Análise comparativa das séries de Taylor e Fourier

Abstract

Sometimes, in the engineering area it is necessary to use the use of function approximations to study complex functions and as a means of approximation for these functions can be used the mathematical series. Within the series, it is possible to mention that there are the series of powers like the one of Taylor and the trigonometric series as the one of Fourier. In this context, this work makes a comparison between the approximations performed by these methods to a specific function. Then, the approximations promoted by the series on a function are compared graphically in order to verify which of the series promotes a better approximation. With the Taylor and Fourier series of the chosen function, the functions formed for the final index of the sums equal to one, two, three, four, five, ten and twenty were analyzed, in a simplified way, to observe that as it rises the final index of the sum of the series is closer to the chosen function, as well as to identify that the Taylor series performs a better approximation of the function and in a simpler way.