Navegando por áreas do CNPq "CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA"
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Os teoremas de existência e unicidade de solução de um PVI e do fluxo tubular
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 03/04/2023)The main objective of this course completion work is to present the foundations of the Qualitative Theory of Ordinary Differential Equations, a branch of Mathematics that is considered one of the most applied. The present ... -
Uma proposta didática para o ensino de áreas e volumes
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 03/04/2023)This monograph discusses plane and spatial geometry in order to investigate the approach of the topics of areas and volumes in selected textbooks, as well as to study the theoretical prerequisites and the Cavalieri's ... -
On the classification of two dimensional flows
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 02/08/2023)Lawrence Markus, a well-known mathematician, published, in 1954, a strong result about classification of planar vector fields. Afterwards, Dean Arnold Neumann generalized such work for continuous flows, and the result ... -
Campos de Yang-Mills fracamente estáveis na esfera de dimensão quatro
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 03/05/2023)In this work we made a quick study on some basic results related to Groups and Lie Algebras, action of Groups and Fiber Bundles with the objective of defining connections in Principal Bundles and, later, in Associated ... -
Explorando o teorema de Pitágoras: uma análise crítica de materiais didáticos e uma proposta de ensino utilizando-se dobradura.
(Universidade Federal de São Carlos, UFSCar, , Câmpus Sorocaba, 06/04/2023)Geometry is a branch of mathematics that is of fundamental importance for the intellectual formation of students. The main objective of this research was to propose a lesson plan for teaching the Pythagorean Theorem through ... -
Problemas elípticos superlineares com ressonância
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 14/08/2015)The aim of this work is to present results about the existence of non-trivial solutions for some classes of resonant and superlinear eliptic systems employing topological methods. More specifcally, we use a-priori bounds ... -
A transformação vetorial de Ribaucour para subvariedades de curvatura constante
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 09/06/2015)In this work we obtain a reduction of the vectorial Ribaucour transformation that preserves the class of submanifolds with constant sectional curvature of space forms. As a consequence, a process is derived to generate ... -
Imersões isométricas de formas espaciais em Sn x R e Hn x R
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 08/06/2015)In this thesis we classify the isometric immersions f : Mm ^ Sm+p x R with m > 3 P < m — ^d c < 1, where Mm denotes a Riemannian manifold with constant sectional curvature equal to c. We obtain partial results on the ... -
A utilização do software GeoGebra no ensino da geometria analítica
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Ensino de Ciências Exatas - PPGECE, Câmpus São Carlos, 19/12/2014)In this thesis we aim, through the use of a technological tool, the computer, show the possibility of teaching Mathematics causing the student to build their knowledge from concepts presented with the help of software ... -
Heat equation and the Yamabe flow on manifolds with fibered boundary metric
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 02/09/2021)This work is dedicated to the study of the Yamabe flow on a class of non-compact complete Riemannian manifolds with fibered boundary and infinite volume, called Phi-manifolds. Some examples of this type of manifold include ... -
Algumas aplicações de p-pontos
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 24/08/2023)In this work we analyze the concept of \(p\)-points in \(\omega\) and its relation with forcing, in particular Sacks forcing and side-by-side Sacks forcing. With this we verify that the existence of \(p\)-points with ... -
Um princípio de tangência e aplicações
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 17/12/2021)We present tools, such as a maximum principle for elliptic functions and properties of a-hyperbolic polynomials, to study a tangency principle between two hypersurfaces with r-mean curvatures of a Riemannian manifold, which ... -
Classificação de centros Hamiltonianos polinomiais biquadrados, e isocronicidade trivial versus formas canônicas para aplicações polinomiais no plano de Jacobiano unitário
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 10/10/2022)This work, we classify a non- degenerate center at the origin of a planar Hamiltonian system associated to a function of the form $H(x,y)=A(x)+B(x)y^2 + C(x)y^4$, where $A$, $B$ and $C$ are polynomials. After seing a ... -
O uso das questões da OBMEP para a recuperação da aprendizagem matemática pós- pandemia: onde estamos e para onde vamos?
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Ensino de Ciências Exatas - PPGECE, Câmpus São Carlos, 31/01/2022)In this dissertation we will use the question bank of the Brazilian Mathematics Olympiad of Public Schools and technological resources to work on the competences and skills of Geometry proposed by the National Common ... -
Ladrilhamentos regulares e semirregulares do plano
(Universidade Federal de São Carlos, UFSCar, , Câmpus São Carlos, 24/11/2021)The tiling technique consists of filling the plane with geometric figures without overlapping or empty spaces. Although this technique is quite old, the science is recent and contains aspects that have not yet been developed ... -
Classes características de variedades topológicas e generalizadas
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 24/03/2022)In this work, we will initially present generalized bundles, a concept developed by Fadell with the objective of generalizing vector bundles, Stiefel-Whitney classes andWu’s formula from the context of smooth manifolds ... -
Categoria de Lusternik-Schnirelmann e aplicações
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 14/02/2022)The Lusternik-Schnirelmann category associates a positive integer to each topological space. This number is an important invariant in algebraic topology, critical point theory and symplectic geometry. In this dissertation ... -
Geometric invariants of groups and property R-infty
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 05/01/2022)In this thesis we study property R_\infty for some classes of finitely generated groups by the use of the BNS invariant \Sigma^1 and some other geometric tools. In the combinatorial chapters of the work (4, 5, 6, 10 and ... -
Germes de funções sobre variedades analíticas
(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, , 03/03/2006)The study of analytic germs of functions (Cn, 0) → (C, 0) under R - equivalence relation is a central point in Singularity Theory and the information we have in this direction is very rich. In this dissertation we ... -
Teorema de Pitágoras, aplicações de demonstrações em sala de aula
(Universidade Federal de São Carlos, UFSCar, Programa de Mestrado Profissional em Matemática em Rede Nacional - PROFMAT, Câmpus São Carlos, 26/10/2016)[ENG]The official curriculum of the state of São Paulo in their spiral character, discusses the Pythagorean Theorem as one of their learning situations for the 9th year of elementary school, and on top of that content, ...