Vai al contenuto principale Vai al footer
Università degli Studi di Parma Università degli Studi di Parma
Degree course in
Mathematics
Università degli Studi di Parma
Department of Mathematical, Physical and Computer Sciences

MODELS OF PHYSICAL MATHEMATICS
cod. 18975

Academic year 2017/18
3° year of course - Second semester
Professor
Maria GROPPI
Academic discipline
Fisica matematica (MAT/07)
Field
Formazione modellistico-applicativa
Type of training activity
Characterising
56 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in ITALIAN
lectures timetable unavailable
exam calls
Print

Learning objectives

Introduction to mathematical modelling through differential equations and their qualitative analysis.

Prerequisites

- - -

Course unit content

Introduction to mathematical modelling through ordinary differential equations:

Dynamical Systems. Equilibria and Stability. Lyapunov Methods.

Linear and nonlinear models in Mechanics.

Mathematical models in population dynamics.

Van der Pol equation.

Bifurcation theory, Hopf theorem, limit cycles.

Poincarè-Bendixon theorem.

Lorenz model and chaos.

Full programme

Dynamical Systems. Equilibria and Stability. Lyapunov Methods.
Linear and nonlinear models in Mechanics.
Mathematical models in Population Dynamics.
Van der Pol equation.
Bifurcation theory, Hopf theorem, limit cycles.
Poincarè-Bendixon theorem.
Lorenz system and chaos.
Discrete dynamical systems. Feigenbaum map.

Bibliography

G.L. CARAFFINI, M. IORI, G. SPIGA, Proprietà elementari dei sistemi dinamici, Appunti per il corso di Meccanica Razionale, UNIVERSITA' DEGLI STUDI DI PARMA, a.a 1998-99;

G. BORGIOLI, Modelli Matematici di evoluzione ed equazioni differenziali, Quaderni di Matematica per le Scienze Applicate/2, CELID, TORINO, 1996;

R. RIGANTI, Biforcazioni e Caos nei modelli matematici delle Scienze applicate, LEVROTTO & BELLA TORINO, 2000;

M.W HIRSCH, S. SMALE, Differential Equations, Dynamical Systems and Linear Algebra, ACADEMIC PRESS, NEW YORK, 1974;

J.D. MURRAY, Mathematical Biology, SPRINGER-VERLAG, NEW YORK, 1989;

J. GUCKENHEIMER, P. HOLMES, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vectors Fields, SPRINGER-VERLAG, NEW YORK, 1983;

M. SQUASSINA, S. ZUCCHER, Introduzione all'analisi qualitativa dei sistema dinamici discreti e continui, Springer Unitext. 2016.

Teaching methods

Lectures and exercises

Assessment methods and criteria

Oral exam in addition to an autonomous project

Other information

- - -

2030 agenda goals for sustainable development

- - -

Contacts

Toll-free number

800 904 084

Student registry office

E. segreteria.scienze@unipr.it
T. +39 0521 905116

Quality assurance office

Education manager
dott.ssa Giulia Bonamartini
T. +39 0521 906968
E. servizio smfi.didattica@unipr.it
E. del manager giulia.bonamartini@unipr.it

President of the degree course

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Faculty advisor

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Career guidance delegate

Prof. Francesco Morandin
E. francesco.morandin@unipr.it

Tutor Professors

Prof. Emilio Acerbi
E. emilio.acerbi@unipr.it

Prof. Marino Belloni
E. marino.belloni@unipr.it

Prof.ssa Maria Groppi
E. maria.groppi@unipr.it

Prof.ssa Chiara Guardasoni
E. chiara.guardasoni@unipr.it

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Prof. Costantino Medori
E. costantino.medori@unipr.it

Prof. Adriano Tomassini
E. adriano.tomassini@unipr.it

Erasmus delegates

Prof.ssa Fiorenza Morini
E. fiorenza.morini@unipr.it

Quality assurance manager

Prof.ssa Maria Groppi
E. maria.groppi@unipr.it

Tutor students

Dott. Matteo Mezzadri
E. matteo.mezzadri@studenti.unipr.it