Uusi opinto-opas (sisältäen myös opetusohjelmat) lukuvuodelle 2018-2019 sijaitsee osoitteessa https://opas.peppi.utu.fi . Tältä sivustolta löytyvät enää vanhat opinto-oppaat ja opetusohjelmat.

The new study guide (incl. teaching schedules) for academic year 2018-2019 can be found at https://studyguide.utu.fi. This site contains only previous years' guides.

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Arkistoitu opetussuunnitelma 2016–2018
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SMAT5308 Calculus of Variations 5 op
Organised by
Applied Mathematics
Person in charge
Department of Mathematics and Statistics, Yury Nikulin
Preceding studies
Recommended:

General description

Calculus of variations is a field of mathematical analysis that deals with maximizing or minimizing functionals, which are mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. The interest is in extremal functions that make the functional attain a maximum or minimum value – or stationary functions – those where the rate of change of the functional is zero.

Learning outcomes

The course provides basis for thorough understanding of the problems, methods and techniques of the calculus of variations and prepares students for the study of modern optimal control theory. The treatment is limited to extensive coverage of single integral problems in one and more unknown functions.

Contents

1 EXTREME VALUES OF FUNCTIONALS
2 THE THEORY OF THE FIRST VARIATION
3 THEORY OF FIELDS AND SUFFICIENT CONDITIONS FOR A STRONG RELATIVE EXTREMUM
4 THE HOMOGENEOUS PROBLEM
5 THE PROBLEM OF LAGRANGE AND THE ISOPERIMETRIC PROBLEM
6. THE MINIMUM PRINCIPLE OF PONTRYAGIN

Teaching methods

Teaching method Contact Online
Lectures 28 h 0 h
Exercises 14 h 0 h

Teaching language

English

Modes of study

Option 1
Available for:
  • Degree Programme Students
  • Other Students
  • Doctoral Students
  • Exchange Students
Exercises Exercise(s)
  • In English
Written exam
  • In English

Evaluation

Numeric 0-5.

Study materials

Introduction to the Calculus of Variations by Hans Sagan. Additionally available lecture notes (in Finnish)

 

Belongs to following study modules

Matematiikan ja tilastotieteen laitos
2016–2017
Teaching
Archived Teaching Schedule. Please refer to current Teaching Shedule.
Implementation details are unavailable.
Matematiikan ja tilastotieteen laitos
MDP in Information Security and Cryptography
Opintokokonaisuudet