Ordinary Differential Equations
- UE code SMATB222
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Schedule
30 22.5Quarter 1
- ECTS Credits 5
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Language
French
- Teacher Carletti Timoteo
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. Section VIII. Applications: population dynamics. Chapter IX. Numerical solution of an ODE.
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 equilibrium.
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 | Study programme | Block | Credits | Mandatory |
---|---|---|---|---|
Bachelier en sciences informatiques | Standard | 0 | 5 | |
Bachelier en sciences mathématiques | Standard | 0 | 5 | |
Bachelier en sciences informatiques | Standard | 2 | 5 | |
Bachelier en sciences mathématiques | Standard | 2 | 5 |