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.

Learning outcomes: understanding of the concepts and proofs presented during the lectures. Ability to develop proofs that are variants of those presented in the course, to construct examples and counterexamples, and to solve exercises related to the topics of the course.

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).

Compensatory and dispensatory measures Disability/Invalidity/Specific Learning Disorder

Dispensatory measures and compensatory tools are intended to enable students to achieve the same learning objectives as their fellow students, not to facilitate the examination.

The use of compensatory tools and the application of dispensatory measures must be authorised in advance by the teacher in agreement with the Referee.

To take advantage of the adaptations during the examination, fill in the Adaptation request form; the request will be automatically sent by the system to the teacher in charge of the teaching, to the Contact Person of your School/Area/Department and in copy to the Sector; you will also receive a copy of the request sent by e-mail.

The adjustments available to students are as follows:

• Additional time (+30% DSA)
• Additional time (+50% disability/invalidity)
• Additional time during oral exams to organise the answer
• Calculator (programmable and graphing calculators are not allowed)
• Conceptual Maps
• Tables and/or Forms
• Take the exam in written form
• Take the exam in oral form
• Tutor reader (for written tests only)
• Tutor-writer (for written tests only)

Your request for adaptations must be submitted at least 7 working days before the scheduled exam date.

All information for students with disabilities and DSA is available on the webpage: Services for students with disabilities or DSA | UniGe | University of Genoa

Reference for inclusion: Sergio Di Domizio - sergio.didomizio@unige.it

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

LESSONS

LESSONS START

Classes will be held according to the schedule available at the following page

https://corsi.unige.it/corsi/11907/studenti-orario

Class schedule

DIFFERENTIAL EQUATIONS 1

EXAMS

EXAM DESCRIPTION

Written and oral exam. Students may access the oral exam only if they have obtained a mark of at least 18/30 in the written 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.

FURTHER INFORMATION

Ask the professor for other information not included in the teaching schedule.