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 technicaladministrative 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, 2020  Jan 29, 2021 
II semestre  Mar 1, 2021  Jun 11, 2021 
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 
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 
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.
Academic staff
Gonzato Guido
guido.gonzato@univr.it 045 802 8303Study 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.
Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

1° Year
Modules  Credits  TAF  SSD 

2° Year activated in the A.Y. 2021/2022
Modules  Credits  TAF  SSD 

3° Year activated in the A.Y. 2022/2023
Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

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.
Mathematical analysis 2 (2021/2022)
Teaching code
4S00031
Academic staff
Coordinatore
Credits
12
Language
Italian
Scientific Disciplinary Sector (SSD)
MAT/05  MATHEMATICAL ANALYSIS
Period
Primo semestre dal Oct 4, 2021 al Jan 28, 2022.
Learning outcomes
Topics treated in this course are: Calculus for functions of several variables, sequences and series of functions, ordinary differential equations, Lebesgue measure and integral. Emphasis will be given to examples and applications.
At the end of the course, students must possess adequate skills of synthesis and abstraction. They must recognize and produce rigorous proofs. They must be able to formalize and solve moderately difficult problems on the arguments of the course.
Program
The entire course will be available online. In addition, a number of the lessons/all the lessons (see the course
schedule) will be held inclass.
i) Calculus in several variables. Neighborhoods in several variables, continuity in several variables, directional derivatives, differential of functions in several variables, Theorem of Total Differential, gradient of scalar functions, Jacobian matrix for vectorvalued functions, level curves of scalar functions. Parametrized surfaces, tangent and normal vectors, changes of coordinates. Higher order derivatives and differentials, Hessian matrix, Schwarz's Theorem, Taylor's Series.
(ii) Optimization problems for functions in several variables. Critical points, free optimization, constrained optimization, Lagrange's Multiplier Theorem, Implicit and inverse function theorem, Contraction Principle.
(iii) Integral of functions in several variables. Fubini and Tonelli theorems, integral on curves, change of variables formula.
(iv) Integral of scalar function on surfaces, vector fields, conservatice vector fields, scalar potentials, curl and divergence of a vector fields, introduction to differential forms, closed and exact forms, Poincare lemma, GaussGreen formulas.
(v) Flux through surfaces, Stokes' Theorem, Divergence Theorem
(vi) Introduction to metric spaces and normed spaces, spaces of functions, sequence of functions, uniform convergence, function series, total convergence, derivation and integration of a series of functions.
(vii) Introduction to Lebesgue's Measure Theory. Measurable sets and functions, stability of measurable functions, simple functions, approximation results, Lebesgue integral. Monotone Convergence Theorem, Fatou's Lemma, Dominated convergence Theorem and their consequences.
(viii) Ordinary differential equation, existence and uniqueness results, CauchyLipschitz's Theorem. Extension of a solution, maximal solution, existence and uniqueness results for systems of ODE, linear ODE of order n, Variation of the constants method,
other resolutive formulas.
(ix) Fourier's series for periodic functions, convergence results, application to solutions of some PDE.
Bibliography
Examination Methods
The final exam consists of a written test followed, in case of a positive result, by an oral test. The written test consists of some exercises on the program: students are exonerated from the first part of the test if they pass a midterm test at the beginning of december. The written test evaluates the ability of students at solving problems pertaining to the syllabus of the course, and also their skills in the analysis, synthesis and abstraction of questions stated either in the natural language or in the specific language of mathematics. The written test is graded on a scale from 0 to 30 points (best), with a pass mark of 18/30..
The oral test will concentrate mainly but not exclusively on the theory. It aims at verifying the ability of students at constructing correct and rigorous proofs and their skills in analysis, synthesis and abstraction. The oral exam is graded on a scale from 5 to +5 point, which are added to the marks earned in the written test.
Both written and oral test will be performed online.
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.
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)

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)

years  Modules  TAF  Teacher  

1°  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: 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.
Further services
I servizi e le attività di orientamento sono pensati per fornire alle future matricole gli strumenti e le informazioni che consentano loro di compiere una scelta consapevole del corso di studi universitario.
Graduation
Attachments
Title  Info File 

1. Come scrivere una tesi  31 KB, 29/07/21 
2. How to write a thesis  31 KB, 29/07/21 
5. Regolamento tesi (valido da luglio 2022)  171 KB, 17/02/22 
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 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 onsite.
Please refer to the Crisis Unit's latest updates for the mode of teaching.