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.

Academic calendar

Course calendar

The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..

Definition of lesson periods
Period From To
I semestre Oct 1, 2020 Jan 29, 2021
II semestre Mar 1, 2021 Jun 11, 2021
Exam sessions
Session From To
Sessione invernale d'esame Feb 1, 2021 Feb 26, 2021
Sessione estiva d'esame Jun 14, 2021 Jul 30, 2021
Sessione autunnale d'esame Sep 1, 2021 Sep 30, 2021
Degree sessions
Session From To
Sessione di laurea estiva Jul 22, 2021 Jul 22, 2021
Sessione di laurea autunnale Oct 14, 2021 Oct 14, 2021
Sessione di laurea autunnale - Dicembre Dec 9, 2021 Dec 9, 2021
Sessione invernale di laurea Mar 16, 2022 Mar 16, 2022
Holidays
Period From To
Festa dell'Immacolata Dec 8, 2020 Dec 8, 2020
Vacanze Natalizie Dec 24, 2020 Jan 3, 2021
Vacanze di Pasqua Apr 2, 2021 Apr 6, 2021
Festa del Santo Patrono May 21, 2021 May 21, 2021
Festa della Repubblica Jun 2, 2021 Jun 2, 2021
Vacanze Estive Aug 9, 2021 Aug 15, 2021

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.

Exam calendar

Should you have any doubts or questions, please check the Enrolment FAQs

Academic staff

A B C D E F G L M N O P R S V Z

Albi Giacomo

giacomo.albi@univr.it +39 045 802 7913

Angeleri Lidia

lidia.angeleri@univr.it 045 802 7911

Baldo Sisto

sisto.baldo@univr.it 045 802 7935

Bos Leonard Peter

leonardpeter.bos@univr.it +39 045 802 7987

Caliari Marco

marco.caliari@univr.it +39 045 802 7904

Canevari Giacomo

giacomo.canevari@univr.it +39 045 8027979

Chignola Roberto

roberto.chignola@univr.it 045 802 7953

Collet Francesca

francesca.collet@univr.it

Cubico Serena

serena.cubico@univr.it 045 802 8132

Daffara Claudia

claudia.daffara@univr.it +39 045 802 7942

Dai Pra Paolo

paolo.daipra@univr.it +39 0458027093

Daldosso Nicola

nicola.daldosso@univr.it +39 045 8027076 - 7828 (laboratorio)

Delledonne Massimo

massimo.delledonne@univr.it 045 802 7962; Lab: 045 802 7058

De Sinopoli Francesco

francesco.desinopoli@univr.it 045 842 5450

Dipasquale Federico Luigi

federicoluigi.dipasquale@univr.it

Enrichi Francesco

francesco.enrichi@univr.it +390458027051

Fioroni Tamara

tamara.fioroni@univr.it 0458028489

Gnoatto Alessandro

alessandro.gnoatto@univr.it 045 802 8537

Gonzato Guido

guido.gonzato@univr.it 045 802 8303

Gregorio Enrico

Enrico.Gregorio@univr.it 045 802 7937

Laking Rosanna Davison

rosanna.laking@univr.it

Lubian Diego

diego.lubian@univr.it 045 802 8419

Mantese Francesca

francesca.mantese@univr.it +39 045 802 7978

Mantovani Matteo

matteo.mantovani@univr.it 045-802(7814)

Mattiolo Davide

davide.mattiolo@univr.it

Mazzi Giulio

giulio.mazzi@univr.it

Mazzuoccolo Giuseppe

giuseppe.mazzuoccolo@univr.it +39 0458027838

Nardon Chiara

chiara.nardon@univr.it

Orlandi Giandomenico

giandomenico.orlandi at univr.it 045 802 7986

Pianezzi Daniela

daniela.pianezzi@univr.it

Raffaele Alice

alice.raffaele@univr.it

Rizzi Romeo

romeo.rizzi@univr.it +39 045 8027088

Segala Roberto

roberto.segala@univr.it 045 802 7997

Solitro Ugo

ugo.solitro@univr.it +39 045 802 7977

Vincenzi Elia

elia.vincenzi@univr.it

Zivcovich Franco

franco.zivcovich@univr.it

Zuccher Simone

simone.zuccher@univr.it

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 enrolment year.

CURRICULUM TIPO:
Modules Credits TAF SSD
Between the years: 1°- 2°- 3°
Between the years: 1°- 2°- 3°
Other activities
6
F
-

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.




SPlacements in companies, public or private institutions and professional associations

Teaching code

4S00244

Credits

9

Coordinatore

Giacomo Canevari

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/05 - MATHEMATICAL ANALYSIS

The teaching is organized as follows:

Teoria parte I

Credits

5

Period

Secondo semestre

Academic staff

Giacomo Canevari

Esercitazioni parte II

Credits

2

Period

Secondo semestre

Academic staff

Giacomo Canevari

Esercitazioni parte I

Credits

1

Period

Secondo semestre

Academic staff

Giacomo Canevari

Teoria parte II

Credits

1

Period

Secondo semestre

Academic staff

Giacomo Canevari

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 study and investigate the stability and the character of an equilibrium and 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 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 I

1. Topics in the theory of ordinary differential equations
Qualitative analysis of ODE: existence and uniqueness of solutions; maximal and global solutions; Gronwall’s Lemma; continuous dependence on the initial data.

2. Vector fields and ordinary differential equations
Vector fields: phase space, integral curves, orbits, equilibria, phase portrait. 1-dimensional examples of phase portraits. Second-order systems of differential equations; phase-space analysis and equilibria.

3. Linear systems
Linearisation of a vector field about an equilibrium. Classification of two-dimensional linear systems (over the real numbers) that are diagonalisable over the complex numbers. (If time permits, we will briefly discuss the nilpotent case as well.) n-dimensional linear systems: invariant subspace decomposition; the stable, unstable and central subspaces. Comparing a vector field with its linearisation about a hyperbolic equilibrium.

4. Flow of a vector field
Flow of a vector field. Change of coordinates: conjugate vector fields; pull-back and push-forward of a vector field by a diffeomorphism. Non-autonomous differential equations: time-dependent change of coordinates; scaling of vector fields and time reparametrisations. The local rectification theorem.

5. First integrals
Invariant sets; first integrals; Lie derivative. Invariant foliations; reduction of the order. First integrals and attractive equilibria.

6. Stability theory
Stability 'à la Lyapunov' of an equilibrium; the method of Lyapunov functions; the spectral method. Applications and examples.

7. 1-dimensional Newton equation.
Phase portraits of the 1-dimensional Newton equation, in the conservative case. Linearisation. Reduction of the order. Systems with friction.


Part II

8. Bifurcations
Bifurcatios from equilibria, with 1-dimensional examples; applications.

9. Introduction to the 1-dimensional Calculus of Variations
The indirect method for one-dimensional integral functionals. Necessary conditions for the existence of minimisers: the Euler-Lagrange equations. Jacobi integral; conservation laws. Geodesics on a surface.

10. Hamiltonian systems
Hamiltonian vector fields. Legendre transform. Poisson brackets. Canonical transformations. Lie conditions, generating functions. The Hamilton-Jacobi equations. Integrability. Geometry of the phase space: Liouville's theorem and Poincaré's recurrence theorem.

Bibliography

Visualizza la bibliografia con Leganto, strumento che il Sistema Bibliotecario mette a disposizione per recuperare i testi in programma d'esame in modo semplice e innovativo.

Examination Methods

The exam consists of two parts: a written part, and an oral one.

The written part consists of exercises - for instance, qualitative analysis of an ordinary differential equation; explicit solution of an ordinary differential equation; phase portrait of a two-dimensional, non-linear system; stability of equilibria; change of coordinates; first integrals; bifurcations; Hamiltonian systems and canonical transformations...
The written part 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.

The oral part consists of 3 questions. The oral part is compulsory and must be completed within the same session as written part of the exam.
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 may vary.

Type D and Type F activities

Le attività formative in ambito D o F comprendono gli insegnamenti impartiti presso l'Università di Verona o periodi di stage/tirocinio professionale.
Nella scelta delle attività di tipo D, gli studenti dovranno tener presente che in sede di approvazione si terrà conto della coerenza delle loro scelte con il progetto formativo del loro piano di studio e dell'adeguatezza delle motivazioni eventualmente fornite.

 

I semestre From 10/1/20 To 1/29/21
years Modules TAF Teacher
1° 2° History and Didactics of Geology D Guido Gonzato (Coordinatore)
1° 2° 3° Algorithms D Roberto Segala (Coordinatore)
1° 2° 3° Scientific knowledge and active learning strategies F Francesca Monti (Coordinatore)
1° 2° 3° Genetics D Massimo Delledonne (Coordinatore)
II semestre From 3/1/21 To 6/11/21
years Modules TAF Teacher
1° 2° 3° Algorithms D Roberto Segala (Coordinatore)
1° 2° 3° Python programming language D Vittoria Cozza (Coordinatore)
1° 2° 3° Organization Studies D Giuseppe Favretto (Coordinatore)
List of courses with unassigned period
years Modules TAF Teacher
Subject requirements: mathematics D Rossana Capuani
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
1° 2° 3° Introduzione all'analisi non standard F Sisto Baldo
1° 2° 3° C Programming Language D Pietro Sala (Coordinatore)
1° 2° 3° LaTeX Language D Enrico Gregorio (Coordinatore)

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.

Graduation

Attachments

List of theses and work experience proposals

theses proposals Research area
Formule di rappresentazione per gradienti generalizzati Mathematics - Analysis
Formule di rappresentazione per gradienti generalizzati Mathematics - Mathematics
Proposte Tesi A. Gnoatto Various topics
Mathematics Bachelor and Master thesis titles Various topics
Stage Research area
Internship proposals for students in mathematics Various topics

Attendance

As stated in point 25 of the Teaching Regulations for the A.Y. 2021/2022, 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.
Please refer to the Crisis Unit's latest updates for the mode of teaching.

Career management


Area riservata studenti