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ELEMENTS OF FUNCTIONAL ANALYSIS AND NUMERICAL METHODS
ELEMENTI DI ANALISI FUNZIONALE E METODI NUMERICI

A.Y. Credits
2020/2021 9
Lecturer Email Office hours for students
Giovanni Molica Bisci
Teaching in foreign languages
Course with optional materials in a foreign language English
This course is entirely taught in Italian. Study materials can be provided in the foreign language and the final exam can be taken in the foreign language.

Assigned to the Degree Course

Applied Informatics (LM-18)
Curriculum: PERCORSO COMUNE
Date Time Classroom / Location
Date Time Classroom / Location

Program

01. Normed spaces, metric spaces, topology
01.01 Normed vector spaces
01.02 Euclidean spaces: inner product
01.03 Metric spaces
01.04 Topological spaces
01.05 Limits
01.06 Product of topological spaces
01.07 Linear functions between vectorial spaces
01.08 Norms. Equivalent norms
01.09 Continuity of multilinear functions
01.10 Sequences and subsequences
01.11 Metric spaces: completeness
01.12 Normed spaces and completeness: canonical examples
01.13 Equivalent norms in finite vectorial spaces
01.14 Sequential notion of compactness
01.15 Subspaces of compact spaces
01.16 Continuous functions on compact spaces
01.17 Product of compact spaces
01.18 Applications
01.19 Connected spaces
01.20 The Banach-Caccioppoli theorem

02 Integrable Riemann functions
02.01 Step functions
02.02 Integral of step function with compact support 
02.03 Measure of a set in the plane
02.04 Integrable Riemann functions
02.05 Properties of the integrals
02.06 Geometrical meaning of the integral
02.07 Observations on the integral concept
02.08 Extended notion in an interval
02.09 Local integrability of continuous functions
02.10 Extended Integral over an oriented interval
02.11 Indefinite integrals
02.12 Dedeking property 

03 Sets
03.1 The Cantor world
03.2 Relations
03.4 Preorders; Equivalence; Orders
03.5 Functions between sets
03.6 Image and preimage
03.7 Cartesian product between sets
03.8 Elements of GBN Theory
03.9 The choice axiom: equivaent versions
03.10 Cardinality (n the Frege sense): generality
03.11 Fundamentals theorems between cardinals and combinatorics

Teaching Material

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

Didactics, Attendance, Course Books and Assessment

Course books

H. Brézis, Functional analysis, Sobolev spaces and partial differential equations, Universitext, Springer, New York, 2011, xiv+599 pp.

G. De Marco, Analisi Due. Teoria ed Esercizi. Zanichelli, Bologna, 1999.

T. Jech, Set Theory. The Third Millennium Edition, revised and expanded. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2003. xiv+769 pp.

W. Rudin. Principles of Mathematical Analysis. Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill, New York-Auckland-Düsseldorf, 1976.

S. Salsa, Partial Differential Equations in Action, From Modelling to Theory  - Springer, 2007. 

Additional Information for Non-Attending Students

Course books

H. Brézis, Functional analysis, Sobolev spaces and partial differential equations, Universitext, Springer, New York, 2011, xiv+599 pp.

G. De Marco, Analisi Due. Teoria ed Esercizi. Zanichelli, Bologna, 1999.

T. Jech, Set Theory. The Third Millennium Edition, revised and expanded. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2003. xiv+769 pp.

W. Rudin. Principles of Mathematical Analysis. Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill, New York-Auckland-Düsseldorf, 1976.

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