italian version

Aims :

We want to give basic knowledge about various ordinary differential equations, and related problems. The theory is developed with analytical, numerical solutions and qualitative analysis. Concrete examples and geometric intuition are stressed

Prerequisiti:

Basic knowledge of Mathematical Analysis and Geometry.

Topics :

Ordinary differential equations: initial and boundary value problem, existence and uniqueness of solutions. Study of some differential equations related to concrete problems, linear equations with constant coefficients or not, first order linear systems and their classification. Numerical solutions: one-step and multi-steps methods. Non linear dynamics: starting with one-dimensional flows , higher-dimensional phase spaces are studied: bifurcation analysis and chaotical evolution are introduced.

Textbooks :

C. King, J. Billingham: “Differential Equations” Cambridge University Press
S.H. Strogatz “Nonlinear Dynamics and Chaos” Addison- Wesley Publishing Company
Saranno distribuiti appunti durante il corso
Lecture notes will be distributed

Exam :

The examination consists in an oral discussion