2023-2024 / MATH0220-2

Complements to complex analysis

Duration

30h Th, 10h Pr, 20h Mon. WS

Number of credits

 Master in mathematics (120 ECTS) (Odd years, organized in 2023-2024) 8 crédits 

Lecturer

Jean-Pierre Schneiders

Language(s) of instruction

French language

Organisation and examination

Teaching in the second semester

Schedule

Schedule online

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/

Association of one or more MOOCs