| 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
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 |
| Start of activities | 01/10/2018 |
|---|---|
| End of activities | 18/01/2019 |
| Show course schedule | 2019/20 Reg.2011 course timetable |
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) |
| 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 Fréchet 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) |
|
- Moodle (files, quizzes, workshops, ...)
- One Note (digital ink)
- Latex
