CODE  86902 

ACADEMIC YEAR  2023/2024 
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.
Students with certification of Specific Learning Disabilities (SLD), disabilities, or other special educational needs are advised to contact the instructor at the beginning of the course to agree on teaching methods and examination procedures that, while respecting the teaching objectives, take into account individual learning styles and provide suitable compensatory tools.
Course Introduction
Part One: Review of Numerical Series and Series of Functions
Part Two: Fourier Series and Fourier Transform
Part Three: Applications to the Solution of Partial Differential Equations
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
The class will start according to the academic calendar.
All class schedules are posted on the EasyAcademy portal.
There will be two midterm exams, one in the middle and one at the end of the semester. They will be twohour written exams, with two or three exercises on the topics already covered in the syllabus. Those who pass both exams with a score above 15 in each and an overall average of at least 18 can directly record their grade without an oral exam. The oral exam is optional for those who want to try to improve their grade. A selection of course topics will be requested during the oral exam, which will be defined at the end of the semester and made available on Aulaweb.
In the regular exams, there will be a twohour written exam, with two or three exercises on solving partial differential equations using Fourier series or Fourier transform methods. The oral exam is optional.
Rules for the written exam. Students are allowed to use handwritten notes of any kind. Electronic devices (calculators, phones, computers) are prohibited, except for tablets, which can be used solely to consult notes.
Students with certification of Specific Learning Disabilities (SLD), disabilities, or other special educational needs are advised to contact the instructor at the beginning of the course to agree on teaching methods and examination procedures that, while respecting the teaching objectives, take into account individual learning styles and provide suitable compensatory tools.
The written exam will assess the ability to solve partial differential equations using Fourier series or Fourier transform methods. Clarity and organization of the presentation, correctness of the solutions, quality, and rigor of the arguments and deductions will be evaluated. The oral exam will assess more specific knowledge on a selection of theoretical topics covered in the course. The ability to present and the correctness of logicaldeductive arguments will be evaluated.
Date  Time  Location  Type  Notes 

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.