Duration
30h Th, 10h Pr, 20h Mon. WS
Number of credits
| Master in mathematics (120 ECTS) | 8 crédits | |||
| Master in mathematics (60 ECTS) | 8 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
This course is a sequel to the course on functions of one complex variable for second year students. This year, it will deal with the following subjects:
- Local structure and prolongation of holomorphic functions
- Biholomorphic functions and conformal representation
- Runge, Mittag-Leffler and Weierstrass theorems
- Elliptic integrals and elliptic functions
- Riemann surfaces
- Holomorphic linear differential equations
Learning outcomes of the learning unit
After this course, the students should have understood how to solve a few classical global problems of the theory of holomorphic functions and gathered important tools for a more advanced study of complex analysis.
Prerequisite knowledge and skills
A good knowledge of the results of the theory of holomorphic functions studied during the second year course is essential.
Planned learning activities and teaching methods
The course consists of blackboard lessons, exercises sessions and a personal work.
During the lessons, the main theoretical results are introduced, established and illustrated with examples.
During the exercises sessions, the students are trained to solve by themselves various problems using the results considered in the lessons
The personal work consists of the preparation of a short paper presenting and establishing a result related to the course but not considered during the lessons.
Mode of delivery (face-to-face ; distance-learning)
Face-to-face course.
Recommended or required readings
Lecture notes are handed out to the students at the beginning of the course.
Assessment methods and criteria
An examination comprising an oral part on the theory and a presentation of the personal work is organized during the first session. A similar examination is organized during the second session.
Work placement(s)
Organizational remarks
The course is given during the second quadrimester of odd academic years. It is therefore given in 2017-2018.
Contacts
Jean-Pierre Schneiders Département de Mathématique (Bât. B37, Bureau 1/60) Allée de la Découverte, 12 - 4000 Liège (Sart-Tilman) Phone: (04) 366.94.01 - E-Mail: jpschneiders@ulg.ac.be Web page: http://www.analg.ulg.ac.be/jps/
Items online
Web page of the course
Web page giving access to various informations on the course and to the electronic version of the notes.