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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 2
cod. 1004200

borrowed from Corso di Laurea magistrale in MATEMATICA - ANALISI SUPERIORE 2 - cod. 1004200
Academic year 2018/19
2° year of course - First semester
Professor
Alberto Giorgio AROSIO
Academic discipline
Analisi matematica (MAT/05)
Field
Attività formative affini o integrative
Type of training activity
Related/supplementary
48 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in ITALIAN
lectures timetable unavailable
exam calls
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Learning objectives

The course aims at providing a first introductory and yet significant knowledge on the problems and the methods of the Calculus of Variations.

Prerequisites

Basic knowledge of Analysis and Measure Theory, and Sobolev Spaces

Course unit content

The course is focused on some classical topics of the Calculus of Variations. It is divided in two parts. The first one deals with a thorough study of firts and second order necessary and sufficient minimality conditions for one-dimensional problems. Among the various examples, a complete treatment of the brachistochrone problem will be given. The second part is devoted to the DIrect Methods of the Calculus of Variations: after proving a general existence theorem for integral functionals in N-dimensions, we will expose De Giorgi's regularity theory.

Full programme

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Bibliography

No specific reference textbooks. The topics of the course are chosen by the instructor and may be found in several different classical books on the Calculus of Variations.

Teaching methods

The course will consist in lectures delivered at the blackboard. The topics will be complemented with motivations, instructive exercises and applications. Emphasis will be placed on the mathematical rigor of the presentation, which will be as much detailed and self-contained as possible.

Assessment methods and criteria

The final exam will consist in an oral interview, aiming at evaluating the learning ability of the student and the quality and rigor of his/her exposition.

Other information

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2030 agenda goals for sustainable development

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Contacts

Toll-free number

800 904 084

Segreteria studenti

E. segreteria.scienze@unipr.it
T. +39 0521 905116

Quality assurance office

Education manager
dott.ssa Giulia Bonamartini
T. +39 0521 906968
Office E. smfi.didattica@unipr.it
Manager E.giulia.bonamartini@unipr.it

President of the degree course

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Faculty advisor

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Career guidance delegate

Prof. Francesco Morandin
E. francesco.morandin@unipr.it

Tutor Professors

Prof.ssa Alessandra Aimi
E. alessandra.aimi@unipr.it

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Prof. Adriano Tomassini
E. adriano.tomassini@unipr.it

 

Erasmus delegates

Prof. Leonardo Biliotti
E. leonardo.biliotti@unipr.it

Quality assurance manager

Prof.ssa Alessandra Aimi
E. alessandra.aimi@unipr.it

Internships

Prof. Costantino Medori
E. costantino.medori@unipr.it

Tutor students

Dott.ssa Fabiola Ricci
E. fabiola.ricci1@studenti.unipr.it