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, 2018 Jan 31, 2019
II semestre Mar 4, 2019 Jun 14, 2019
Exam sessions
Session From To
Sessione invernale d'esame Feb 1, 2019 Feb 28, 2019
Sessione estiva d'esame Jun 17, 2019 Jul 31, 2019
Sessione autunnale d'esame Sep 2, 2019 Sep 30, 2019
Degree sessions
Session From To
Sessione di laurea estiva Jul 22, 2019 Jul 22, 2019
Sessione di laurea autunnale Oct 15, 2019 Oct 15, 2019
Sessione di laurea autunnale straordinaria Nov 21, 2019 Nov 21, 2019
Sessione di laurea invernale Mar 19, 2020 Mar 19, 2020
Holidays
Period From To
Sospensione attività didattica Nov 2, 2018 Nov 3, 2018
Vacanze di Natale Dec 24, 2018 Jan 6, 2019
Vacanze di Pasqua Apr 19, 2019 Apr 28, 2019
Vacanze estive Aug 5, 2019 Aug 18, 2019

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 Enrollment FAQs

Academic staff

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

Agostiniani Virginia

symbol email virginia.agostiniani@univr.it symbol phone-number +39 045 802 7979

Albi Giacomo

symbol email giacomo.albi@univr.it symbol phone-number +39 045 802 7913

Angeleri Lidia

symbol email lidia.angeleri@univr.it symbol phone-number 045 802 7911

Baldo Sisto

symbol email sisto.baldo@univr.it symbol phone-number 0458027935

Bos Leonard Peter

symbol email leonardpeter.bos@univr.it symbol phone-number +39 045 802 7987

Boscaini Maurizio

symbol email maurizio.boscaini@univr.it

Busato Federico

symbol email federico.busato@univr.it

Caliari Marco

symbol email marco.caliari@univr.it symbol phone-number +39 045 802 7904

Canevari Giacomo

symbol email giacomo.canevari@univr.it symbol phone-number +390458027979

Chignola Roberto

symbol email roberto.chignola@univr.it symbol phone-number 045 802 7953

Daffara Claudia

symbol email claudia.daffara@univr.it symbol phone-number +39 045 802 7942

Dai Pra Paolo

symbol email paolo.daipra@univr.it symbol phone-number +39 0458027093

Daldosso Nicola

symbol email nicola.daldosso@univr.it symbol phone-number +39 045 8027076 - 7828 (laboratorio)

De Sinopoli Francesco

symbol email francesco.desinopoli@univr.it symbol phone-number 045 842 5450

Di Persio Luca

symbol email luca.dipersio@univr.it symbol phone-number +39 045 802 7968

Fioroni Tamara

symbol email tamara.fioroni@univr.it

Gnoatto Alessandro

symbol email alessandro.gnoatto@univr.it symbol phone-number 045 802 8537

Gonzato Guido

symbol email guido.gonzato@univr.it symbol phone-number 045 802 8303

Gregorio Enrico

symbol email Enrico.Gregorio@univr.it symbol phone-number 045 802 7937

Liptak Zsuzsanna

symbol email zsuzsanna.liptak@univr.it symbol phone-number +39 045 802 7032
foto,  June 25, 2020

Magazzini Laura

symbol email laura.magazzini@univr.it symbol phone-number 045 8028525

Mantese Francesca

symbol email francesca.mantese@univr.it

Mariotto Gino

symbol email gino.mariotto@univr.it
Foto,  October 5, 2015

Mazzuoccolo Giuseppe

symbol email giuseppe.mazzuoccolo@univr.it symbol phone-number +39 0458027838

Migliorini Sara

symbol email sara.migliorini@univr.it symbol phone-number +39 045 802 7908

Monti Francesca

symbol email francesca.monti@univr.it symbol phone-number 045 802 7910

Orlandi Giandomenico

symbol email giandomenico.orlandi at univr.it symbol phone-number 045 802 7986

Piccinelli Fabio

symbol email fabio.piccinelli@univr.it symbol phone-number +39 045 802 7097

Rizzi Romeo

symbol email romeo.rizzi@univr.it symbol phone-number +39 045 8027088

Sansonetto Nicola

symbol email nicola.sansonetto@univr.it symbol phone-number 045-8027976

Schuster Peter Michael

symbol email peter.schuster@univr.it symbol phone-number +39 045 802 7029

Solitro Ugo

symbol email ugo.solitro@univr.it symbol phone-number +39 045 802 7977

Zuccher Simone

symbol email 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 enrollment year.

CURRICULUM TIPO:

2° Year   activated in the A.Y. 2019/2020

ModulesCreditsTAFSSD
6
A
MAT/02
6
B
MAT/03
6
C
SECS-P/01
6
C
SECS-P/01
6
B
MAT/06
English B1
6
E
-

3° Year   activated in the A.Y. 2020/2021

ModulesCreditsTAFSSD
6
C
SECS-P/05
Final exam
6
E
-
activated in the A.Y. 2019/2020
ModulesCreditsTAFSSD
6
A
MAT/02
6
B
MAT/03
6
C
SECS-P/01
6
C
SECS-P/01
6
B
MAT/06
English B1
6
E
-
activated in the A.Y. 2020/2021
ModulesCreditsTAFSSD
6
C
SECS-P/05
Final exam
6
E
-
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.




S Placements in companies, public or private institutions and professional associations

Teaching code

4S00244

Credits

9

Language

Italian

Also offered in courses:

Scientific Disciplinary Sector (SSD)

MAT/05 - MATHEMATICAL ANALYSIS

The teaching is organized as follows:

Parte I teoria

Credits

5

Period

II semestre

Academic staff

Nicola Sansonetto

Parte II Esercitazioni

Credits

2

Period

II semestre

Academic staff

Alberto Benvegnu'

Parte II teoria

Credits

1

Period

II semestre

Academic staff

Nicola Sansonetto

Parte I esercitazioni

Credits

1

Period

II 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 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.
First and second order differential equations. Methods of the variations of the constants. Existence and uniqueness theorem. Qualitative analysis of ODE: maximal solutions, Gronwall’s Lemma. Esplicit solutions of particular equations: separations of variable, Riccati and total equations. Linear systems.

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 biforcation in R2.
Linear systems in Rn, stable, unstable and central subspeces. Linearization 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.riscalamenti di campi vettoriali e riparametrizzazioni del tempo.
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.

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

Reference texts
Activity Author Title Publishing house Year ISBN Notes
Parte I teoria G. Benettin Appunti per il corso di Fisica Matematica 2017
Parte I teoria G. Benettin Appunti per il corso di Meccanica Analitica 2018
Parte I teoria F. Fasso` Primo sguardo ai sistemi dinamici CLEUP 2016
Parte I teoria G. Benettin Una passeggiata tra i Sistemi Dinamici 2012
Parte II Esercitazioni M.W. Hirsch e S. Smale Differential equations, dynamical systems, and linear algebra Academic Press 1974
Parte II Esercitazioni S. Strogatz Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering Westview Press 2010
Parte II Esercitazioni F. Fasso` Primo sguardo ai sistemi dinamici CLEUP 2016
Parte II teoria M.W. Hirsch e S. Smale Differential equations, dynamical systems, and linear algebra Academic Press 1974
Parte II teoria S. Strogatz Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering Westview Press 2010
Parte II teoria F. Fasso` Primo sguardo ai sistemi dinamici CLEUP 2016

Examination Methods

A written exam with exercises: phase portrait in 2D for a non-linear dynamical system; computation of trajectories and stability for a discrete-time system, phase portrait in 2D for a non-linear dynamical system; computation of trajectories and stability for a discrete-time system; stability analysis for a system.
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 2-3 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.

Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE

Type D and Type F activities

Modules not yet included

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 soon also via the Univr app.

Graduation

For schedules, administrative requirements and notices on graduation sessions, please refer to the Graduation Sessions - Science and Engineering service.

Documents

Title Info File
File pdf 1. Come scrivere una tesi pdf, it, 31 KB, 29/07/21
File pdf 2. How to write a thesis pdf, it, 31 KB, 29/07/21
File pdf 5. Regolamento tesi pdf, it, 171 KB, 20/03/24

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
THESIS_1: Sensors and Actuators for Applications in Micro-Robotics and Robotic Surgery Various topics
THESIS_2: Force Feedback and Haptics in the Da Vinci Robot: study, analysis, and future perspectives Various topics
THESIS_3: Cable-Driven Systems in the Da Vinci Robotic Tools: study, analysis and optimization Various topics
Stage Research area
Internship proposals for students in mathematics Various topics

Attendance

As stated in the Teaching Regulations for the A.Y. 2022/2023, 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.
 


Career management


Student login and resources


Erasmus+ and other experiences abroad


Commissione tutor

La commissione ha il compito di guidare le studentesse e gli studenti durante l'intero percorso di studi, di orientarli nella scelta dei percorsi formativi, di renderli attivamente partecipi del processo formativo e di contribuire al superamento di eventuali difficoltà individuali.

E' composta dai proff. Sisto Baldo, Marco Caliari, Francesca Mantese, Giandomenico Orlandi e Nicola Sansonetto