Obligatory / Optional

Langugue: English

Credit: 8 ECTS

Topics: 

Complex numbers. Homographies. C-differentiability. Holomorphic functions. Primitive. Integrals over piecewise smooth curves. Cauchy-Goursat theorem. Cauchy formula. Morera theorem. Identity principle. Maximum principle. Cauchy inequalities. Liouville theorem. Weierstrass theorem. Montel theorem. Index. Cauchy-Dixon theorem. Laurent series. Singularities. Sochocki-Casorati-Weierstrass theorem. Residue theorem. Rouche theorem. Conformal mappings. Schwarz lemma. Authomorphisms groups. Riemann theorem. Harmonic functions.

Sample reading list: 

      1. W. Rudin "Real and Complex Analysis" McGraw-Hill, 1987
       
      2. R. Remmert "Theory of complex functions" Springer-Verlag, 1991
     
      3. J. Conway "Functions of one complex variable" Springer-Verlag 1973

Reading/Writing Assignment: Weekly problems sets

Requirements/Grading: Exam

Prerequisites and Restrictions: