Métodos numéricos para encontrar zeros de funções: aplicações para o Ensino Médio

• Ano de defesa: 2014
• Autor(a) principal: Afuso, Anderson Yassuhiro [UNESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Mathematics - Study and teaching; Matemática - Estudo e ensino; Newton-Raphson, Metodo; Equações de diferença; Métodos gráficos; Ensino médio
• Link de acesso: http://hdl.handle.net/11449/123895; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/29-05-2015/000832285.pdf

The functions studied in high school are summarized in polynomials of first and second degree, modular, exponential, logarithmic and trigonometric. The problems to find zeros of functions are recurrent and assist in constructing the graphs and their analysis. Thus, this dissertation aims to present three numerical methods (methods of bisection, Newton-Raphson and secant) to find the zeros of function. In particular, the Newton-Raphson method is an example of a discrete equation which the fixed point will be the zero of function. The theory of discrete equations will be discussed in Chapter 3. Chapter 4 outlines the graphical method which introduces the numerical methods. Following, in Chapter 5, 6 and 7, is that, in fact, we'll discuss the three numerical methods. Finally, we present a proposed activity for high school. In addition to finding the zeros of function, the numerical methods motivate the initial study of recurrence, limits and derivatives. Furthermore, the applications of methods in the classroom can be performed with the aid of mathematical software to work with spreadsheets and charts