68486 - EQUAZIONI DIFFERENZIALI ORDINARIE

Learning outcomes

At the end of the course the student is familiar with the fundamental notions of the differential and integral calculus for functions of several variables and with related arguments (differential equations, linear integrals, etc). Moreover the student is able to use classical instruments from Mathematical Analysis in several different areas.

Course contents

Ordinary differential equations. Existence, uniqueness, extension of solutions. Dependence on initial data. Linear systems: periodic solutions. Stability of equilibrium points for linear and non-linear systems. Lyapunov function method. Stability for gradient and hamiltonian systems. Stability of periodic orbits. Basics on bifurcation theory.

Readings/Bibliography

Parenti Parmeggiani, Algebra lineare ed equazioni differenziali ordinarie, 2a edizione, Springer.

Shair Ahmad, Antonio Ambrosetti, A textbook for ordinary differential equations, Unitext series, vol. 73, Springer

Gerald Teschl, Ordinary Differential Equations and Dynamical Systems, Providence, American Mathematical Society, 2012

Hirsch, Smale, Devaney, Differential Equations, Dynamical Systems & An Introduction to Chaos, Elsevier, 2004

Teaching methods

Lectures given by the teachers, in class.

Assessment methods

Oral discussion on the topics treated in the course.

Teaching tools

All lectures will be made available online, via pdf files, on the platform Virtuale. Additional material will be made available during the course.

Office hours

See the website of Maria Carla Tesi

See the website of Simonetta Abenda