Complex analysis and Riemann Surfaces

Course Code :1001WETCRO
Study domain:Mathematics
Academic year:2017-2018
Semester:2nd semester
Sequentiality:Min. 8/20 for Calculus and Metric spaces and calculus.
Contact hours:60
Credits:6
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:Dutch
Exam period:exam in the 2nd 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 (including the relation with conformal mappings and rotational invariance)

* 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

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

* elementary notions from the theory of Riemann surfaces