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Università degli Studi di Parma Università degli Studi di Parma
Second cycle degree course in
Mathematics
Università degli Studi di Parma
Department of Mathematical, Physical and Computer Sciences

ADVANCED ANALYSIS 1
cod. 19052

borrowed from Corso di Laurea magistrale in MATEMATICA - ANALISI SUPERIORE 1 - cod. 19052
Academic year 2009/10
1° year of course - First semester
Professor
Academic discipline
Analisi matematica (MAT/05)
Field
Formazione teorica avanzata
Type of training activity
Characterising
72 hours
of face-to-face activities
9 credits
hub:
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

Introduction to modern Mathematical Analysis

Prerequisites

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Course unit content

 L^p spaces<br />
Convolution and smoothing, density theorems; <br />
The Frechet-Kolmogorov compactness theorem <br />
<br />
Compact operators<br />
The Fredholm alternative<br />
Spectral decompositions of self-adjoint compact operators<br />
<br />
Distributions<br />
Test functions, convergence of distributions, derivatives<br />
<br />
Sobolev Spaces in dim=1 <br />
Extension operators; density theorems; imbedding theorems;<br />
weak formulation of boundary value problems; <br />
eigenfunctions of  Sturm-Liouville problem<br />
<br />
Sobolev Spaces in   dim >1 <br />
Approximation by smooth functions: Friedrichs theorem; <br />
coordinates transformations, <br />
extension operators; density theorems; <br />
Sobolev inequality; <br />
imbedding theorems; compactness properties. <br />
<br />
Weak formulation of elliptic boundary value problems; <br />
 H^2 regularity; <br />
maximum principle; <br />
eigenfunctions and spectral decomposition

Full programme

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Bibliography

H. Brezis, Analisi funzionale, Liguori Editore <br />
L.C. Evans, Partial Differential Equations, American Mathematical Society

Teaching methods

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Assessment methods and criteria

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Other information

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