First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
SCP3050960, A.A. 2015/16

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2015/16
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
Website of the academic structure http://matematica.scienze.unipd.it/2015/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge FABIO ANCONA MAT/05

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
INP5070341 INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS FABIO ANCONA IN2191

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/05 Mathematical Analysis 8.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Practice 4.0 32 68.0 No turn
Lecture 4.0 32 68.0 No turn

Calendar
Start of activities 01/10/2015
End of activities 28/01/2016
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
6 Introduzione alle Equazioni alle Derivate Parziali - a.a. 2018/2019 01/10/2018 30/09/2019 ANCONA FABIO (Presidente)
ROSSI FRANCESCO (Membro Effettivo)
MARSON ANDREA (Supplente)
MONTI ROBERTO (Supplente)
SORAVIA PIERPAOLO (Supplente)
5 Introduzione alle Equazioni alle Derivate Parziali - 2017/2018 01/10/2017 30/09/2018 ANCONA FABIO (Presidente)
ROSSI FRANCESCO (Membro Effettivo)
CARAVENNA LAURA (Supplente)
MARSON ANDREA (Supplente)
MONTI ROBERTO (Supplente)
SORAVIA PIERPAOLO (Supplente)
4 Introduzione alle Equazioni alle Derivate Parziali - 2016/2017 01/10/2016 30/11/2017 ANCONA FABIO (Presidente)
SORAVIA PIERPAOLO (Membro Effettivo)
CARAVENNA LAURA (Supplente)
MARSON ANDREA (Supplente)
MONTI ROBERTO (Supplente)
3 Introduzione alle Equazioni alle Derivate Parziali - a.a. 2015/2016 01/10/2015 30/09/2016 ANCONA FABIO (Presidente)
SORAVIA PIERPAOLO (Membro Effettivo)
CARAVENNA LAURA (Supplente)
MARSON ANDREA (Supplente)
MONTI ROBERTO (Supplente)

Syllabus
Prerequisites: Differential and integral calculus.
Elementary theory of ordinary differential equations.
Basic theory of complex analysis (functions of complex variables, holomorphic and analytic functions).
Fourier transform.
Target skills and knowledge: Basic notions of the theory of linear partial differential equations. It's a fundamental course suggested to students with interests both in pure and in applied mathematics, and in particular to students with a curriculum in analysis.
Examination methods: The exam consists of a final oral examination on the topics treated in class. There will be both theoretical questions and the discussion of some exercise to solve.
Assessment criteria: The evaluation criteria will be the following:
- coherence and rigor in the exposure of statements and theorems
- thoroughness and adherence to the topics of discussion
- ability to use the acquired knowledge to solve problems and exercises.
Course unit contents: Didactic plan:
- Laplace equation: foundamental solution, harmonic functions and main properties, maximum principle. Poisson equation. Perron method.
- Maximum principle for degenerate elliptic operators.
- Heat equation: foundamental solution, existence of solutions for the Cauchy problem and rapresentation formula. Uniqueness and regularity of solutions.
- Wave equation: existence of solutions, D'alembert formnula, uniqueness, finite speed of propagation.
Planned learning activities and teaching methods: The methodology of teaching used will be the traditional lesson.
Textbooks (and optional supplementary readings)
  • S. Salsa, Partial Differential Equations in Action: From Modelling to Theory. Springer: Milano, 2015. Cerca nel catalogo
  • L.C. Evans, Partial Differential Equations, 2nd edition. Providence, Rhode Island: American Mathematical Society, 2010. Cerca nel catalogo
  • W. A. Strauss, Partial Differential Equations. An Introduction. New York: Wiley, 1992. Cerca nel catalogo