In a lot of branches in science from physics, engineering to ecology, economics, sociology Ordinary Differential Equations (ODEs) are used to describe and understand particular problems. Knowing the existence of solutions to such equations is the first step in the analysis. However, often explicit solutions are not available so that the study of the qualitative behaviour is key to an understanding of the problem.

In this seminar we are giving an introduction into ODEs and the study of their qualitative behaviour. We begin with fundamental existence and uniqueness theorems. As a basis for the qualitative study we discuss linear autonomous and non-autonomous systems of ODEs as well as perturbations of these equations. Furthermore, we will consider stability problems of equilibrium points of ODEs. Throughout the seminar we will discuss particular examples from e.g. physics, ecology, etc.

The Seminar will follow closely parts of the book:

Gerald Teschl, “Ordinary Differential Equations and Dynamical Systems”, Graduate Studies in Mathematics 140, American Mathematical Society 2012

INFO: If you are not familiar with writing in LaTeX, the Mathematics Students Association is organising a preperation course on the 16th and 18th of Spetember.

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