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.

Study Plan

A.A. 2024/2025 A.A. 2023/2024 A.A. 2022/2023 A.A. 2021/2022 A.A. 2020/2021 A.A. 2019/2020 A.A. 2018/2019 A.A. 2017/2018 A.A. 2016/2017 A.A. 2015/2016 A.A. 2014/2015 A.A. 2013/2014 A.A. 2012/2013 A.A. 2011/2012 A.A. 2010/2011 A.A. 2009/2010

This information is intended exclusively for students already enrolled in this course.
If you are a new student interested in enrolling, you can find information about the course of study on the course page:

Laurea in Matematica applicata - Enrollment from 2025/2026

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

ModulesCreditsTAFSSD
12
A
MAT/02 ,MAT/03
12
A
MAT/05
12
A
FIS/01
6
B
MAT/01
6
E
-
12
A
INF/01

2° Year  activated in the A.Y. 2016/2017

ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
12
B
MAT/08
One course to be chosen among the following
6
C
SECS-P/01
6
C
FIS/01
6
B
MAT/03
One course to be chosen among the following
6
C
MAT/05
6
C
SECS-P/01
6
B
MAT/06
6
B
MAT/05

3° Year  activated in the A.Y. 2017/2018

ModulesCreditsTAFSSD
One/two courses to be chosen among the following
12
C
SECS-S/06
6
C
MAT/07
6
C
MAT/05
6
C
SECS-P/05
6
B
MAT/08
6
B
MAT/09
6
B
MAT/06
Prova finale
6
E
-
activated in the A.Y. 2016/2017
ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
12
B
MAT/08
One course to be chosen among the following
6
C
SECS-P/01
6
C
FIS/01
6
B
MAT/03
One course to be chosen among the following
6
C
MAT/05
6
C
SECS-P/01
6
B
MAT/06
6
B
MAT/05
activated in the A.Y. 2017/2018
ModulesCreditsTAFSSD
One/two courses to be chosen among the following
12
C
SECS-S/06
6
C
MAT/07
6
C
MAT/05
6
C
SECS-P/05
6
B
MAT/08
6
B
MAT/09
6
B
MAT/06
Prova finale
6
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°- 3°
12
D
-
Between the years: 1°- 2°- 3°
Other activitites
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.

A Basic activities
B Characterizing activities
C Related or complementary activities
D Activities to be chosen by the student
E Final examination
F Other training activities
S Placements in companies, public or private institutions and professional associations

Mathematical analysis 2 (2016/2017)

Teaching code

4S00031

Credits

12

Coordinator

Sisto Baldo

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/05 - MATHEMATICAL ANALYSIS

MoodleMoodle Seminars 0

The teaching is organized as follows:

Teoria 2

Credits

5

Period

I sem.

Academic staff

Giandomenico Orlandi

Esercitazioni

Credits

4

Period

I sem.

Academic staff

Antonio Marigonda

Teoria 1

Credits

3

Period

I sem.

Academic staff

Sisto Baldo

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.

Program

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 vector-valued 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, Gauss-Green 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, Cauchy-Lipschitz'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

Reference texts
Activity Author Title Publishing house Year ISBN Notes
Esercitazioni Giuseppe De Marco Analisi 2. Secondo corso di analisi matematica per l'università Lampi di Stampa (Decibel Zanichelli) 1999 8848800378
Esercitazioni M. Conti, D. L. Ferrario, S. Terracini, G. Verzini Analisi matematica. Dal calcolo all'analisi, Vol. 1 (Edizione 1) Apogeo 2006 88-503-221
Esercitazioni V. Barutello, M. Conti, D.L. Ferrario, S. Terracini, G. Verzini Analisi matematica. Dal calcolo all'analisi Vol. 2 Apogeo 2007 88-503-242
Esercitazioni Conti M., Ferrario D.L., Terracini S,. Verzini G. Analisi matematica. Dal calcolo all'analisi. Volume 1. Apogeo  
Esercitazioni Conti F. et al. Analisi Matematica, teoria e applicazioni McGraw-Hill, Milano 2001 8838660026
Esercitazioni Giuseppe de Marco Analisi uno. Primo corso di analisi matematica. Teoria ed esercizi Zanichelli 1996 8808243125
Esercitazioni Giuseppe de Marco Analisi Zero, presentazione rigorosa di alcuni concetti base di matematica per i corsi universitari (Edizione 3) Edizione Decibel/Zanichelli 1997 978-8808-19831-0

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.
The oral test will concentrate mainly but not exclusively on the theory.

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