16º problema de Hilbert: uma motivação para o estudo de funções periódicas

Abstract

Periodic situations are found in many aspects of general knowledge, such as the measurement of hours in a day, the movement of the waves and the translation of celestial bodies. Perhaps this is why the study of journals always attracts many mathematicians. To understand the complex mathematical concepts that involve these events, it is important to understand the basic knowledge of trigonometric functions. This work intends to present a motivation for the study of such functions, bringing mathematics closer to everyday situations, proposing simple models. For this, a qualitative study of the general aspects of Differential Equations was initially carried out, involving linear systems, Existence and Uniqueness Theorem, vector fields, limit sets of trajectories, among others. To end this first part, a study of the Averaging Theory and its application will be developed. After these studies, a proposal was made for the teaching of trigonometric functions in the classroom, suggesting different activities, involving the use of digital applications to assist in the modelling of student’s daily situations such as temperature variation and the movement of sea waves. Therefore, we hope that this work will serve as a support for the teaching of trigonometric concepts, using everyday situations to encourage students in their learning.