Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.12202/4230
Title: On Different Aspects of Differentiability and the Calculus of Variations
Authors: Herzberg, Steven
Keywords: Calculus of variations.
Fréchet spaces.
Linear topological spaces.
Generalized spaces.
Space and time.
Surfaces.
Directional derivatives.
Differential calculus.
Convergence.
Issue Date: Jun-2016
Publisher: Yeshiva College
Abstract: We explore the notion of differentiability in finite and infinite dimensional spaces, including a geometric interpretation. This includes, in finite dimensions, the relationship between the existence of directional derivatives and that of a tangent hyperplane, and in infinite dimensions, Gˆateaux and Fr´echet differentiability. We apply these notions to the Calculus of Variations, and to finding the shortest path between two points on a flat plane and on a torus. To account for the domain, often a space of distributions, we define weak derivatives.
Description: The file is restricted for YU community access only.
URI: https://hdl.handle.net/20.500.12202/4230
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Appears in Collections:Jay and Jeanie Schottenstein Honors Student Theses

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