The course introduces some of the most important results in the theory of ordinary differential equations : existence et uniqueness of the Cauchy problem, linear equations, stability of equilibria and resolution methods for some nonlinear equations
Chapter I. Introduction and first definitions.
Chapter II. The Cauchy problem.
Chapter III. Continuation of solutions.
Chapter IV. Continuous dependence with respect to parameters.
Chapter V. Some explicit solutions.
Chapter VI. Linear Ordinary Differential Equations.
Chapter VII. Equilibrium points and local dynamics.
Chapter VIII. Applications: population dynamics.
Chapter IX. Numerical solution of an ODE.
Chapter I. Introduction and first definitions.
Chapter II. Cauchy's problem.
(Chapter III. Extension of solutions).
(Chapter IV. Continued Dependence on Parameters).
Chapter V. Some explicit solutions.
Chapter VI. Linear Ordinary Differential Equations.
Chapter VII. Equilibrium points and local dynamics.
Chapter VIII. Applications: population dynamics.
(Chapter IX. Numerical solution of an ODE).
The chapters between ( ) are normally not covered by the course and are not part of the examination material.
Exercises describe concepts analyzed in the theoretical part. Chapters are :
I. Existence and unicity.
II. ODE of the first order.
III. ODE of higher order with constant coefficients.
IV. Autonomous linear systems.
V. ODE with non-constant coefficients.
VI. Classification of equilibria.
The lectures will be given using both the blackboard and the slides. Some short tests based on wooclap will be proposed to the students
written exam: 3 hours of exercises taken from those seen during the lectures / TD and are in the syllabus
oral exam: presentation on the blackboard of a question of theory in 20-25 minutes, extracted in advance, without notes.
The exam score is calculated as follows:
- if the student takes both examns and obtains at least 2/20 in each one, then the total mark is given by: (2 x Written mark + 1 x Oral mark)/3
- if the student takes both examns and obtains less than 2/20 in at least one or she signs one of the two tests, then the total mark will be 0 (SG)
If the total mark is strictly smaller than 10/20, then the student can keep from one exam session to the next (in the same academic year) the written or oral marks if they are higher than 7/20.
V. Arnol'd : Equations différentielles ordinaires E. Hairer, S.P. Nørsett et G. Wanner : Solving Ordinary Differential Equations I. Nonstiff problems L. Pontriaguine : Equations différentielles ordinaires G. Sansone et R. Conti : Non-linear differential equations Z. Zhang :Qualitative theory of differential equations
| Training | Block | Credits | Mandatory |
|---|---|---|---|
| Additional teaching units for the master's degree in mathematical sciences (200P) | 1 | 5 | No |
| Bachelor in Mathematics | 2 | 5 | Yes |