Equações de diferenças: aplicações no ensino médio

• Ano de defesa: 2015
• Autor(a) principal: Eller, Elcie Sanches [UNESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Matemática - Estudo e ensino; Matemática (Ensino médio); Equações diferenciais - Estudo e ensino; Mathematics Study and teaching
• Link de acesso: http://hdl.handle.net/11449/138479; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/11-04-2016/000863439.pdf

The equations of differences have applications in Mathmatics (Fractal geometry, for example), in Economy, in Pharmacology, among other subjects. They are used to modeliny dynamical systems that evolute in discrete time intervals. The equations of differences also are called recurrences and can be resolved through iterations. The main objective of this work is to have a study about equations of differences of 1st and 2nd degreed. The main theoretical results and the resolutions methods are showed. The used of difference operators and anti difference operators to resolve the equations of differencesof 1st order and the displacement operator are highlighted, to resolve the equations of differences of 2nd order, in particular, the constant coefficients. Also a behavior study of the equations of differences solutions is made example of applications in the classroom are presented such as contextualized problem situations like the Sierpinski Triangle, the Hanoi Tower and the Fibonacci Sequence, serving as a basis of technology through the GeoGebra Software, of concrete materials and mathematical modeling