Contorno aparente, envoltórias e equações diferenciais implícitas

• Ano de defesa: 2015
• Autor(a) principal: Riul, Pedro Benedini [UNESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Matemática; Equações diferenciais ordinárias; Teoria das singularidades; Envoltórias (Geometria)
• Link de acesso: http://hdl.handle.net/11449/127792; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/31-08-2015/000843896.pdf

Given a smooth regular surface M in R3 we can locally consider it as an inverse image of a regular value of a smooth function F : R3 → R. The apparent contour of M in a given direction coincides with the envelope of a family of curves associated to F. The study of such objects is of great interest to the Singularity Theory and it can be related to Implicit Differential Equations (IDE's). An IDE is an equation of the form F(x, y, p) = 0 where p = dxdy and F : R3 → R is a smooth function. This work presents a study on apparent contour of a regular surface, envelope of family of curves, and implicit differential equations in order to analyze the relationship between ...