Insegnamento
ANALYTICAL AND STOCHASTIC MATHEMATICAL METHODS FOR ENGINEERING
INP5070357, A.A. 2016/17

Principali informazioni sull'insegnamento
Corso di studio Corso di laurea magistrale in
MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA
IN2191, ordinamento 2015/16, A.A. 2016/17
1146606
Curriculum Percorso Comune
Crediti formativi 12.0
Denominazione inglese ANALYTICAL AND STOCHASTIC MATHEMATICAL METHODS FOR ENGINEERING
Dipartimento di riferimento Dipartimento di Ingegneria Civile, Edile e Ambientale (ICEA)
Sito E-Learning https://elearning.unipd.it/dicea/course/view.php?idnumber=2016-IN2191-000ZZ-2016-INP5070357-N0
Obbligo di frequenza No
Lingua di erogazione INGLESE
Sede PADOVA

Docenti
Responsabile GIORGIA CALLEGARO MAT/06
Altri docenti NICOLA GAROFALO MAT/05

Dettaglio crediti formativi
Tipologia Ambito Disciplinare Settore Scientifico-Disciplinare Crediti
CARATTERIZZANTE Discipline matematiche, fisiche e informatiche MAT/05 6.0
CARATTERIZZANTE Discipline matematiche, fisiche e informatiche MAT/06 6.0

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
LEZIONE 12.0 96 204.0 Nessun turno

Calendario
Inizio attività didattiche 01/10/2016
Fine attività didattiche 20/01/2017

Commissioni d'esame
Commissione Dal Al Membri
2 2016 01/10/2016 30/11/2017 CALLEGARO GIORGIA (Presidente)
GAROFALO NICOLA (Membro Effettivo)
GRASSELLI MARTINO (Supplente)
VARGIOLU TIZIANO (Supplente)
1 2015 01/10/2015 30/11/2016 CALLEGARO GIORGIA (Presidente)
GUIOTTO PAOLO (Membro Effettivo)
GRASSELLI MARTINO (Supplente)
VARGIOLU TIZIANO (Supplente)

Syllabus
Prerequisiti: None
Conoscenze e abilita' da acquisire: Objective
Introduce the students to the basic knowledge of mathematical and probability tools for engineers.
Outcomes
A student who has met the objectives of the course will have a comprehensive knowledge of :
• Basic mathematical tools of functional analysis and measure theory
• Basic concepts of probability
Modalita' di esame: Final examination based on: written examination.
Criteri di valutazione: Critical knowledge of the course topics. Ability to present the studied material.
Contenuti: 1. Lebesgue Measure and Integral — Lebesgue measure and integral on R^d, limit theorems, dependence by parameters, reduction formula and change of variables. Introduction to abstract measure and integral.
2. Normed spaces — Concept of norm; uniform, L^1 and L^p norms; sequences, limits, completeness and Banach spaces. Concept of scalar product and Hilbert space; the space L^2; separable spaces and concept of orthonormal base.
3. Fundamentals of Complex Analysis — Power series in C and elementary analytic functions; concept of holomorphic function, Cauchy-Riemann equations, analyticity of holomorphic functions; isolated singularities; residue theorem and applications.
4. Introduction to Fourier Analysis — Fourier series: Euler formulas, convergence and sum (point-wise, uniform, L^2). Fourier transform: L^1 definition, convolution and approximate units, inversion formula. Schwarz functions and L^2 Fourier transform. Applications.
5. Introduction to probability — probability spaces, axioms of probability, conditional probabilities, independence of events.
6. Random variables (discrete and continuous) — definition, expectation and moments. Examples of random variables and applications, with a focus on Gaussian random variables.
7. Random vectors.
8. Characteristic function.
9. Convergence of random variables: weak, in probability, in L^p, almost sure.
10. The law of large numbers and the central limit theorem with applications.
11. Conditional expectation.
Attivita' di apprendimento previste e metodologie di insegnamento: Lectures supported by exercises.
Eventuali indicazioni sui materiali di studio: Lecture notes relative to the Analytical Methods part will be provided.
See the reference book below for the Probability part.
Testi di riferimento:
  • Sheldon Ross, A first course in Probability. --: Pearson, 1976. Ninth edition Cerca nel catalogo