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## DIFFERENTIAL EQUATIONS

CODE 29032 2021/2022 7 cfu during the 3nd year of 8760 MATEMATICA (L-35) - GENOVA 7 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA 7 cfu during the 2nd year of 9011 MATEMATICA(LM-40) - GENOVA MAT/05 Italian GENOVA 2° Semester AULAWEB

## 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.

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

Date Time Location Type Notes
11/01/2022 09:00 GENOVA Scritto Appello riservato agli studenti che hanno frequentato l'insegnamento nell'a.a.2020/21 o a.a. precedenti
01/02/2022 09:00 GENOVA Scritto Appello riservato agli studenti che hanno frequentato l'insegnamento nell'a.a.2020/21 o a.a. precedenti
13/06/2022 14:00 GENOVA Scritto
06/07/2022 09:00 GENOVA Scritto
07/09/2022 09:00 GENOVA Scritto