Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Academic calendar
The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technical-administrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.
Course calendar
The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..
Period | From | To |
---|---|---|
I semestre | Oct 1, 2019 | Jan 31, 2020 |
II semestre | Mar 2, 2020 | Jun 12, 2020 |
Session | From | To |
---|---|---|
Sessione invernale d'esame | Feb 3, 2020 | Feb 28, 2020 |
Sessione estiva d'esame | Jun 15, 2020 | Jul 31, 2020 |
Sessione autunnale d'esame | Sep 1, 2020 | Sep 30, 2020 |
Session | From | To |
---|---|---|
Sessione estiva di laurea | Jul 22, 2020 | Jul 22, 2020 |
Sessione autunnale di laurea | Oct 14, 2020 | Oct 14, 2020 |
Sessione autunnale di laurea solo triennale | Dec 10, 2020 | Dec 10, 2020 |
Sessione invernale di laurea | Mar 16, 2021 | Mar 16, 2021 |
Period | From | To |
---|---|---|
Festa di Ognissanti | Nov 1, 2019 | Nov 1, 2019 |
Festa dell'Immacolata | Dec 8, 2019 | Dec 8, 2019 |
Vacanze di Natale | Dec 23, 2019 | Jan 6, 2020 |
Vacanze di Pasqua | Apr 10, 2020 | Apr 14, 2020 |
Festa della Liberazione | Apr 25, 2020 | Apr 25, 2020 |
Festa del lavoro | May 1, 2020 | May 1, 2020 |
Festa del Santo Patrono | May 21, 2020 | May 21, 2020 |
Festa della Repubblica | Jun 2, 2020 | Jun 2, 2020 |
Vacanze estive | Aug 10, 2020 | Aug 23, 2020 |
Exam calendar
Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.
To view all the exam sessions available, please use the Exam dashboard on ESSE3.
If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.
Academic staff
Aielli Gian Piero
Imperio Michele
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2020/2021
Modules | Credits | TAF | SSD |
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3° Year activated in the A.Y. 2021/2022
Modules | Credits | TAF | SSD |
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Dynamical Systems (2020/2021)
Teaching code
4S00244
Credits
9
Language
Italian
Also offered in courses:
- Dynamical Systems of the course Bachelor's degree in Applied Mathematics
- Dynamical Systems of the course Bachelor's degree in Applied Mathematics
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
The teaching is organized as follows:
Parte I teoria
Parte II Esercitazioni
Parte II teoria
Parte I esercitazioni
Learning outcomes
The aim of the course is the introduction of the theory and of some applications of continuous and discrete dynamical systems, that describe the time evolution of quantitative variables. At the end of the course a student will be able to investigate the stability and the character of an equilibrium and to produce and investigate the qualitative analysis of a system of ordinary differential equations and the phase portrait of a dynamical system in dimension 1 and 2. Moreover a student will be able to study the presence and the nature of limit cycles and to analyse some basic applications of dynamical systems arising from population dynamics, mechanics and traffic flows. Eventually a student will be also able to produce proofs using the typical tools of modern dynamical systems and will be able to read and report specific books and articles on dynamical systems and related applications.
Program
Part 1
Module 1. Complements of ordinary differential equations.
Existence and uniqueness theorem. Qualitative analysis of ODE: maximal solutions, Gronwall’s Lemma.
Module 2. Vector fields and ODE.
Orbits and phase space. Equilibria, phase portrait in 1 dimension. ODE of the second order and their equilibria. Linearisation about an equilibrium and periodic solutions of an ODE.
Module 3. Linear systems.
Linear systems in in R2, real and complex eigenvalues. Elements of Jordan theory. Diagram of bifurcation in R2.
Linear systems in Rn, stable, unstable and central subspaces. Linearisation about an equilibrium.
Module 4. Flows and flows conjugations.
Flow of a vector field. Dependance on the parameters. time dependent vector fields.
Change of coordinates, conjugations of flows, pull-back and push-forward of functions and vector fields. Time dependent change of coordinates. scaling of vector fields and time reparametrisations.
Rectification theorem.
Module 5. First integrals.
Invariant sets, first integrals and Lie derivative. Invariant foliations, reduction of order. First integrals and attractive equilibria.
Module 6. 1-dimensional Newton equation. Phase portrait in the conservative case. Linearisation. Reduction of order. Systems with friction.
Module 7. Stability theory.
Lyapunov Stability, Lyapunov functions and spectral method.
Part 2.
Module 8. Bifurcations and applications.
Definition of bifurcation, bifurcation at equilibria. Applications and numerical simulations.
Module 9. Calculus of variations in dimensione 1.
Module 10. Hamiltonian dynamics.
Hamiltonian systems, basic properties, Poisson bracket and canonical transformations. Lie conditions, generating functions, action-angle variables, integrability and Hamilton-Jacobi equation.
Bibliography
Activity | Author | Title | Publishing house | Year | ISBN | Notes |
---|---|---|---|---|---|---|
Parte I teoria | F. Fassò | Dispense per il corso di Istituzioni di Fisica Matematica | CLEUP | 2021 | ||
Parte II Esercitazioni | F. Fasso` | Dispense per il corso di Istituzioni di Fisica Matematica | CLEUP | 2021 | ||
Parte II teoria | F. Fassò | Dispense per il corso di Istituzioni di Fisica Matematica | CLEUP | 2021 | ||
Parte I esercitazioni | F. Fasso` | Dispense per il corso di Istituzioni di Fisica Matematica | CLEUP | 2021 |
Examination Methods
A written exam with exercises: phase portrait in 2D for a non-linear dynamical system; computation of trajectories and stability, first integrals, change of coordinates, bifurcations and hamiltonian systems.
The written exam tests the following learning outcomes:
- To have adequate analytical skills;
- To have adequate computational skills;
- To be able to translate problems from natural language to mathematical formulations;
- To be able to define and develop mathematical models for physics and natural sciences.
An oral exam with 3 theoretical questions. The oral exam is compulsory and must be completed within the session
in which the written part has been done.
The oral exam tests the following learning outcomes:
- To be able to present precise proofs and recognise them.
According to the pandemic situation the structure of the exam could vary.
Type D and Type F activities
years | Modules | TAF | Teacher |
---|---|---|---|
1° 2° 3° | Python programming language | D |
Maurizio Boscaini
(Coordinator)
|
1° 2° 3° | SageMath | F |
Zsuzsanna Liptak
(Coordinator)
|
1° 2° 3° | History of Modern Physics 2 | D |
Francesca Monti
(Coordinator)
|
1° 2° 3° | History and Didactics of Geology | D |
Guido Gonzato
(Coordinator)
|
years | Modules | TAF | Teacher |
---|---|---|---|
1° 2° 3° | C Programming Language | D |
Sara Migliorini
(Coordinator)
|
1° 2° 3° | C++ Programming Language | D |
Federico Busato
(Coordinator)
|
1° 2° 3° | LaTeX Language | D |
Enrico Gregorio
(Coordinator)
|
years | Modules | TAF | Teacher |
---|---|---|---|
1° 2° 3° | Corso Europrogettazione | D | Not yet assigned |
1° 2° 3° | Corso online ARPM bootcamp | F | Not yet assigned |
1° 2° 3° | ECMI modelling week | F | Not yet assigned |
1° 2° 3° | ESA Summer of code in space (SOCIS) | F | Not yet assigned |
1° 2° 3° | Google summer of code (GSOC) | F | Not yet assigned |
Career prospects
Module/Programme news
News for students
There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details: only in this way will you be able to receive notification of all the notices from your teachers and your secretariat via email and also via the Univr app.
Graduation
Documents
Title | Info File |
---|---|
![]() |
pdf, it, 31 KB, 29/07/21 |
![]() |
pdf, it, 31 KB, 29/07/21 |
![]() |
pdf, it, 171 KB, 20/03/24 |
List of thesis proposals
theses proposals | Research area |
---|---|
Formule di rappresentazione per gradienti generalizzati | Mathematics - Analysis |
Formule di rappresentazione per gradienti generalizzati | Mathematics - Mathematics |
Mathematics Bachelor and Master thesis titles | Various topics |
Attendance modes and venues
As stated in the Teaching Regulations , except for specific practical or lab activities, attendance is not mandatory. Regarding these activities, please see the web page of each module for information on the number of hours that must be attended on-site.
Part-time enrolment is permitted. Find out more on the Part-time enrolment possibilities page.
The course's teaching activities take place in the Science and Engineering area, which consists of the buildings of Ca‘ Vignal 1, Ca’ Vignal 2, Ca' Vignal 3 and Piramide, located in the Borgo Roma campus.
Lectures are held in the classrooms of Ca‘ Vignal 1, Ca’ Vignal 2 and Ca' Vignal 3, while practical exercises take place in the teaching laboratories dedicated to the various activities.
Career management
Student login and resources
Erasmus+ and other experiences abroad
Ongoing orientation for students
The committee has the task of guiding the students throughout their studies, guiding them in their choice of educational pathways, making them active participants in the educational process and helping to overcome any individual difficulties.
It is composed of professors Lidia Angeleri, Sisto Baldo, Marco Caliari, Paolo dai Pra, Francesca Mantese, and Nicola Sansonetto
To send an email to professors: name.surname@univr.it