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Expositio paper exp-20260809-4d0c94

Calculus of Variations: An Introduction to the Optimization of Functionals

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This paper describes the mathematical technique of calculus of variations starting with the derivation of key equations such as the Euler-Lagrange equation and the Beltrami Identity. These equations are then applied in the following scenarios: geodesic on a f…

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exp-20260809-4d0c94v1 Latest public version Public since August 10, 2026 Submitted August 9, 2026 0 saves
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Vedansh Gupta (UWCSEA East Campus, Singapore)

Abstract

This paper describes the mathematical technique of calculus of variations starting with the derivation of key equations such as the Euler-Lagrange equation and the Beltrami Identity. These equations are then applied in the following scenarios: geodesic on a flat plane, solving the Brachistochrone problem, geodesic on a sphere, and finding the equation of the function formed by a string under the influence of gravity(catenary problem).

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Mathematics
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Calculus of variations and optimal control; optimization Existence theories in calculus of variations and optimal control Existence theories for free problems in two or more independent variables

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exp-20260809-4d0c94v1

Calculus of Variations: An Introduction to the Optimization of Functionals

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Uploaded Aug 9, 2026 261835 bytes Selected Latest
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