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## DIFFERENTIAL EQUATIONS

CODE 29032 2018/2019 7 credits during the 3nd year of 8760 Mathematics (L-35) GENOVA 7 credits during the 2nd year of 9011 Mathematics (LM-40) GENOVA 7 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA MAT/05 Italian GENOVA (Mathematics) 1° 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 Partial Differential Equations Theory.

### 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"

### 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 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. First order quasilinear equations. Conservation laws.

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

S. Salsa - Partial differential equations in action: from modelling to theory - Springer 2008

## TEACHERS AND EXAM BOARD

### Exam Board

GIANFRANCO BOTTARO (President)

GIOVANNI ALBERTI

FRANCESCA ASTENGO

## LESSONS

### TEACHING METHODS

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

### 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
22/01/2019 09:00 GENOVA Scritto Prenotarsi almeno 4 giorni prima per e-mail presso il docente
18/02/2019 09:00 GENOVA Scritto Prenotarsi almeno 4 giorni prima per e-mail presso il docente
28/06/2019 09:00 GENOVA Scritto Prenotarsi almeno 4 giorni prima per e-mail presso il docente
22/07/2019 09:00 GENOVA Scritto Prenotarsi almeno 4 giorni prima per e-mail presso il docente
12/09/2019 09:00 GENOVA Scritto Prenotarsi almeno 4 giorni prima per e-mail presso il docente