Duration
25h Th, 25h Pr
Number of credits
| Bachelor in mathematics | 5 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
The first part of the course is devoted to the local theory of systems of non-linear equations (implicit functions, rank theorem, Morse lemma, ...).
The second part contains a detailed study of systems of ordinary differential equations (existence and uniqueness of local and global solutions, special properties of autonomous and linear systems, dependance on initial conditions, ...)
Learning outcomes of the learning unit
At the end of the course, the students should have understood completely the results presented during the lectures. They should be able to establish these results and to use them to solve various problems.
Prerequisite knowledge and skills
A good understanding of the previous analysis, algebra and geometry courses is essential.
Planned learning activities and teaching methods
The course consists of blackboard lessons and exercises sessions.
During the lessons, the main theoretical results are introduced, established and illustrated with examples. Mathematica software is also used to clarify some points.
During the exercises sessions, the students are trained to solve by themselves various problems using the results considered in the lessons.
Mode of delivery (face-to-face ; distance-learning)
Face-to-face course
Recommended or required readings
Lecture notes are handed out to students at the beginning of the course.
Assessment methods and criteria
An examination comprising an oral part on the theory and a written part on the exercices is organized during the first session.
A similar examination is organized during the second session.
Work placement(s)
Organizational remarks
The course follows the official schedule handed out to the students at the beginning of the academic year.
Contacts
Jean-Pierre Schneiders Département de Mathématique (Build. B37, Office 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.