Utilização do software GeoGebra para aproximar funções através de mínimos quadrados

Abstract

For this work a detailed study of approximations by least squares in orthogonal vector spaces. In particular, we use this theory to get the best approximation of a function f in space W generated by functions 1, cos(t), cos(2t),..., cos(nt),sen(t),sen(2t),...,sen(nt), using an appropriate internal product. This function is called a trigonometric polynomial and coincides with the nth partial sum of the Fourier series of the function f , once their coefficients coincide with the Fourier coefficients of f . The obtained polynomial was used to approximate a force that acts on a mechanical system with the use of the software GeoGebra which allowed to better understand the construction of the function and, at the same time, the graphic representation showed that increasing the degree of the polynomial better is the approximation obtained.