Licenciatura em Matemática (Sede)

URI permanente desta comunidadehttps://arandu.ufrpe.br/handle/123456789/24

Siglas das Coleções:

APP - Artigo Publicado em Periódico
TAE - Trabalho Apresentado em Evento
TCC - Trabalho de Conclusão de Curso

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Espaços métricos: continuidade, completude e compacidade
(2021-02-19) Oliveira, Alessandra Arcanjo Lisboa de; Araújo, Yane Lísley Ramos; Carvalho, Gilson Mamede de; http://lattes.cnpq.br/0044877127514130; http://lattes.cnpq.br/6642941380570085; http://lattes.cnpq.br/2572639684291501
This work has as main objective to study continuity, completeness and compactness in the theory of metric spaces. A metric space is a non-empty set in which the notion of distance between its elements is well defined. The present study is interesting because the results presented here generalize some of the results observed in the theory of continuity and compactness in Euclidean spaces, Rn, with n [greater than or equal to] 1. Furthermore, these results are valid in more abstract spaces such as some sequence or function spaces, whose notion of distance escapes from intuition and entails intriguing facts, such as the fact that closed balls are not necessarily compact.
Existência e unicidade de solução para problemas envolvendo o operador Laplaciano
(2019-12-17) Nunes, Thays Ingrid dos Santos; Araújo, Yane Lísley Ramos; http://lattes.cnpq.br/6642941380570085; http://lattes.cnpq.br/3740642465035306
In this work we approach some basic concepts related to the theory of partial differential equations guaranteeing the existence of solution for problems involving the Laplacian operator. Initially, we use the method of variable separation and Fourier Analysis tools to ensure the existence of classical solutions to Dirichlet problems in the rectangle and unit disk involving the Laplace equation, as well as a maximum principle to ensure the uniqueness of the solution. Then, we use results from Functional Analysis and Sobolev spaces to ensure under certain conditions that there is only one weak solution to the Dirichlet problem involving the Poisson equation.