First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
ADVANCED ANALYSIS
SCP6076557, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2018/19
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination ADVANCED ANALYSIS
Website of the academic structure http://matematica.scienze.unipd.it/2018/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA
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

Lecturers
Teacher in charge FRANCO RAMPAZZO MAT/05
Other lecturers GIOVANNI COLOMBO MAT/05

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/05 Mathematical Analysis 8.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Practice 4.0 32 68.0 No turn
Lecture 4.0 32 68.0 No turn

Calendar
Start of activities 01/10/2018
End of activities 18/01/2019

Examination board
Board From To Members of the board
3 Analisi Superiore - a.a. 2018/2019 01/10/2018 30/09/2019 RAMPAZZO FRANCO (Presidente)
COLOMBO GIOVANNI (Membro Effettivo)
ANCONA FABIO (Supplente)
GUIOTTO PAOLO (Supplente)
LAMBERTI PIER DOMENICO (Supplente)
MARSON ANDREA (Supplente)

Syllabus
Prerequisites: Basic real and functional analysis
Target skills and knowledge: Students will be gradually introduced to some of the main methods and ideas of modern nonlinear analysis. At the end the this should provide the students with the ability of approaching a broad spectrum of topics, both applied and theoretical.
Examination methods: An oral exam on the topics covered by the course, that may include doing some simple exercises.
Assessment criteria: A good understanding of subjects, results, and main ideas presented in the course will be evaluated. Possibly, the student's focusing on a particular subject or application will be also taken into consideration.
Course unit contents: Fixed point theorems by Brouwer and Schauder, with applications; the hairy ball theorem.
Gateaux and Fr├ęchet differentiability. The differential of the norm in L^p spaces.

Ekeland variational principle with some applications (Banach fixed point theorem; Bishop-Phelps theorem; local inveribility of smooth functions in infinite dimensional spaces).

An introduction to Convex analysis: regularity of convex functions ; subdifferential and normal vectors to convex sets; the convex conjugate; convex minimization problems and variational inequalities.

An introduction the the mathematical Control Theory. Closedness of the set of trajectories under convexity assumptions; existence of optimal controls for minimum problems. Set separation and cone (non-)transversality as basic tools for abstract constrained minimization.
Optimal Control.
Nonlinear ordinary differential equations and transport of vectors and co-vectors.
Necessary conditions for constrained minima. Pontryagin Maximum principle.
Families of vector fields and controllability of control systems. Theorem di Rashewskii-Chow.
Planned learning activities and teaching methods: Lectures and exercises during the classes, with the possibility of personal focusing on particular subjects.
Additional notes about suggested reading: All lectures will be made on a tablet projected on a screen, and will be put on the Moodle platform in pdf.format during the same day. Moreover, in the second part of the course printed lecture notes will be available.
Textbooks (and optional supplementary readings)
  • Ekeland,Temam, Convex analysis and variational problems (Classics in Applied Mathematics).. --: --, --. Cerca nel catalogo
  • Bressan, Piccoli, Introduction to the Mathematical Theory of Control ( AIMS on Applied Mathematics). --: American Institute on Applied Mathematics, --. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Problem based learning

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • One Note (digital ink)
  • Latex

Sustainable Development Goals (SDGs)
Quality Education