Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2022.tde-17012023-155330
Document
Author
Full name
Evandro Aloisio Guilherme
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2022
Supervisor
Committee
Picon, Tiago Henrique (President)
Almeida, Marcelo Fernandes de
Ebert, Marcelo Rempel
Zugliani, Giuliano Angelo
Title in Portuguese
Introdução às séries de Fourier e critérios de convergência.
Keywords in Portuguese
Convergência de séries de funções
Funções periódicas
Séries de Fourier
Teorema de Fourier
Abstract in Portuguese
Title in English
Introduction to Fourier Series and convergence criteria
Keywords in English
Convergence of series of function
Fourier Series
Fouriers Theorem
Functions parity
Periodic functions
Abstract in English
There are several gaps in the training of mathematics teachers in Brazil. Whether for a short time or for an extensive menu of subjects that make up the curriculum of undergraduate courses, many teachers graduate without having learned the Fourier Series in depth, or even without ever having studied them. In this sense, this dissertation aims to offer students and future mathematics teachers a detailed material on the introductory foundations of Fourier Series. In order to achieve this objective, this dissertation began with a preliminary study on periodicity and parity of functions; in the sequence, seeking to encourage the study of Fourier Series, the physical problem of heat conduction in a metallic object was approached, a problem that motivated the emergence of this theory due to Fourier; then, the coefficients and the expression of the Fourier Series were defined, whose calculations were illustrated by an expressive number of examples; later, the interesting application of how to obtain series of numbers that approximate the value of was presented; and finally, the uniform and pointwise convergence of the Fourier Theorem was demonstrated. In the last chapter, a didactic tutorial was presented teaching how to construct the graphs of partial sums of Fourier Series using the Geogebra software.