OVERVIEW

Some basic topics in partial differential equations are covered.

The lectures are delivered in Italian.

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

To provide some basic contents in Mathematical Analysis (Partial Differential Equations Theory) that are considered important to get a well grounded knowledge in the basic branches of Mathematics for the students who want to get a master's degree in Applied Mathematics.

Expected learning outcomes:
The students will become acquainted with the concepts and proofs carried out in class and how they are used in practice to solve exercises; moreover they will know how to produce easy variants of demonstrations seen and construct examples on topics covered in this course.

PREREQUISITES

Mathematical Analysis I, 2 and 3, the first semester of Geometry, "IAS 1" (Functional analysis and L^p spaces)

TEACHING METHODS

Both theory and exercises are presented by the teacher in the classroom on the blackboard.

SYLLABUS/CONTENT

Fundamental linear partial differential equations with constant coefficients: the transport equation, the Laplace equation, Poisson, the heat and the wave equation. General properties of the solutions: mean value property, maximum principles, energy estimates and their consequences. Some general techniques to obtain explicit formulas for solutions: separation of variables, Green’s functions, reflection method, Perron's method, some potential theory, Duhamel’s principle, spherical means, method of descent. Conservation laws.

RECOMMENDED READING/BIBLIOGRAPHY

S. Salsa - Partial differential equations in action: from modelling to theory - Springer 2016

TEACHERS AND EXAM BOARD

Exam Board

FILIPPO DE MARI CASARETO DAL VERME (President)

GIOVANNI ALBERTI

SIMONE DI MARINO (President Substitute)

MATTEO SANTACESARIA (President Substitute)

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

DIFFERENTIAL EQUATIONS

EXAMS

EXAM DESCRIPTION

Written and oral.

Exam schedule