Estudio de series de fourier y algunas aplicaciones

Abstract

Fourier series is not part of the undergraduate Mathematics curriculum at Escuela Superior Politécnica de Chimborazo (ESPOCH). This is a common situation in several Higher Educational Institutions in Ecuador that offer these programs, different from the engineering faculties, in which this is an essential topic for the professional training. The aim of this documentary research is to provide an integral and referential document for the students from ESPOCH, who are interested in the study of Fourier series. Thus, the methodology used is qualitative non-interactive with a descriptive scope and focused on the review and analysis of documentary sources. This allowed gathering information from bibliographic sources, including classic and updated books, to understand the theoretical concepts and applications of Fourier series. As a result, a referential document was created to provide a solid basis for the study of Fourier series, highlighting definitions, theorems, propositions, lemmas and properties, as well as examples of didactic problems for applications in real contexts, which can improve the academic training of mathematics students. On the other hand, it must be flexible enough to be adapted for engineering majors. This paper is specifically organized in three modules as an effective strategy to approach the study of Fourier series. The first one establishes preliminary concepts to provide a solid foundation, while the second one deepens the theoretical development and finally, the third one presents some applications on the practical relevance in several fields. In conclusion, the referential document represents a substantial contribution both for the mathematics major and for those who consider the study of Fourier Series at ESPOCH, mainly for students who want to be introduced to the study of Fourier series, especially for those learners with a view to carry out in-depth studies, fourth level studies and teaching activities focused on the study of Fourier Series.