Stampa
Anno immatricolazione
2018/2019
Anno offerta
2018/2019
Normativa
DM270
SSD
MAT/05 (ANALISI MATEMATICA)
Dipartimento
DIPARTIMENTO DI INGEGNERIA INDUSTRIALE E DELL'INFORMAZIONE
Corso di studio
ELECTRONIC ENGINEERING
Curriculum
PERCORSO COMUNE
Anno di corso
Periodo didattico
Primo Semestre (01/10/2018 - 18/01/2019)
Crediti
9
Ore
76 ore di attività frontale
Lingua insegnamento
English
Tipo esame
SCRITTO E ORALE CONGIUNTI
Docente
ROCCA ELISABETTA (titolare) - 9 CFU
Prerequisiti
Differential and integral calculus, complex functions, sequence and series of functions, linear algebra, differential operators, power and Fourier series, Laplace and Fourier transforms for classical signals, linear differential equations with constant coefficients.
Obiettivi formativi
The course is an introduction to some basic elements of linear functional analysis (Hilbert spaces and distributions), variational principles, ordinary differential equations and dynamical systems, with simple applications to basic partial differential equations.
Programma e contenuti
Ordinary differential equations

Basic definitions, examples and properties
Existence and uniqueness, comparison
Linear systems, exponential matrix, Liouville Theorem

Basic tools of functional analysis

Functional spaces, norms and Hilbert spaces
Best approximation and projection theorem, orthonormal basis
Linear operators: boundedness and continuity, symmetry,
Problems.
Applications to simple PDE's

Partial differential equations

Examples and modelling
Wave equations, D'Alembert formula, characteristics and
boundary value problems, spherical waves, solutions in two
and three dimensions
The Laplace and heat equations
Simple techniques for calculating explicit solutions; separation of
variables.

Distributions

Introduction, examples and applications.
Operating on distributions: sum, products, shift, rescaling, derivatives.
Sequence and series of distributions: Fourier series.
Fourier transform, temeperate distributions, convolutions
Metodi didattici
Lectures (hours/year in lecture theatre): 54
Practical class (hours/year in lecture theatre): 22
Practicals / Workshops (hours/year in lecture theatre): 0
Testi di riferimento
Ordinary Differential Equations and Systems
E.A. Coddington, An Introduction to Ordinary Differential Equations, Dover Publications, Inc., New York, 1961.
M.W. Hirsch and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, New York, 1974.
V.V. Nemytskii and V.V. Stepanov, Qualitative Theory of Differential Equations, Dover Publications, Inc., New York, 1989.
W.T. Reid, Sturmian Theory for Ordinary Differential Equations, Applied Mathematics Series 31, Springer-Verlag, New York Heidelberg Berlin, 1980.

Basic Tools of Functional Analysis
B. D. Reddy, Introductory Functional Analysis, Texts in Applied Mathematics n. 27, Springer Verlag, New York, (1998).
W. Rudin, Functional Analysis, Mc Graw Hill, New York, (1973).
W. Rudin, Real and Complex Analysis, Mc Graw Hill, New York, (1966).

Distributions
E. DiBenedetto, Real Analysis, Birkhauser, Boston, (2002): Chapter VII.
F.G. Friedlander, Introduction to the theory of distributions, Cambridge University Press, Cambridge, (1998).
S. Salsa, Partial Differential Equations in Action. From Modelling to Theory, Springer-Verlag Italia, (2008): Chapter 7.

Partial Differential Equations
E. DiBenedetto, Partial Differential Equations, 2nd Edition, Birkhaüser, (2009): Chapter 6.
S. Salsa, Partial Differential Equations in Action. From Modelling to Theory, Springer-Verlag Italia, (2008): Chapter 5.
W. Strauss. Partial Differential Equations: an introduction. Wiley.
Modalità verifica apprendimento
Written and oral examination
Altre informazioni
A more detailed description of the course can be found on the web page at the URL
http://matematica.unipv.it/rocca/
Obiettivi Agenda 2030 per lo sviluppo sostenibile