OVERVIEW

The course introduces the study of partial differential equations (PDE). Given the richness and the variety of physical, geometric and probabilistic phenomena that these equations can describe, there is no general theory that allows them to be studied and solved in a unified way. We therefore aim to analyze equations and methods that are the most important for applications. Large attention will be given to some specific linear PDEs of the first and second order (linear transport equation, Laplace and Poisson equations, heat equation, wave equation); hints of theory for some non-linear PDEs will also be provided.

AIMS AND CONTENT

LEARNING OUTCOMES

The aim of this course is to provide a first introduction to the theory of partial differential equations.

AIMS AND LEARNING OUTCOMES

Learn to classify partial differential equations and identify the most appropriate resolution or analysis methods for each of the "classical" ones; know how to apply them to find formulas for representing solutions or to establish their qualitative properties.

PREREQUISITES

A basic knowledge of measure theory, Lebesgue spaces and ordinary differential equations is recommended.

TEACHING METHODS

Traditional teaching (theoretical lessons on the blackboard and exercises).

Students with disabilities or specific learning disorders (DSA) are reminded that in order to request adaptations during the exam, they must follow the instructions described in detail on Aulaweb https://2023.aulaweb.unige.it/enrol/index.php?id=12490#section-3 In particular, adaptations must be requested significantly in advance (at least 10 days) with respect to the exam date by writing to the teacher and to the School Contact teacher and the competent office (see instructions).

SYLLABUS/CONTENT

Linear transport equation, Laplace and Poisson equations, harmonic functions, Perron method, heat equation, wave equation, method of characteristics, various methods for representing solutions.

RECOMMENDED READING/BIBLIOGRAPHY

Evans, "Partial Differential Equations"

Salsa, "Equazioni a derivate parziali"

TEACHERS AND EXAM BOARD

Exam Board

FLAVIANA IURLANO (President)

SIMONE DI MARINO

FILIPPO DE MARI CASARETO DAL VERME (President Substitute)

ANDREA BRUNO CARBONARO (Substitute)

MATTEO SANTACESARIA (Substitute)

LESSONS

LESSONS START

The start of the lessons is fixed according to the academic calendar.

EXAMS

EXAM DESCRIPTION

Written and oral exam

ASSESSMENT METHODS

The written exam will verify:

• the ability to identify suitable methods to solve the proposed problems;
• the ability to apply the identified methods;
• the ability to argue and justify the steps taken.

The oral exam will verify:

• demonstrative and argumentative skills;
• knowledge not positively assessed in the written exam.

Exam schedule