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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2016.tde-26102016-165330
Document
Author
Full name
Walter Fernandes da Silva Junior
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2016
Supervisor
Committee
Bena, Maria Aparecida (President)
Aki, Sueli Mieko Tanaka
Gadotti, Marta Cilene
Santos, Jair Silverio dos
Title in Portuguese
Equações de diferenças lineares de ordem superior e aplicações
Keywords in Portuguese
Equação característica
Equação de diferenças
Estabilidade
Solução
Abstract in Portuguese
As equações de diferenças desempenham papel fundamental na modelagem de problemas em que o tempo é medido em intervalos discretos, por exemplo, horas, dia, mês, ano. Elas têm aplicações em Matemática, Física, Engenharia, Economia, Biologia e Sociologia. O objetivo desse trabalho é estudar as equações de diferenças lineares de ordem superior, focando aspectos teóricos, métodos de determinação das soluções destas equações e análise da estabilidade de soluções de equações de diferenças de 2a ordem com coeficientes constantes. Exemplos e aplicações ilustram a teoria desenvolvida. É apresentada uma proposta didática relacionada ao tema para ser trabalhada no ensino médio.
Title in English
Higher-order linear difference equations and applications
Keywords in English
Characteristic equation
Difference equation
Solution
Stability
Abstract in English
The difference equations play a key role in shaping problems in which time is measured in discrete intervals, e.g., hour, day, month, year. They may be applied to Mathematics, Physics, Engineering, Economics, Biology and Sociology. The aim of this work is to study the higher-order linear difference equations, focusing on the theoretical aspects, on the methods used to determine the solutions of these equations and also on the analysis of the stability of 2nd-order difference equations with constants coefficients. Examples and applications depict the developed theory. In addition, a didactic proposal related to the topic to be worked on high school is presented.
 
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Publishing Date
2016-10-26
 
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