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 Partial Differential Equations Theory.

LEARNING OUTCOMES (FURTHER INFO)

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.

TEACHING METHODS

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

SYLLABUS/CONTENT

First order quasilinear equations. Classification of second order equations. Some classical linear equations of Mathematical Physics: the equations of Laplace, Poisson, the heat and the wave equation. General properties of the solutions: mean value property, maximum principle, energy estimates and their consequences. Some general techniques to obtain explicit formulas for solutions: separation of variables, Green’s function, reflection method, Duhamel’s principle, spherical means, method of descent.

RECOMMENDED READING/BIBLIOGRAPHY

Lawrence C. Evans, Partial Differential Equations, Graduate Studies in Math. Vol. 19, 1998, American Mathematical Society, Providence , Rhode Island.

Sandro Salsa, Partial differential equations in action: from modelling to theory, Springer 2008.

TEACHERS AND EXAM BOARD

Exam Board

GIANFRANCO BOTTARO (President)

GIANCARLO MAUCERI (President)

ADA ARUFFO

ANDREA BRUNO CARBONARO

LESSONS

LESSONS START

February 20, 2016

Class schedule

DIFFERENTIAL EQUATIONS

EXAMS

EXAM DESCRIPTION

Written and oral tests.

ASSESSMENT METHODS

The written examination consists in some exercises about the topics covered in this course. In the oral exam some questions are asked on the course content.

Exam schedule

FURTHER INFORMATION

Attendance is recommended.

Prerequisite: Mathematical Analysis I, 2 and 3, Linear Algebra and Analitic Geometry, the first semester of Geometry, Elements of Advanced Analysis 1.