Introduction to the Calculus of Variations

Sever Angel Popescu and Marilena Jianu
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Sever Angel Popescu: Technical University of Civil Engineering of Bucharest, Department of Mathematics and Computer Science
Marilena Jianu: Technical University of Civil Engineering of Bucharest, Department of Mathematics and Computer Science

Chapter Chapter 8 in Advanced Mathematics for Engineers and Physicists, 2022, pp 435-483 from Springer

Abstract: Abstract This chapter presents the basic theory of Calculus of Variations applied to fundamental types of variational problems with applications in Physics and Engineering. We begin by stating several classical problems (such as: the brachistochrone problem, the minimal surface of revolution, Dido’s problem). Then we introduce the general frame of Calculus of Variation, focusing on necessary conditions of extremum of a functional. We deduce the basic differential equations of Calculus of Variations and apply them to solve some classical variational problems.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-21502-5_8

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DOI: 10.1007/978-3-031-21502-5_8

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