The Trigonometrical Series of Fourier: A Visual Approximation

Abstract

This work gives an account of the staging of a didactic proposal for the construction of the notion of Trigonometric Fourier Series (TFS), with the aim of promoting in the student that the mathematical object has meaning and significance to the engineer in training. The theoretical perspective is the social construction of knowledge, identified through the institutional and social context to the analysis of signals as a driving force of knowledge throughout the across the academic career, due to the fact that any physical phenomenon to be studied is a signal. Hence the proposal promotes visual thinking and the development of advanced mathematical thinking. Given the academic background and content of the subjects prior to the issue is considered the TFS as a linear combination of orthogonal functions and aims to visually characterize the concepts involved correlating the physical phenomenon in this case the signals are linear time-invariant. Research has established that the construction of knowledge and the development of mathematical visualization achieved by students is encouraged by the interaction of different registers of representation, with the help of a technological medium, the computer in this case.