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
Primo semestre Oct 3, 2022 Jan 27, 2023
Secondo semestre Mar 6, 2023 Jun 16, 2023
Exam sessions
Session From To
Sessione invernale d'esame Jan 30, 2023 Feb 28, 2023
Sessione estiva d'esame Jun 19, 2023 Jul 31, 2023
Sessione autunnale d'esame Sep 4, 2023 Sep 29, 2023
Holidays
Period From To
Festa di Ognissanti Nov 1, 2022 Nov 1, 2022
Festa dell'Immacolata Dec 8, 2022 Dec 8, 2022
Vacanze di Natale Dec 24, 2022 Jan 1, 2023
Vacanze di Pasqua Apr 7, 2023 Apr 10, 2023
Festa della Liberazione Apr 25, 2023 Apr 25, 2023
Festa dei Lavoratori May 1, 2023 May 1, 2023
Festa del Santo Patrono May 21, 2023 May 21, 2023
Festa della Repubblica Jun 2, 2023 Jun 2, 2023
Chiusura estiva Aug 14, 2023 Aug 19, 2023

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

B C D F L M O P Q R S

Bombieri Nicola

nicola.bombieri@univr.it +39 045 802 7094

Bontempi Pietro

pietro.bontempi@univr.it +39 045 802 7614

Boscolo Galazzo Ilaria

ilaria.boscologalazzo@univr.it +39 045 8127804

Brusini Lorenza

lorenza.brusini@univr.it +39 045 802 7803

Calderan Laura

laura.calderan@univr.it 0458027562

Combi Carlo

carlo.combi@univr.it 045 802 7985

Di Marco Roberto

roberto.dimarco@univr.it

Fiorini Paolo

paolo.fiorini@univr.it 045 802 7963

Fummi Franco

franco.fummi@univr.it 045 802 7994

Maris Bogdan Mihai

bogdan.maris@univr.it +39 045 802 7074

Oliboni Barbara

barbara.oliboni@univr.it +39 045 802 7077

Quaglia Davide

davide.quaglia@univr.it +39 045 802 7811

Romeo Alessandro

alessandro.romeo@univr.it +39 045 802 7974-7936; Lab: +39 045 802 7808

Sansonetto Nicola

nicola.sansonetto@univr.it 049-8027932

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: 2°- 3°
Between the years: 1°- 2°- 3°
Altre attività formative: lo studente può scegliere tra le 2 seguenti opzioni: a) 2 CFU di seminari - di cui 1 CFU al 1 anno e 1 CFU al 2 anno - e 7 CFU di tirocinio al 3 anno; b) 9 CFU di tirocinio al 3 anno. Non sono previste ulteriori opzioni.
9
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

4S009864

Coordinatore

Mauro Bonafini

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/05 - MATHEMATICAL ANALYSIS

Period

Primo semestre dal Oct 3, 2022 al Jan 27, 2023.

Learning objectives

The course will treat the fundamental concepts of mathematical analysis: the aim is to provide a bet- ter consciousness of the analytic methods in view of applications of analysis. At the end of the course, the students shall prove of being able: to apply mathematical analysis techniques to the solution of problems about functions, derivatives, integrals and series also in different contexts even not strictly mathematical; to apply mathematical analysis techniques to solution of problems; to choose among the various techniques the one better suited to the problem at hand; to describe the solution of a problem employing correct terminology; to widen their knowledge starting from what they learned.

Prerequisites and basic notions

Basic knowledge required for enrollment in the course of study.

Program

Introduction.
Intuitive notion of set, notions of logic, elementary set operations, numerical sets, lower and upper bound, infimum and supremum, minimum and maximum, continuity axiom for real numbers, complex numbers. Definition of a function, injective function, surjective function, function composition and inverse function.

Sequences.
Definition of a sequence, monotone sequences, bounded sequences, definition of limit for a sequence, uniqueness of the limit, algebra of limits, comparisons and asymptotic estimates. Indeterminate forms and calculation of limits.

Real functions of a real variable.
Bounded functions, maximum and minimum, periodic functions, monotone functions. Graph of a function, elementary operations on the graph.

Continuity.
Notion of continuity for a real valued function of a real variable. Continuous functions on a closed and bounded interval: existence of zeros, Weierstrass' theorem, intermediate values theorem.

Limits.
Accumulation points, limits for real valued functions of a real variable, algebra of limits. Simple limits, comparisons, asymptotic estimates, change of variable within limits and calculation of limits.

Derivative.
Definition of derivative of a real valued function of a real variable, tangent line. Calculus of derivatives for elementary functions, algebra of derivatives, derivative of the composition, derivative of the inverse function. Angular points, cusps, inflections with vertical tangents, continuity and derivability. Stationary points, local maximums and minimums. Differentiable functions on an interval: Fermat's theorem, Lagrange's (or mean value) theorem, monotony test. De l'Hospital's theorem. Second derivative: geometric meaning, concavity, convexity. Study of the graph of a function. Approximations: notion of ``small o'', MacLaurin / Taylor polynomial, MacLaurin-Taylor formula with Peano and Lagrange remainder. Application to the calculation of limits by asymptotic expansion.

Series.
Numerical series and convergence criteria (comparison, asymptotic comparison, ratio and root criteria, Leibniz criterion). Taylor series.

Integral calculus.
Definition of integral and various interpretations, classes of integrable functions, properties of the integral, mean-value theorem. Notion of primitive and fundamental theorem of integral calculus. Methods for finding a primitive: immediate integrals, integrals by substitution, integrals by parts, integrals of rational functions. Integral functions and second fundamental theorem of integral calculus. Applications of integral calculus. Generalized integrals: integrals of unbounded functions and integrability criteria; integration over unlimited intervals and integrability criteria.

Differential equations.
Concept of differential equation and its solution. First order differential equations with separable variables, how to solve them, existence and uniqueness theorem for the Cauchy problem. Linear differential equations of the first and second order: existence of solutions, structure of the general integral, how to solve them.

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.

Didactic methods

Lecture.

Learning assessment procedures

The exam consists of a 3-hour written test and covers all the topics covered during the course, theory and exercises. Regarding the theoretical part, all definitions / statements are subject to examination. As for the proofs, at the end of the course a list of proofs to know will be identified and the exam will include at least one question such as "State and prove theorem X".

Cheat sheet.
It is allowed to bring cheat sheet, that is
- single A4 page
- handwritten (by yourself)
- name-surname-matriculation number written at the top
- on the space available you can write whatever you want.
The cheat sheet must be delivered together with the exam.

Structure.
The exam is divided into two parts.
The first part, the preliminary test, includes 8 short exercises. The preliminary test is considered passed by solving at least 6 out of 8 exercises, otherwise the candidate is automatically rejected.
The second part, the complete test, it includes exercises and theoretical questions.

Score.
Passing the preliminary test assigns 3 points, the various exercises of the complete test assign 30 points, for a total of 33 points.

Registration of the exam.
The final grade is given by the minimum between the score obtained and 30. Each sufficient grade, i.e. from 18/30 upwards, can be accepted and consequently recorded.

Oral exam (optional).
The oral exam focuses on theory, is optional and can be taken by all candidates who have achieved at least 17/30. Attention: with the oral test, even if you start with a sufficient grade, you may be rejected and forced to repeat the written test. The oral exam is a necessary condition for "30 e lode''.

Evaluation criteria

Understanding of the topics covered during the course and ability to apply the notions acquired in solving exercises and constructing new sentences.

Criteria for the composition of the final grade

Mark of the written exam (plus an optional oral if requested).

Exam language

Italiano

Type D and Type F activities

Le attività formative di tipologia D sono a scelta dello studente, quelle di tipologia F sono ulteriori conoscenze utili all’inserimento nel mondo del lavoro (tirocini, competenze trasversali, project works, ecc.). In base al Regolamento Didattico del Corso, alcune attività possono essere scelte e inserite autonomamente a libretto, altre devono essere approvate da apposita commissione per verificarne la coerenza con il piano di studio. Le attività formative di tipologia D o F possono essere ricoperte dalle seguenti attività.

1. Insegnamenti impartiti presso l'Università di Verona

Comprendono gli insegnamenti sotto riportati e/o nel Catalogo degli insegnamenti (che può essere filtrato anche per lingua di erogazione tramite la Ricerca avanzata).

Modalità di inserimento a libretto: se l'insegnamento è compreso tra quelli sottoelencati, lo studente può inserirlo autonomamente durante il periodo in cui il piano di studi è aperto; in caso contrario, lo studente deve fare richiesta alla Segreteria, inviando a carriere.scienze@ateneo.univr.it il modulo nel periodo indicato.

2. Attestato o equipollenza linguistica CLA

Oltre a quelle richieste dal piano di studi, per gli immatricolati dall'A.A. 2021/2022 vengono riconosciute:

  • Lingua inglese: vengono riconosciuti 3 CFU per ogni livello di competenza superiore a quello richiesto dal corso di studio (se non già riconosciuto nel ciclo di studi precedente).
  • Altre lingue e italiano per stranieri: vengono riconosciuti 3 CFU per ogni livello di competenza a partire da A2 (se non già riconosciuto nel ciclo di studi precedente).

Tali cfu saranno riconosciuti, fino ad un massimo di 6 cfu complessivi, di tipologia F se il piano didattico lo consente, oppure di tipologia D. Ulteriori crediti a scelta per conoscenze linguistiche potranno essere riconosciuti solo se coerenti con il progetto formativo dello studente e se adeguatamente motivati.

Gli immatricolati fino all'A.A. 2020/2021 devono consultare le informazioni che si trovano qui.

Modalità di inserimento a librettorichiedere l’attestato o l'equipollenza al CLA e inviarlo alla Segreteria Studenti - Carriere per l’inserimento dell’esame in carriera, tramite mail: carriere.scienze@ateneo.univr.it

3. Competenze trasversali

Scopri i percorsi formativi promossi dal TALC - Teaching and learning center dell'Ateneo, destinati agli studenti regolarmente iscritti all'anno accademico di erogazione del corso https://talc.univr.it/it/competenze-trasversali

Modalità di inserimento a libretto: non è previsto l'inserimento dell'insegnamento nel piano di studi. Solo in seguito all'ottenimento dell'Open Badge verranno automaticamente convalidati i CFU a libretto. La registrazione dei CFU in carriera non è istantanea, ma ci saranno da attendere dei tempi tecnici.  

4. Periodo di stage/tirocinio

Oltre ai CFU previsti dal piano di studi (verificare attentamente quanto indicato sul Regolamento Didattico): qui informazioni su come attivare lo stage. 

Verificare nel regolamento quali attività possono essere di tipologia D e quali di tipologia F.

Insegnamenti e altre attività che si possono inserire autonomamente a libretto

List of courses with unassigned period
years Modules TAF Teacher
Seminari di sistemi medicali (I anno) F Not yet assigned
Seminari di sistemi medicali (II anno/1) F Not yet assigned
Seminari di sistemi medicali (II anno/2) 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.

Modalità di frequenza

La natura interateneo del corso di studi è data dalla cooperazione dei tre Atenei nella messa a disposizione dei docenti. L'erogazione didattica avviene pertanto nella sede amministrativa e didattica di Verona e non negli Atenei partner. Non è quindi possibile frequentare questo corso di laurea triennale nell'Ateneo di Trento o di Modena-Reggio Emilia; tuttavia, è possibile usufruire degli spazi studio degli Atenei partner, grazie all'accordo che intercorre.

Come riportato nel Regolamento Didattico per l'A.A. 2021/2022, la frequenza al corso di studio non è obbligatoria.
Per le modalità di erogazione della didattica, si rimanda alle informazioni in costante aggiornamento dell'Unità di Crisi.


Career management


Area riservata studenti


Graduation

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