Instructor: Dr. Károly BÖRÖCZKY

Text:  J.B. Conway,  Functions of One Complex Variable (Springer)+  handout about Riemann mapping theorem

Prerequisite: Calculus

Topics:

1.  Elementary properties of complex numbers
2.  Basic functions linear, exponential, branches of Öz
3.  Analytic functions
4.  Complex integral
5.  Cauchy integral formula, Fundamental Theorem of Algebra
6.  Taylor and Laurent series
7.  Applications: Harmonic functions, Dirichlet problem
8.  Zeros, poles and residues
9.  Applications of residues evaluating integrals, winding number
10. Riemann mapping theorem (handout)

This is an introductory course. The aim of this course is to present and illustrate the basic methods and to show various applications of
the theory of complex analytic functions.