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Title: :  A Brief History of the Calculus of Variations and its Applications
PaperId: :  21072
Published in:   International Journal Of Advance Research And Innovative Ideas In Education
Publisher:   IJARIIE
e-ISSN:   2395-4396
Volume/Issue:    Volume 9 Issue 4 2023
DUI:    16.0415/IJARIIE-21072
Licence: :   IJARIIE is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Author NameAuthor Institute
Surjeet SinghHNBGU

Abstract

Mathematical science
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,
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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IJARIIE Surjeet Singh. "A Brief History of the Calculus of Variations and its Applications" International Journal Of Advance Research And Innovative Ideas In Education Volume 9 Issue 4 2023 Page 340-360
MLA Surjeet Singh. "A Brief History of the Calculus of Variations and its Applications." International Journal Of Advance Research And Innovative Ideas In Education 9.4(2023) : 340-360.
APA Surjeet Singh. (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.
Chicago Surjeet Singh. "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.
Oxford 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, 2023, p. 340-360. Available from IJARIIE, https://ijariie.com/AdminUploadPdf/A_Brief_History_of_the_Calculus_of_Variations_and_its_Applications_ijariie21072.pdf (Accessed : 27 June 2024).
Harvard Surjeet Singh. (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. 340-360IJARIIE [Online]. Available at: https://ijariie.com/AdminUploadPdf/A_Brief_History_of_the_Calculus_of_Variations_and_its_Applications_ijariie21072.pdf (Accessed : 27 June 2024)
IEEE 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, Jul-Aug 2023. [Online]. Available: https://ijariie.com/AdminUploadPdf/A_Brief_History_of_the_Calculus_of_Variations_and_its_Applications_ijariie21072.pdf [Accessed : 27 June 2024].
Turabian Surjeet Singh. "A Brief History of the Calculus of Variations and its Applications." International Journal Of Advance Research And Innovative Ideas In Education [Online]. volume 9 number 4 (27 June 2024).
Vancouver Surjeet Singh. A Brief History of the Calculus of Variations and its Applications. International Journal Of Advance Research And Innovative Ideas In Education [Internet]. 2023 [Cited : 27 June 2024]; 9(4) : 340-360. Available from: https://ijariie.com/AdminUploadPdf/A_Brief_History_of_the_Calculus_of_Variations_and_its_Applications_ijariie21072.pdf
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