CdSMATEMATICA
Codice527AA
CFU6
PeriodoSecondo semestre
LinguaItaliano
| Moduli | Settore/i | Tipo | Ore | Docente/i | |
| ANALISI SUPERIORE | MAT/05 | LEZIONI | 42 |
|
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.
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
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
Spazi localmente convessi. Topologia delle funzioni test. Distribuzioni. Convoluzione. Trasformata di Fourier. Applicazioni alle EDP: esistenza di una soluzione fondamentale, regolarità ellittica.
Locally convex spaces. Topology of test functions. Distributions. Convolution. Fourier transforms. Applications to PDE: existence of fundamental solutions, elliptic regularity.
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.
Yes