Course Code : | 1001WETCRO |

Study domain: | Mathematics |

Academic year: | 2019-2020 |

Semester: | 1st semester |

Sequentiality: | - |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 1st semester |

Lecturer(s) | David Eelbode |

At the start of this course the student should have acquired the following competences:

an active knowledge of

an active knowledge of

- Dutch

The student should have some notions about he following topics: convergence of series, limit theorems, continuity, power series (all treated in the courses mentioned below).

*Sequentiality

Calculus and Sets (1BWIS-032) AND Metric spaces and differential calculus (1BWIS-042)

- being able to reconstruct proofs from the course notes
- being able to understand a given proof for theorems which were not covered during the classes
- being able to solve exercises related to the theory

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

Class contact teachingLectures Practice sessions

Personal workExercises

Personal work

ExaminationWritten with oral presentation Open book Open-question

1. Course text (in Dutch)

2. extra slides may be handed out during classes (possibly in English)

(see https://cursussen.uantwerpen.be)

David Eelbode: e-mail: david.eelbode@uantwerpen.be (G. 312)