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O grau de uma aplicação: uma abordagem via aplicação diferencial
(Universidade Federal de São Carlos, 2023-09-01)
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 ...
Aspectos históricos e matemáticos da resolução de equações de 3o., 4o. e 5o. graus
(Universidade Federal de São Carlos, 2023-09-06)
During the years from 1530 to 1576, there were great mathematical advances in Europe, one of the greatest being the great duel of the resolution of the cubic equations, fought between Niccolò Tartaglia and Gerolamo Cardano, ...
Um estudo sobre índices de campos de vetores
(Universidade Federal de São Carlos, 2023-04-03)
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.