Corsi di Laurea Corsi di Laurea Magistrale Corsi di Laurea Magistrale
a Ciclo Unico
Scuola di Ingegneria
MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA
Insegnamento
INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
INP5070341, A.A. 2017/18

Informazioni valide per gli studenti immatricolati nell'A.A. 2017/18

Principali informazioni sull'insegnamento
Corso di studio Corso di laurea magistrale in
MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA (Ord. 2017)
IN2191, ordinamento 2017/18, A.A. 2017/18
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Curriculum Percorso Comune
Crediti formativi 9.0
Tipo di valutazione Voto
Denominazione inglese INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
Dipartimento di riferimento Dipartimento di Ingegneria Civile, Edile e Ambientale (ICEA)
Sito E-Learning https://elearning.unipd.it/dicea/course/view.php?idnumber=2017-IN2191-000ZZ-2017-INP5070341-N0
Obbligo di frequenza No
Lingua di erogazione INGLESE
Sede PADOVA
Corso singolo È possibile iscriversi all'insegnamento come corso singolo
Corso a libera scelta È possibile utilizzare l'insegnamento come corso a libera scelta

Docenti
Responsabile NICOLA GAROFALO MAT/05

Dettaglio crediti formativi
Tipologia Ambito Disciplinare Settore Scientifico-Disciplinare Crediti
CARATTERIZZANTE Discipline matematiche, fisiche e informatiche MAT/05 9.0

Modalità di erogazione
Periodo di erogazione Primo semestre
Anno di corso I Anno
Modalità di erogazione frontale

Organizzazione della didattica
Tipo ore Crediti Ore di
Corso
Ore Studio
Individuale
Turni
ESERCITAZIONE 4.0 32 68.0 Nessun turno
LEZIONE 5.0 40 85.0 Nessun turno

Calendario
Inizio attività didattiche 02/10/2017
Fine attività didattiche 19/01/2018

Syllabus
Prerequisiti: This course will be completely self-contained, and can be profitably followed by any student who has had a good exposure to the fundamentals of calculus of one and several variables. Some of these fundamentals will be recalled in detail during the lectures.
Conoscenze e abilita' da acquisire: Fourier transform in the Euclidean space. Solution of the Cauchy problem for the wave equation in the physical space-time. Huyghens principle. Cauchy problem for the heat equation. Properties of the heat semigroup. Laplace equation, sub- and super-harmonic functions. Koebe's theorem. Hypoellipticity of Laplace equation: the theorem of Caccioppoli-Cimmino-Weyl. Strong maximum principle. Overdetermination and symmetry. The geometry of a beam that undergoes torsion at one of its ends. The soap-bubble theorem of A.D. Alexandrov.
Modalita' di esame: The students will be provided with take home written exams of increasing level of difficulty. By taking these exams each student pledges that he/she will work on the test without communicating with any of his/her classmates or
anybody else. Each student is only allowed to discuss the exam with Prof. Garofalo.
Infringement of these rules will be considered academic cheating
and adversely affect the final grade in this course.
Criteri di valutazione: A final grade will be assigned on the basis of the grades in the take-home exams.
Contenuti: Partial differential equations (PDEs) are expressions involving an unknown function of two or more variables and a certain number of its partial derivatives. Such equations govern the phenomena of the physical world, and they play a preeminent role both in pure mathematics and in the applied sciences:
1. The small vibrations of the string of a violin are described by the wave equation, a PDE that is ubiquitous in the description of undulatory phenomena.
2. The potential of the gravitational field generated by a certain distribution of mass satisfies (away from the mass itself) a PDE that is known as Laplace equation.
3. The distribution of temperature in a conducting body is described (at least near the source) by yet another PDE known as the heat equation. These are instances of PDEs of linear type.

The principal aim of this course is to bring the audience to mastering some of the basic aspects of PDEs, beginning with the linear models described above. The second part of the course will be devoted to providing the audience with a glimpse into some of the fascinating aspects of nonlinear PDEs.
Attivita' di apprendimento previste e metodologie di insegnamento:
Eventuali indicazioni sui materiali di studio: Lecture notes will be made available to the students.
Testi di riferimento:
  • Nicola Garofalo, An Introductions to Partial Differential Equations. --: --, 2017. Lecture Notes