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Master's Dissertation
DOI
10.11606/D.55.2016.tde-30112016-154343
Document
Author
Full name
Rafael de Freitas Manço
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2016
Supervisor
Committee
Azevedo, Katia Andreia Gonçalves de (President)
Godoy, Sandra Maria Semensato de
Mitrowsky, Rafael Andres Rosales
Nicola, Selma Helena de Jesus
Title in Portuguese
Integrais e aplicações
Keywords in Portuguese
Integral de Riemann
Integral de Riemann-Stieltjes
Variáveis aleatórias
Abstract in Portuguese
O intuito deste trabalho é fazer uma análise sobre o processo de integração de funções. Existem muitas generalizações do conceito de integração abordado inicialmente por meio da integral de Riemann, como por exemplo, a integral de Riemann-Stieltjes, Lebesgue, Henstock-Kurzweil entre outras. Abordaremos especialmente a integral de Riemann-Stieltjes, e mostraremos a limitação da integral de Riemann no estudo de convergência de funções, indicando a necessidade de se generalizar o processo de integração. Faremos uma aplicação da integral de Riemann-Stieltjes no estudo de variáveis aleatórias e apresentamos uma proposta de abordagem, para a sala de aula, sobre o deslocamento e distância percorrida por um objeto em movimento retilíneo uniforme associado a área.
Title in English
Integral and applications
Keywords in English
Random variables
Riemann integral
Riemann-Stieltjes integral
Abstract in English
The aim of this work is analizing the process of integration of functions. There are many generalizations of the integration concept originally addressed by Riemann integral such as the Riemann-Stieltjes integral, Lebesgue integral, Henstock-Kurzweil integral, among others. We will be specially concerned with the integral of Riemann-Stieltjes and we will show the limitations of Riemann integral about convergence of functions, leading to the need to generalize the integration process. We will apply Riemann-Stieltjes integral for the study of random variables and present an approach to the classroom, on the displacement and distance traveled by an object in uniform rectilinear motion associated to concept of area.
 
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Publishing Date
2016-11-30
 
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