Instructor: Dr. Gergely AMBRUS (and Dr. Máté MATOLCSI, if needed)

Text:  classnotes, handouts and J.B. Conway, Functions of One Complex Variable

Prerequisite: Calculus

Topics:

1.  Elementary properties of complex numbers
2.  Basic functions linear, exponential, complex logarithmz
3.  Analytic functions
4.  Complex integral
5.  Cauchy integral formula, Fundamental Theorem of Algebra
6.  Taylor and Laurent series
7.  Zeros, poles and residues
8.  Applications of residues evaluating integrals, winding number
9.   A further topic: conformal mappings and/or Riemann Surfaces

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.