First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
DIFFERENTIAL EQUATIONS
SC01111294, A.A. 2015/16

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2015/16
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination DIFFERENTIAL EQUATIONS
Website of the academic structure http://matematica.scienze.unipd.it/2015/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
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 MARTINO BARDI MAT/05

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

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

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

Calendar
Start of activities 01/03/2016
End of activities 15/06/2016
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
7 Equazioni Differenziali - a.a. 2019/2020 01/10/2019 30/09/2020 BARDI MARTINO (Presidente)
MANNUCCI PAOLA (Membro Effettivo)
ANCONA FABIO (Supplente)
COLOMBO GIOVANNI (Supplente)
SORAVIA PIERPAOLO (Supplente)
6 Equazioni Differenziali - a.a. 2018/2019 01/10/2018 30/09/2019 BARDI MARTINO (Presidente)
MANNUCCI PAOLA (Membro Effettivo)
ANCONA FABIO (Supplente)
COLOMBO GIOVANNI (Supplente)
SORAVIA PIERPAOLO (Supplente)
5 Equazioni Differenziali - 2017/2018 01/10/2017 30/09/2018 BARDI MARTINO (Presidente)
MANNUCCI PAOLA (Membro Effettivo)
ANCONA FABIO (Supplente)
COLOMBO GIOVANNI (Supplente)
SORAVIA PIERPAOLO (Supplente)
4 Equazioni Differenziali - 2016/2017 01/10/2016 30/11/2017 BARDI MARTINO (Presidente)
ANCONA FABIO (Membro Effettivo)
COLOMBO GIOVANNI (Supplente)
MANNUCCI PAOLA (Supplente)
SORAVIA PIERPAOLO (Supplente)
3 Equazioni Differenziali - a.a. 2015/2016 01/10/2015 30/11/2016 BARDI MARTINO (Presidente)
ANCONA FABIO (Membro Effettivo)
CESARONI ANNALISA (Supplente)
MANNUCCI PAOLA (Supplente)
MARCHI CLAUDIO (Supplente)

Syllabus
Prerequisites: Differential and integral calculus for functions of several variables; elementary theory of ordinary differential equations.
Target skills and knowledge: Understanding some methods of analysis for Hamilton-Jacobi; getting an introduction to the classical theory of games and to differential games.
Examination methods: Oral exam.
Assessment criteria: The exam will concern the concepts introduced in the course and the capability of the student to handle them.
Course unit contents: Part 1:
- Classical examples of Hamilton-Jacobi equations; the method of characteristics and the onset of singularities.
- The Hopf-Lax formula.
- Viscosity solutions: motivations and basic theory.
- The Comparison Principle and some consequences.
- Introduction to optimal control and the Dynamic Programming method; existence of solutions to H-J equations with convex Hamiltonians; synthesis of optimal feedbacks.
Part 2.
- Zero-sum games, matrix games: the min-max theorem and its consequences.
- Games with N players: Nash equilibria.
- Two-person differential games: verification theorems and feedback Nash equilibria.
- Zero-sum differential games: causal strategies and the definitions of value.
- Dynamic Programming and the H-J-Isaacs equation; existence of the value.
Planned learning activities and teaching methods: Lectures at the tablet, the text is made available to the student at the end of each week.
Additional notes about suggested reading: Three reference text are suggested.
Textbooks (and optional supplementary readings)
  • L.C. Evans, Partial Differential Equations. Providence: A.M.S., 1998. 2nd edition 2010 Cerca nel catalogo
  • M. Bardi, I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Boston: Birkhauser, 1997. 2nd printing, 2008. Cerca nel catalogo
  • E.N. Barron, Game theory. Hoboken: Wiley, 2008. Cerca nel catalogo