Scheda programma d'esame
ANALISI SUPERIORE
EMANUELE PAOLINI
Anno accademico2016/17
CdSMATEMATICA
Codice527AA
CFU6
PeriodoSecondo semestre
LinguaItaliano

ModuliSettoreTipoOreDocente/i
ANALISI SUPERIOREMAT/05LEZIONI42
EMANUELE PAOLINI unimap
Learning outcomes
Knowledge

The student who successfully completes the course will demonstrate an advanced knowledge of Distributions Theory and Fourier Transform as well as a basic knowledge of classical theory of linear PDEs.

Assessment criteria of knowledge

The student will be assessed on

-knowledge of the content of the course.

-ability to use the content of the course to expand is/her knwoledge via the study of new topics.

Methods:

  • Final oral exam
  • Oral report
Teaching methods

Delivery: face to face

Learning activities:

  • attending lectures
  • participation in seminar
  • preparation of oral/written report
  • participation in discussions
  • individual study

Attendance: Advised

Teaching methods:

  • Lectures
  • project work
Programma (contenuti dell'insegnamento)

Spazi localmente convessi. Topologia delle funzioni test. Distribuzioni. Convoluzione. Trasformata di Fourier. Applicazioni alle EDP: esistenza di una soluzione fondamentale, regolarità ellittica.

Syllabus

Locally convex spaces. Topology of test functions. Distributions. Convolution. Fourier transforms. Applications to PDE: existence of fundamental solutions, elliptic regularity.

Bibliography

Recommended reading includes some chapters from the books: H.L.Royden, Real Analysis . E.H.Lieb, M.Loss, Analysis. N. Dunford, J.T.Schwartz, Operator Theory (Part II) P.R.Halmos, Introduction to Hilbert Space. V.S.Vladimirov, Le distribuzioni nella fisica matematica. G.Talenti, Calcolo delle Variazioni. E.Giusti, Calcolo delle Variazioni. W.Rudin, Functional Analysis.

Work placement

Yes

Ultimo aggiornamento 10/05/2017 17:49