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 https://ezproxy.yu.edu/login?url=https://repository.yu.edu/handle/20.500.12202/4230 |
Appears in Collections: | Jay and Jeanie Schottenstein Honors Student Theses |
Files in This Item:
File | Description | Size | Format | |
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Steven-Herzberg.pdf Restricted Access | 259.47 kB | Adobe PDF | View/Open |
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