CODE  86902 

ACADEMIC YEAR  2022/2023 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/05 
LANGUAGE  Italian 
TEACHING LOCATION 

SEMESTER  1° Semester 
TEACHING MATERIALS  AULAWEB 
The course focuses on Fourier analysis methods as applied to the solutions of boundary value problems for classical partial differential equations. Thus, a mathematical presentation of Fourier series and transforms is presented, combining a reasonable amount of formal precision with applications to explicit problems, to be solved with workable formulae. The basic facts about analytic functions of one complex variable are also introduced because of their pervasive use in applications, with particular emphasis on the elementary and fundamentally geometric aspects of analyticity.
The main objective is to achieve a solid basic operative knowledge of Fourier analysis techniques (Fourier series and Fourier transform) for functions of one real variable as applied to boundary value problems for the classical partial differential equations (heat, Poisson, waves), and to understand the main properties of analytic functions of one complex variable.
Students are expected to master the basic Fourier analysis techniques (series and transforms) that are needed in order to solve standard boundary value problems for classical partial differential equations (heat, LaplacePoisson, waves), both using series expansions and integral formulae. Basic operative knowledge concerning analytic functions of one complex variable is also expected.
Calculus of functions of one and several real variables, linear algebra
Blackboard and computer illustrations
Fourier series for periodic functions and Fourier transform on R; main properties and applications to finding solutions of boundary value problems for the classical PDE, essentially through separation of variables techniques or via Fourier transform methods. The notion of holomorphic map is introduced and the main properties of analytic functions are investigated.
S. Salsa  Partial differential equations in action: from modelling to theory  Springer 2016
Marco Codegone e Luca Lussardi, Metodi Matematici per l'Ingegneria, Zanichelli, 2021.
Office hours: On appointment
MATTEO SANTACESARIA (President)
FILIPPO DE MARI CASARETO DAL VERME (President Substitute)
ERNESTO DE VITO (President Substitute)
The class will start according to the academic calendar.
All class schedules are posted on the EasyAcademy portal.
Written and (optional) oral examination
Students are required to work on standard problems in series expansions, Fourier transforms, applications to boundary value problems for classical PDE and basic properties of analytic functions.
Date  Time  Location  Type  Notes 

27/01/2023  09:30  GENOVA  Scritto  
10/02/2023  09:30  GENOVA  Scritto  
16/06/2023  09:30  GENOVA  Scritto  
07/07/2023  09:30  GENOVA  Scritto  
11/09/2023  09:30  GENOVA  Scritto 
Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.