As recorrências lineares de 1ª e 2ª ordem: um olhar para as soluções particulares das equações não homogêneas de 2ª ordem e aplicações.

Abstract

This work addresses the use of first and second order Linear Recurrences aimed at students (basic education teachers) of the PROFMAT Professional Master’s Program in Mathematics on a national network, with particular emphasis on the study of non homogeneous second order linear recurrences. and its techniques used in problem solving. The great differential of this work to those found in the literature is the look at the solutions of 2nd order homogeneous linear recurrences as a combination of linearly independent solutions and at the particular solutions of non-homogeneous 2nd order linear recurrences, where we will present a method that will reduce the number of attempts to obtain the particular solution for such recurrences. This occurs when we are looking for a closed formula that relies only on a natural unknown. We will finish our work with a miscellany of problems that we come across in various areas of Mathematics and that we can model through 1st and 2nd order linear recurrences, both homogeneous and non homogeneous.