رياضيات أساسية وتطبيقية

In this course handout, we present the subject entitled Perturbations of dierential

equations, which I taught to second year master's students in fundamental mathematics,

at Echahid Hamma Lakhdar University - El-Oued. With this modest contribution, my goal

is to provide course support that will, I hope, be benecial not only to our master's students,

but also to others whose theory of dierential equations interests them.

This module consists of ve chapters. The rst is an introductory chapter on the theory

of disturbance and all the notions relating to it. The second is devoted to two types of

regular and singular disturbances. The third is on the Lindstedt-Poincaré method, and its

applications. In the fourth chapter another method is presented, that of the average known

as "averaging method". The last one is on the Hopf Bifurcation.