Cálculo variacional: uma breve introdução e aplicações

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2023_TCC_Vinícius_Marques_da_Silva.pdf (2.38 MB)

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2024-02-06

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Universidade Federal de São Carlos

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The aim of this end-of-course work is to present a brief introduction to variational calculus and its applications. In this way, the development consists of recalling concepts of normed vector spaces, metric spaces and differential and integral calculus. Subsequently, these concepts will be refined for the study of functionals, where concepts about the Fréchet and Gâteaux derivatives, as well as the Euler equation, will inevitably arise. Finally, we will discuss sufficient conditions for extrema.

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Cálculo variacional , Equação de Euler , Espaços vetoriais normados , Derivada de Fréchet , Derivada Gâteaux , Variational calculus , Euler equation , Normed vector spaces , Fréchet derivative , Gâteaux derivative

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SILVA, Vinícius Marques da. Cálculo variacional: uma breve introdução e aplicações. 2024. Trabalho de Conclusão de Curso (Graduação em Matemática) – Universidade Federal de São Carlos, São Carlos, 2024. Disponível em: https://repositorio.ufscar.br/handle/20.500.14289/20115.

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https://repositorio.ufscar.br/handle/20.500.14289/20115

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Attribution-NonCommercial-NoDerivs 3.0 Brazil
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivs 3.0 Brazil