**Title of the course:** Some qualitative aspects of ordinary differential equation**
Instructor:** Asst. Prof. Serge Randriambololona

**Institution:**Galatasaray Ü.

**Dates:**14-20 August 2017

**Prerequisites:**Some analysis

**Level:**Graduate, advanced undergraduate, beginning undergraduate

**Abstract:**Contrary to what students may have concluded from their classes on differential equations, most differential equation do not have a "nice" solution (that is, one that can be explicitely written by a simple formula). Furthermore, even when they do have such a "nice" explicit solution, the formula obtained may not give much insight about the "geometric" behaviour of such a solution or on how the solution vary as the equation varies. Qualitative study of differential equations deal with such questions. The course will mainly be interested in 1) theorems of existence, unicity and maximality of solutions and some consequences, and 2) first results concerning planar vector fields.

**Language:**EN