Кто читает:: Факультет математики

Статус:: Дисциплина общефакультетского пула

Когда читается:: 3, 4 модуль

Преподаватель

Мариани Мауро

Full Syllabus

Abstract

The lectures provide an introduction to Calculus of Variations, addressing both classical subjects (action functionals, isoperimetric problems), and modern approaches (direct methods, applications to physics and optimal control). The student will be required to understand the theoretical aspects of the theory, as well as to apply it to specific cases.

Learning Objectives

Understanding the modeling and interpretation of classical and modern variational problems. Knowledge of the basic techniques to identify optimal solutions to variational models.

Expected Learning Outcomes

Being able to model various classes of a variational and optimal control problems, and derive sufficient and necessary conditions for extremality.

Course Contents

Historical model problems and preliminaries: convex analysis, Sobolev spaces.
Classical methods: Euler-Lagrange equations, optimal control, the Hamiltonian approach, viscosity solutions, applications.
Direct methods: basic theory, elliptic problems (existence, uniqueness, regularity), Euler–Lagrange revisited, relaxation of integral functionals, applications.

Assessment Elements

cumulative
controls during the semester
oral final exam
written final exam

Interim Assessment

Interim assessment (4 module)
0.3 * cumulative + 0.35 * oral final exam + 0.35 * written final exam

Bibliography

Recommended Core Bibliography

A first course in optimization theory, Sundaram, R. K., 2011
Hogg, R. V., McKean, J. W., & Craig, A. T. (2014). Introduction to Mathematical Statistics: Pearson New International Edition. Harlow: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1418145

Recommended Additional Bibliography

Larsen, R. J., & Marx, M. L. (2015). An introduction to mathematical statistics and its applications. Slovenia, Europe: Prentice Hall. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.19D77756

Бакалаврская программа «Математика»

Research Seminar "Calculus of Variations"