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O ensino de polinômios e gráficos na educação básica
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 11/12/2019)In this monography, we study polynomial functions, starting with a brief historical research about how the general solutions of the first to third degree polynomial equations were constructed, then we proceed to analyze ... -
Um estudo sobre índices de campos de vetores
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 03/04/2023)One of the main goals of this project is to study the index of vector fields in compact surfaces and present the Poincar´e-Hopf Theorem, remarking that such a result connects topological elements to geometric objects. -
Geometria Conforme e Invertibilidade Global
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 25/06/2021)This work contains the studies done to the reading of the paper ``Conformas geometry, Euler numbers, and global invertibility in higher dimensions'' de Frederico Xavier [4], as well as a detailed study of the mentioned ... -
Geometria Diferencial via Referenciais Móveis
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 25/06/2021)In this work, we present a study on the theory of differential geometry of surfaces with a language of moving references. At first, we will introduce some groups of matrices and their actions in Euclidean space. Once this ... -
O grau de uma aplicação: uma abordagem via aplicação diferencial
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 01/09/2023)In this work, we study the concepts of degree and local degree for maps between manifolds. Furthermore, we define the Poincaré-Hopf index and study some relevant proprieties of this index such as the famous Poincaré-Hopf ... -
Introdução à geometria diferencial e à análise complexa
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 06/01/2021)The paper "Conformal geometry, Euler numbers, and global invertibility in higher dimensions”, by Frederico Xavier, crosses different areas of Mathematics in order to obtain its main result. Among them we have Differential ... -
Introdução à teoria da medida e integração
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 27/11/2022)The Lebesgue measure is an important concept with applications in the Lebesgue integral, in the axiomatization of probabilities, and in the definion of integral of spaces more general than the euclidian spaces. This essay ... -
Uma proposta de análise de desempenho de estudantes do ENEM
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 07/01/2021)In the international education field, it is relevant to predict the students' performance for future courses and/or disciplines. In that matter, Rajalaxmi et al. (2019), Abledu (2012) and Gadhavi, Patel (2017) works show ... -
Superfícies de Weingarten no Espaço Hiperbólico
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 26/06/2020)Desde o surgimento da definição de superfícies parametrizadas, foi questionado sobre suas propriedades que independem da parametrização. Propriedades essas que caracterizam objetivamente a geometria dessa família facilitando ... -
O Teorema de classificação de superfícies fechadas
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 28/09/2022)In this work we will study some concepts of algebraic topology such as fundamental group and simplicial complexes, then we will present a proof of the closed surface classification theorem. -
Visitando algumas ferramentas da análise moderna para soluções EDP's
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 09/02/2024)In 1856, Riemann introduced the Dirichlet Principle as an innovative approach to the Dirichlet Problem, proposing a treatment based on a variational problem. Essentially, this principle aimed to minimize an energy functional ...