Équations différentielles ordinaires
Section outline
-
University: Djilali Bounaama University of Khemis Miliana
Faculty: Faculty of Materials Science and Computer Science
Department: Department of Mathematics
Level: Master 1 (Mathematics)
Course Title: Ordinary Differential Equations
Semester: Semester 1
Credits: 5
Coefficient: 3
Lecturer: Dr. Fouzia CHITA
Academic Degree: PhD in Differential Equations
Academic Rank: Associate Professor (MCA)
Contact: You may contact me at the following email address: f.chita@univ-dbkm.dz
-
Course Objectives:
The main objective of this course is to study Cauchy problems in infinite-dimensional Banach spaces. Fixed point theory constitutes a very important tool in this context. Some stability problems will also be examined.Recommended Prerequisites:
Standard undergraduate-level courses.Course Content:
-
General topics on differential equations
-
Concept of a solution and types of solutions (local, maximal, global, and saturated solutions).
-
Qualitative study of ordinary differential equations in finite dimensions (Peano’s theorem and the Cauchy–Lipschitz theorem).
-
Qualitative study of ordinary differential equations in infinite dimensions (Peano’s theorem and the Cauchy–Lipschitz theorem).
-
-
Constrained ordinary differential equations
-
Bouligand–Severi tangent cone.
-
Other types of tangent cones.
-
Nagumo’s theorem.
-
-
Stability theory
-
General concepts.
-
Stability of linear differential systems.
-
Stability in the sense of Lyapunov.
-
Assessment Method:
Examination (60%), continuous assessment (40%).References:
-
I. I. Vrabie, Differential Equations, World Scientific Publishing, 2011.
-
V. I. Arnold, Ordinary Differential Equations, Springer, 1992.
-