Mathematical Methods and Models for the Applications

A.Y. 2019/2020
Overall hours
Learning objectives
The course aims at providing the fundamentals of models, methods and mathematical tools used in connection with applicative problems. This will be pursued with the aid of laboratory sessions, where suitable numerical schemes will be developed.
Expected learning outcomes
At the end of the course, the students should be able to study some mathematical models arising from applicative problems, and should be able to develop suitable numerical tools supprting the aforementioned study.
Course syllabus and organization

Unique edition

Lesson period
First semester
Course syllabus
1. One dimensional discrete systems: fixed points and periodic orbits; attractors and repulsors; stability; bifurcations; logistic model of population dynamics; chaotic and symbolic dynamics.

2. Two dimensional systems: stationary orbits; linear systems; stability of equilibria; asymptotic orbits; strange attractors; relations with differential equations; Poincare' index and section; bifurcations.

3. Oscillations: forced and dumped linear systems; nonlinear oscillations; averaging method; limit cycles and Van der Pol oscillator; synchronization; resonances; Henon-Heiles model.

4. Chaotic behaviour: hyperbolic maps and shadowing lemma; homoclinic points; symbolic dynamics.
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
: 24 hours
Lessons: 36 hours