Duration
30h Th, 10h Pr, 20h Mon. WS
Number of credits
| Master in mathematics (120 ECTS) (Odd years, organized in 2023-2024) | 8 crédits | |||
| Master in mathematics (60 ECTS) (Odd years, organized in 2023-2024) | 8 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the second semester
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 third year or master students. Its content may vary but here are a few typical 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 local theory of holomorphic functions 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, hybrid learning)
Face-to-face course
Recommended or required readings
Lecture notes are handed out to the students at the beginning of the course.
Exam(s) in session
Any session
- In-person
oral exam
Written work / report
Additional information:
The report consists of a written presentation of a result in complex analysis not considered during the course and chosen in agreement with the professor. It can be prepared by groups of two students.
The oral exam includes two questions on the theory and a discussion on the report.
Work placement(s)
Organisational remarks and main changes to the course
The course is given during the second quadrimester of odd academic years. It is therefore given in 2021-2022.
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@uliege.be Web page: http://www.analg.ulg.ac.be/jps/