Unit MATHEMATICAL PHYSICS II
- Course
- Mathematics
- Study-unit Code
- A002024
- Curriculum
- Didattico-generale
- Teacher
- Francesca Di Patti
- Teachers
-
- Francesca Di Patti
- Hours
- 42 ore - Francesca Di Patti
- CFU
- 6
- Course Regulation
- Coorte 2021
- Offered
- 2021/22
- Learning activities
- Caratterizzante
- Area
- Formazione modellistico-applicativa
- Academic discipline
- MAT/07
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- English
- Contents
- One dimensional flows: flows on a line, bifurcations, flows on the circle. Two-dimensional flows: linear systems, phase plane, limite cycles. Chaos: Lorenz equations, one-dimensional maps. Introduction to Turing patterns.
- Reference texts
- S. H. Strogatz, Nonlinear dynamics and chaos, Westview Press.
E. Ott, Chaos in Dynamical Systems, Cambridge University Press. - Educational objectives
- This course is aimed at newcomers to nonlinear dynamics, chaos and pattern formation. The principal themes of dynamical systems are introduced, both through examples and by explaining and proving fundamental and accessible results. The main goal is to understand behavior of states in a system, given a rule for how the state evolves and to predict the emergence of unexpected dynamics.
- Prerequisites
- The essential prerequisite is single-variable calculus and linear algebra, including curve-sketching, Taylor series, differential equations and eigenvalues and eigenvectors. Basic knowledge of multivariable calculus like partial derivatives, Jacobian matrix and divergence theorems is also recommended.
- Teaching methods
- Lectures on all subjects of the course and respective exercises.
- Learning verification modality
- The oral examination consists on an interview about 2/3 arguments treated during the course. This allows to verify the ability of knowledge and understanding, the ability to apply the acquired skills, the ability to display and learn. Operating time up to 30/45 minutes.