First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP6076297, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2019/20
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination FUNCTIONAL ANALYSIS
Website of the academic structure
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit


ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/05 Mathematical Analysis 6.0

Course unit organization
Period Second semester
Year 3rd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 3.0 24 51.0 No turn
Lecture 3.0 24 51.0 No turn

Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2008 course timetable

Examination board
Board From To Members of the board
2 Analisi Funzionale - a.a. 2019/2020 01/10/2019 30/09/2020 LAMBERTI PIER DOMENICO (Presidente)
ANCONA FABIO (Supplente)

Prerequisites: Classical topics in differential, integral, multi-variable calculus, as well as basic notions of linear algebra and a few basic elements of measure and integration theory for which a lecture course in Real Analysis is recommended.
Target skills and knowledge: To get acquainted with the terminology, the fundamental notions and theorems of classical functional analysis in Banach and Hilbert space.
To acquire the ability to recognize the typical arguments of functional analysis in view of its possible applications.
Examination methods: Oral exam on all topics of the course, including all proofs of all propositions. The exam consists in answering questions aiming at estimating the knowledge gained by the student, and in discussing the notions and the presented results in order to estimate the level of familiarity of the student with the those notions, in particular by analyzing the details of the proofs of the theorems and the proposed examples and exercises.
Assessment criteria: Grades are decided starting from a first level (18-23 out of 30) in which case the mere knowledge of all topics is required, passing to a second level (24-27 out of 30) for which
familiarity with the studied notions is required, and finally
getting to a level of excellence (28-30 out of 30) in which case critical thinking is required.
Course unit contents: The fundamental theorems of functional anlysis, Hahn-Banach Theorem, Banach-Steinhaus Theorem, Open mapping and Closed graph Theorem. Weak and weak* topologies, reflexivity, separability, compactness. Applications to classical function spaces, L^p spaces and spaces of continuous functions in particular. Hilbert spaces, compact and self-adjoint operators, elements of spectral theory.
Planned learning activities and teaching methods: Traditional lectures with classical blackboard by using which it is possible to represent a large part of the proof of a theorem and analyze and discuss it in a critical way.
Textbooks (and optional supplementary readings)
  • Brezis, Haim, Functional analysis, sobolev spaces and partial differential equationsHaim Brezis.. New York: Springer, 2011. Cerca nel catalogo
  • Kolmogorov, Andrej Nikolaevič; Fomin, Sergej Vasilevic, Elementi di teoria delle funzioni e di analisi funzionaleAndrej N. Kolmogorov, Sergej V. Fomin. Roma: Editori riuniti, 2012. Cerca nel catalogo
  • Riesz, Frigyes; Szokefalvi-Nagy, Bela; Boron, Leo F., Functional analysisFrigyes Riesz and Bela Sz. Nagytranslated from the 2. French edition by Leo F. Boron. New York: Dover, 1990. Cerca nel catalogo
  • Rudin, Walter, Functional analysisWalter Rudin. New York [etc.]: McGraw-Hill, --. Cerca nel catalogo
  • Lax, Peter, Functional analysisPeter D. Lax. New York: Wiley, --. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Interactive lecturing
  • Story telling
  • Problem solving

Innovative teaching methods: Software or applications used
  • Latex

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