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

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:

1° Year 

ModulesCreditsTAFSSD
6
B
MAT/07
6
B
MAT/03
12
B
MAT/05
6
B
MAT/05
6
B
MAT/06

2° Year   It will be activated in the A.Y. 2025/2026

ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
It will be activated in the A.Y. 2025/2026
ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°
1 module between the following:
- A.A. 2024/2025 Computational algebra not activated;
- A.A. 2025/2026 Homological Algebra not activated.
6
B
MAT/02
6
B
MAT/02
Between the years: 1°- 2°
1 module between the following
6
B
MAT/08
6
B
MAT/08
Between the years: 1°- 2°
3 modules among the following
6
C
MAT/03
6
C
MAT/02 ,MAT/03
6
C
MAT/02
6
C
MAT/08
6
C
MAT/08
6
C
MAT/02
6
C
MAT/06
6
C
INF/01
6
C
MAT/05
6
C
MAT/09
6
C
MAT/02
6
C
MAT/08
6
C
MAT/08
6
C
MAT/07
6
C
INF/01 ,MAT/06
Between the years: 1°- 2°
12
D
-
Between the years: 1°- 2°
Further activities
4
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

Partial differential equations  (2024/2025)

Teaching code

4S001097

Teacher

Antonio Marigonda

Coordinator

Antonio Marigonda

Credits

6

Language

English en

Scientific Disciplinary Sector (SSD)

MAT/05 - MATHEMATICAL ANALYSIS

Period

Semester 2 dal Mar 3, 2025 al Jun 13, 2025.

Courses Single

Authorized

Lessons timetable MoodleMoodle Seminars 0

Learning objectives

The course aims to give a general overview of the theoretical aspects of the most important partial differential equations arising as fundamental models in the description of main phenomena in Physics, Biology, economical/social sciences and data analysis, such as diffusion, transport, reaction, concentration, wave propagation, with a particular focus on well-posedness (i.e. existence, uniqueness, stability with respect to data). Moreover, the theoretical properties of solutions are studied in connection with numerical approximation methods (e.g. Galerkin finite dimensional approximations) which are studied and implemented in the Numerical Analysis courses.

Prerequisites and basic notions

Real functions of several real variables, integration, ordinary differential equations.

Program

Part I: classical solutions.
We will address some linear equations important for applications: the transport equation, the Poisson equation, the heat equation, the wave equation. We will prove their well-posedness and focus on representantion fomrulae for the solutions in all these cases. We will also address solutions to nonlinear first-order equations (Hamilton-Jacobi) equations via the method of characteristics.
Part II: weak solutions.
We will discuss the weak formulations of some problems, mainly linear ones. Possible topics for the second part of the course include: the variational formulation of divergence-form problems (e.g., Poisson and heat equations); the Hille-Yosida theorem for evolution equations; viscosity solutions for equations that are notin divergence form (for example, Hamilton-Jacobi equations).

Bibliography

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Didactic methods

Classroom lessons and exercises. Individual study. Notes, exercises and additional material will be available on Moodle.

Learning assessment procedures

The exam consists of a written and an oral test, which includes exercises and questions on the course program. There is no difference in the exam according to whether students have attended the course or not.

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

Evaluation criteria

- Knowledge and understanding: part of the exam is devoted to assess the knowledge and understanding of the course contents.
- Applying knowledge and understanding: students are required to solve problems based on the course's contents.
- Critical thinking: some of the questions may require a personal contribution from the student, based on autonomous work on the course contents.
- Communication skills: students are required to formulate their answers in a clear, complete and concise manner.
- Learning skills: part of the course materials consists of textbooks or scientic papers that are left to the students' personal reading.

Criteria for the composition of the final grade

The exam will be assigned a grade out of thirty. The exam will focus on the entire course program.

Exam language

English

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