Fundamental concepts on Fourier Analysis (with exercises and applications)

Abstract

In this work we present the main concepts of Fourier Analysis (such as Fourier series, Fourier transforms, Parseval and Plancherel identities, correlation, and convolution) and illustrate them by means of examples and applications. Most of the concepts presented here can be found in the book "A First Course in Fourier Analysis" by David W.Kammler. Similarly, the examples correspond to over 15 problems posed in the same book which have been completely worked out in this report. As applications, we include Fourier's original approach to the heat flow using Fourier series and an application to filtering one-dimensional signals.