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 (SLD) are reminded that, in order to request exam accommodations, it is first necessary to upload the relevant certification to the university website at servizionline.unige.it, under the "Students" section. The documentation will be verified by the University’s Office for the Inclusion of Students with Disabilities and SLD.

After this step, students must send an email to the professor responsible for the exam at least 7 days in advance of the exam date. The email must also be cc'ed to both the School Disability and SLD Inclusion Officer (sergio.didomizio@unige.it) and the Inclusion Office mentioned above. The email must include the following details:

• the course title

• the exam date

• the student’s last name, first name, and student ID number

• the compensatory tools and dispensatory measures deemed necessary and being requested.

The Inclusion Officer will confirm to the professor that the student is eligible to request exam accommodations and that such accommodations must be discussed with the professor. The professor will then reply to confirm whether the requested accommodations can be granted.

Requests must be submitted at least 7 days before the exam date to give the professor sufficient time to review them. In particular, if the student intends to use concept maps during the exam (which must be significantly more concise than those used for study purposes), late submission will not allow sufficient time for any necessary revisions.

For more information on requesting services and accommodations, please refer to the document:
"Guidelines for the Request of Services, Compensatory Tools and/or Dispensatory Measures, and Specific Aids".

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

The start date of the lessons is set for 23 February 2026.

Class schedule

DIFFERENTIAL EQUATIONS 1

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.

FURTHER INFORMATION

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