Polinômios e aproximação de funções: uma abordagem da educação básica ao ensino superior

Abstract

This work has as main objective the improvement of the Mathematics teacher, specifically in relation to the content of polynomial functions. In pursuit of this objective, a study is presented on the concept, and properties of polynomial functions at the level of Higher Education, deepen their knowledge of the subject and, moreover, improvement of the teacher reflects positively in the process teaching-learning, bringing an improvement for the same. In this sense, it is also presented a survey of the years of Basic Education in which the contents about polynomial functions are studied, as well as their abilities, both for the Curriculum of the State of Mato Grosso do Sul, and for the BNCC (Base Nacional Comum Curricular). Both are compared to a discussion/analysis by the SBM (Sociedade Brasileira de Matematica) about contents ande skills in the years of Basic Education, leading the teacher to a reflection on this subject. To illustrate the importance of polynomial functions, we present approximation of functions using polynomials. This technique was developed many years ago and is used nowadays. There are numerous advantages in, instead of manipulating a complex function, to approximate it by a polynomial, which is given by a simple expression, with derivate and integral easy to be calculated as well as their roots. Therefore, different interpolation methods were studied in this work, namely: Lagrange method, linear Interpolation, Newton method and Spline.