A study about Fourier series: Mathematical and graphical models and application in electric current and square oscillations

Abstract

The present work aims to study the Fourier series with the intention of creating a didactic and understandable text. There are several ways to introduce the Fourier series, the simplest and most pedagogical way, at least for beginners in the subject, is to explore intuitively the basic idea through graphics. This analysis facilitates the understanding of the methodology behind the series and the Fourier. The mathematical formulation will be a simple extension of the physical (geometric) image presented by the graphics. The popular saying goes that a figure is worth a thousand words. Mathematicians, in turn, argue that an equation is worth a thousand figures. Maybe that is why in Fourier's analysis books, mathematical formulation comes first, followed by the graphics.