Complex analysis

Course Code :1001WETCRO
Study domain:Mathematics
Academic year:2019-2020
Semester:1st semester
Contact hours:60
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:Dutch
Exam period:exam in the 1st semester
Lecturer(s)David Eelbode

3. Course contents *

The following topics will be treated during the classes:

* the complex numbers and the Riemann sphere

* the notion of a holomorphic function and its properties 

* elementary complex functions

* the integral representation formulae for complex holomorphic functions (Cauchy-Goursat and Cauchy)

* power series representations (Taylor and Laurent series)

* residue calculus and applications

* principle of the argument and Rouché's theorem

* the Moebius group and conformal transformations (Riemann Mapping Theorem)

* harmonic functions in the plane and their link with holomorphic functions