Learning outcomes

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 and resolution methods for non linear equations

Content

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.

Table of contents

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.

Exercices

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.

Assessment method

written part : 3 h only exercises oral part : presentation of a question from the course during 10 minutes, the question is drawn before. Note = (2 x written + 1 x oral)/3

Sources, references and any support material

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

Language of instruction

French