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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2016.tde-07012016-162615
Document
Author
Full name
Fabricio Raimundo Fernandes
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2015
Supervisor
Committee
Bena, Maria Aparecida (President)
Arita, Andréa Cristina Prokopczyk
Godoy, Sandra Maria Semensato de
Mesquita, Jaqueline Godoy
Title in Portuguese
Equações de diferenças de 1ª ordem e aplicações
Keywords in Portuguese
Diagrama de Cobweb
Equação de diferenças
Estabilidade
Ponto de equilíbrio
Abstract in Portuguese
As equações de diferenças (ou equações discretas) desempenham papel fundamental na modelagem de problemas em que o tempo é medido em intervalos discretos, por exemplo, dia, mês, ano. Elas estão presentes em sistemas físicos, químicos, biológicos, sociais e econômicos. O objetivo desse trabalho é estudar as equações de diferenças de primeira ordem, focando aspectos teóricos, análise do comportamento assintótico das soluções através de técnicas analíticas (teoremas de estabilidade) e técnicas gráficas (diagramas de Cobweb). Também são desenvolvidas algumas aplicações. Além disso, são apresentadas três propostas didáticas relacionadas ao tema para serem trabalhadas no Ensino Médio.
Title in English
First-order difference equations and applications
Keywords in English
Cobweb diagram
Difference equation
Equilibrium point
Stability
Abstract in English
The difference equations (or discrete equations) play a key role in shaping problems in which time is measured at discrete intervals, e.g., day, month, year. They may be applied to physical, chemical, biological, social and economic systems. The aim of this work is to study the first-order difference equations, focusing on theoretical aspects, asymptotic behavior of solutions throughout analytical techniques (stability theorems) and graphical techniques (Cobweb diagrams). Some applications are also shown. Three teaching proposals related to the theme are presented in order to be developed in High School.
 
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Publishing Date
2016-01-07
 
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