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
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 magistrale in Mathematics - Enrollment from 2025/2026The 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 |
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| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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3 modules to be chosen among the followingTo be chosen betweenLegend | 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 (2018/2019)
Teaching code
4S001097
Teacher
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
Period
II semestre dal Mar 4, 2019 al Jun 14, 2019.
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 Advanced Numerical Analysis and Scientific Computing courses.
Program
First order partial differential equations : Transport equation, Method of Characteristics. Introduction to Calculus of Variations and Hamilton-Jacobi equations. Introduction to Scalar Conservation laws. Second order partial differential equations : heat equation, Laplace equation, second order parabolic equations, second order hyperbolic equations, wave equation. Introduction to Semigroup theory.
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| D. Gilbarg - N. S. Trudinger | Elliptic Partial Differential Equations of Second Order | Springer | 1998 | 3-540-13025-X | Revised printing |
| Evans, L. C. | Partial Differential Equations (Edizione 1) | American Mathematical Society | 1998 | 0821807722 | |
| András Vasy | Partial Differential Equations - An Accessible Route through Theory and Applications | American Mathematical Society | 2015 | 978-1-4704-1881-6 | |
| S. Salsa | Partial Differential Equations in Action | Springer Verlag Italia | 2008 | 978-88-470-0751-2 |
Examination Methods
The assesment is based on an oral presentation of selected topics of the course program together with an individual project on PDE modelling in open form to be agreed with course instructors.
The aim is to evaluate the skills of the students in understanding what are the appropriate mathematical tools and techniques, among those studied in the course, that have to be used to effectively solve problems arising as PDE modelling of different phenomena.
