28410 - Differential Equations 1

Learning outcomes

At the end of the course the student is familiar with the fundamentals of the theory of ordinary differential equations.He/she can apply the knowledge acquired to solve various types of problems, inherent, in particular, periodic motions and their stability, the evolution of species, radioactive decays.

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. Stability of periodic orbits.

Readings/Bibliography

Parenti Parmeggiani, Algebra lineare ed equazioni differenziali ordinarie, 2nd edition, 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. In case of necessity (due to the persistence of the pandemic), it will be possible to follow the lectures also remotely.

Assessment methods

Oral discussion on the topics treated in the course.

Teaching tools

Some 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