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
Differential equations of order two on manifold and linear connections
On studies the geometrical counter part over a smooth manifold of an ordinary differential equation of order two. Special attention is paid to the case of isochronal equation and their exponential map. This very general concept has many useful particular cases: exponential map of Lie groups, exponential map of matrices, of real or complex numbers, affine maps. It leads to the notion of geodesics. Various charactrizations of a second order differential equation are proposed, among which horizontal distributions on the tangent bundle, the case of linear connection corresponding to isochronal equations that can also be described using covariant derivatives. Flat linear connections are also studied.
Learning outcomes of the learning unit
Prerequisite knowledge and skills
Elements of differential geometry.
Planned learning activities and teaching methods
Mode of delivery (face-to-face ; distance-learning)
Details are given at the beginning of the academic year.
Recommended or required readings
A pdf file is avaiable at the http://www.geothalg.ulg.ac.be/GD_Option_I.pdf
Assessment methods and criteria
Practical organization to be discussed with the student.