A Brief History of the Calculus of Variations and its Applications

Surjeet Singh

A Brief History of the Calculus of Variations and its Applications

July 2023

Vol-9, Issue-4

Paper ID: 21072

ISSN: 2395-4396

Downloads: 0

Abstract & Details

Research Area

Mathematical science

Keywords

Calculus of variations Hilbert's work development of mathematical theory minimum surface and maximum surface lagrange equation hamilton-Jacobi Theory nineteenth century application to other fields Riemann equation Dirichlet principles weierstrass equation twenty century developments Morse theory optimal control theory mathematical science math

Abstract

In this paper, we trace the development of the theory of the calculus of variations. From its roots in the work of Greek thinkers and continuing through to the Renaissance, we see that advances in physics serve as a catalyst for developments in the mathematical theory. From the 18th century onwards, the task of establishing a rigourous framework of the calculus of variations is studied, culminating in Hilbert’s work on the Dirichlet problem and the development of optimal control theory. Finally, we make a brief tour of some applications of the theory to diverse problems.

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Author Information

#	Name	Institute / Affiliation
1	Surjeet Singh	HNBGU

How to Cite

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APA Style

Singh, Surjeet (2023). A Brief History of the Calculus of Variations and its Applications. International Journal of Advance Research and Innovative Ideas In Education, 9(4), 340-360.

MLA Style

Singh, Surjeet. "A Brief History of the Calculus of Variations and its Applications." International Journal of Advance Research and Innovative Ideas In Education, vol. 9, no. 4, 2023, pp. 340-360.

IEEE Style

Surjeet Singh, "A Brief History of the Calculus of Variations and its Applications," International Journal of Advance Research and Innovative Ideas In Education, vol. 9, no. 4, pp. 340-360, 2023.

Vancouver Style

Singh Surjeet. A Brief History of the Calculus of Variations and its Applications. International Journal of Advance Research and Innovative Ideas In Education. 2023;9(4):340-360.

Harvard Style

Singh, Surjeet (2023) 'A Brief History of the Calculus of Variations and its Applications', International Journal of Advance Research and Innovative Ideas In Education, 9(4), pp. 340-360.

Chicago Style

Singh, Surjeet. "A Brief History of the Calculus of Variations and its Applications." International Journal of Advance Research and Innovative Ideas In Education 9, no. 4 (2023): 340-360.

Turabian Style

Singh, Surjeet. "A Brief History of the Calculus of Variations and its Applications." International Journal of Advance Research and Innovative Ideas In Education 9, no. 4 (2023): 340-360.