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.
1° Year
| Modules | Credits | TAF | SSD |
|---|
| Modules | Credits | TAF | SSD |
|---|
| Modules | Credits | TAF | SSD |
|---|
1 module between the following1 module between the following3 modules among the followingLegend | 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.
Partial differential equations (2021/2022)
Teaching code
4S001097
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
The teaching is organized as follows:
Teoria 2
Teoria 1
Learning outcomes
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.
Program
Derivation of some partial differential equations from the modelling. Partial differential equations of first order: characteristics' method, eikonal equation. Weak solutions: scalar Conservation Law, introduction to the Calculus of Variations and to the Hamilton- Jacobi equation. Linear partial differential equations of second order: classification. Laplace equation and Poisson equation: fundamental solution, harmonic functions, Green's identity, Green's function, Poisson's formula for the ball, gradient estimates, Liouville's Theorem. Elliptic equations: maximum principles, Hopf Lemma. Uniqueness theorems. Weak solutions to evolution equations of parabolic and hyperbolic type. Vector valued Sobolev spaces. A priori estimates. Existence via the Galerkin Method.
Examination Methods
Oral exam based on a Seminar (discussion of one of the topics discussed in class or of a project). The aim is to evaluate the understanding of the methods and techniques discussed in class and/or the ability to apply them to concrete situations, as well as the communicative skills of the students.
