Professional paper

Introduction to the calculus of variations and its history

Krešimir Burazin ; Odjel za matematiku, Sveučilište J.J. Strossmayera u Osijeku, Osijek
Una Radojičić ; student, Odjel za matematiku, Sveučilište J.J. Strossmayera u Osijeku, Osijek

Abstract

The paper presents the basics of the calculus of variations in case when the extreme searched for depends only on one real variable, and gives an overview of its historical development. We derive a necessary condition for optimality in the form of the Euler-Lagrange equation, and show that it is also a sufficient condition in the case of a convex Lagrangian. The theory is illustrated by the historically important examples of the shortest path, geodesics on the sphere, and Brachistohrone problem.

Keywords

optimization; variation; Euler-Lagrange equation; extrema of function

Hrčak ID:

179726

URI

https://hrcak.srce.hr/179726

Publication date:

20.12.2016.

Article data in other languages: croatian

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