250011 VO Ordinary differential equations (2013W)

Whatever you may want to model, in physcis, biology, engineering or economy, usually it will be by means of differential equations. This course is an introduction to the theory of ordinary differential equations, with an outlook on dynamical systems (evolution equations). The latter is less about finding the explicit solutions (which is possible only in the most simple cases anyhow), but more about the qualitative properties of solutions (e.g. the long-term behaviour). The themes of this course include:
- Specific solving methods;
- Existence and uniqueness results for the solution of differential equations;
- Solution of linear systems of differential equations;
- Interpretation of differential equations as dynamical systems;
- Classification of equilibrium points (Hartman-Grobman Theorem);