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Jan 28, 2025
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2014-2016 Undergraduate and Graduate Bulletin (without addenda) [ARCHIVED CATALOG]
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MA-GY 6583 Calculus of Variations3 Credits
This course covers: classical problems, such as geodesics, brachistochrones, isoperimetric problems. Euler equations. Geodesic coverings. Weierstrass condition. Hamilton-Jacobi equation. First and second variations. Transversality. Convex sets and functions. Duality. Existence theorems. Generalized curves. Control theory. Time-optimal problems. Optimal processes. Extension of elementary theory of maxima and minima. Euler equations, conditions of Weierstrass, Legendre and Jacobi, Mayer fields, Hamilton-Jacobi equations, transversality, conjugate and focal points. Applications to geodesics, minimal surfaces, isoperimetric problems, Hamilton’s principle, Fermat’s principle, brachistochrones.
Prerequisite(s): MA-UY 4623 or MA-GY 6223 .
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0
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