Raiz de função polinomial pelo método de Newton-Raphson
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
dARK ID: | ark:/38995/001300000f13n |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/8735 |
Resumo: | Determining roots of polynomial functions is a quite frequent content in the subject of Mathematics in Primary and Higher Education. But Galois has shown that it is not possible to develop algebraic formulas to find such roots in polynomials with a degree greater than 4. The present work aims to use Newton-Raphson’s Numerical and Iterative method to find roots of polynomial function. For this, the GeoGebra software is used as a computational and pedagogical tool to illustrate the procedure adopted by the mentioned method through spreadsheets, Geometry and algebraic calculations. Thus, the proposed methodology can help in the understanding of the Newton-Raphson Method and contribute to the process of teaching and learning the content of polynomials for teachers and students of Basic Education. |
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Rodrigues, Paulo Henrique de Azevedohttp://lattes.cnpq.br/8910130626123426Rodrigues, Paulo Henrique de AzevedoSouza, Flávio Raimundo deSantos, Ronaldo Antônio doshttp://lattes.cnpq.br/7911057390921183Silva, Renato de Sousa e2018-07-26T10:43:33Z2018-07-10SILVA, Renato de Sousa. Raiz de função polinomial pelo método de Newton-Raphson. 2018. 73 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2018.http://repositorio.bc.ufg.br/tede/handle/tede/8735ark:/38995/001300000f13nDetermining roots of polynomial functions is a quite frequent content in the subject of Mathematics in Primary and Higher Education. But Galois has shown that it is not possible to develop algebraic formulas to find such roots in polynomials with a degree greater than 4. The present work aims to use Newton-Raphson’s Numerical and Iterative method to find roots of polynomial function. For this, the GeoGebra software is used as a computational and pedagogical tool to illustrate the procedure adopted by the mentioned method through spreadsheets, Geometry and algebraic calculations. Thus, the proposed methodology can help in the understanding of the Newton-Raphson Method and contribute to the process of teaching and learning the content of polynomials for teachers and students of Basic Education.Determinar raízes de funções polinomiais é um conteúdo bastante frequente na disciplina de Matemática do Ensino Básico e Superior. Mas, Galois demonstrou que não é possível desenvolver fórmulas algébricas para encontrar tais raízes em polinômios com grau maior que 4. Então o presente trabalho tem o objetivo de utilizar o Método Numérico e Iterativo de Newton-Raphson para encontrar raízes de função polinomial. Para isto, utiliza-se o software GeoGebra como ferramenta computacional e pedagógica para ilustrar o procedimento adotado pelo método citado por meio de planilhas eletrônicas, da Geometria e de cálculos algébricos. Assim, a metodologia proposta pode auxiliar na compreensão do Método de Newton-Raphson e colaborar para o processo de ensino e aprendizagem do conteúdo de polinômios para professores e alunos do Ensino Básico.Submitted by Franciele Moreira (francielemoreyra@gmail.com) on 2018-07-25T14:02:43Z No. of bitstreams: 2 Dissertação - Renato de Sousa e Silva - 2018.pdf: 2985862 bytes, checksum: 893b26d388119df4da6d373c1ce19d3b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-07-26T10:43:33Z (GMT) No. of bitstreams: 2 Dissertação - Renato de Sousa e Silva - 2018.pdf: 2985862 bytes, checksum: 893b26d388119df4da6d373c1ce19d3b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2018-07-26T10:43:33Z (GMT). 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dc.title.eng.fl_str_mv |
Raiz de função polinomial pelo método de Newton-Raphson |
dc.title.alternative.eng.fl_str_mv |
Polynomial function root by Newton-Raphson method |
title |
Raiz de função polinomial pelo método de Newton-Raphson |
spellingShingle |
Raiz de função polinomial pelo método de Newton-Raphson Silva, Renato de Sousa e Polinômio Método de Newton-Raphson GeoGebra Polynomial Newton-Raphson method GeoGebra MATEMATICA::ALGEBRA |
title_short |
Raiz de função polinomial pelo método de Newton-Raphson |
title_full |
Raiz de função polinomial pelo método de Newton-Raphson |
title_fullStr |
Raiz de função polinomial pelo método de Newton-Raphson |
title_full_unstemmed |
Raiz de função polinomial pelo método de Newton-Raphson |
title_sort |
Raiz de função polinomial pelo método de Newton-Raphson |
author |
Silva, Renato de Sousa e |
author_facet |
Silva, Renato de Sousa e |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Rodrigues, Paulo Henrique de Azevedo |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8910130626123426 |
dc.contributor.referee1.fl_str_mv |
Rodrigues, Paulo Henrique de Azevedo |
dc.contributor.referee2.fl_str_mv |
Souza, Flávio Raimundo de |
dc.contributor.referee3.fl_str_mv |
Santos, Ronaldo Antônio dos |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/7911057390921183 |
dc.contributor.author.fl_str_mv |
Silva, Renato de Sousa e |
contributor_str_mv |
Rodrigues, Paulo Henrique de Azevedo Rodrigues, Paulo Henrique de Azevedo Souza, Flávio Raimundo de Santos, Ronaldo Antônio dos |
dc.subject.por.fl_str_mv |
Polinômio Método de Newton-Raphson GeoGebra |
topic |
Polinômio Método de Newton-Raphson GeoGebra Polynomial Newton-Raphson method GeoGebra MATEMATICA::ALGEBRA |
dc.subject.eng.fl_str_mv |
Polynomial Newton-Raphson method GeoGebra |
dc.subject.cnpq.fl_str_mv |
MATEMATICA::ALGEBRA |
description |
Determining roots of polynomial functions is a quite frequent content in the subject of Mathematics in Primary and Higher Education. But Galois has shown that it is not possible to develop algebraic formulas to find such roots in polynomials with a degree greater than 4. The present work aims to use Newton-Raphson’s Numerical and Iterative method to find roots of polynomial function. For this, the GeoGebra software is used as a computational and pedagogical tool to illustrate the procedure adopted by the mentioned method through spreadsheets, Geometry and algebraic calculations. Thus, the proposed methodology can help in the understanding of the Newton-Raphson Method and contribute to the process of teaching and learning the content of polynomials for teachers and students of Basic Education. |
publishDate |
2018 |
dc.date.accessioned.fl_str_mv |
2018-07-26T10:43:33Z |
dc.date.issued.fl_str_mv |
2018-07-10 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
SILVA, Renato de Sousa. Raiz de função polinomial pelo método de Newton-Raphson. 2018. 73 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2018. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/8735 |
dc.identifier.dark.fl_str_mv |
ark:/38995/001300000f13n |
identifier_str_mv |
SILVA, Renato de Sousa. Raiz de função polinomial pelo método de Newton-Raphson. 2018. 73 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2018. ark:/38995/001300000f13n |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/8735 |
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por |
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por |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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Universidade Federal de Goiás |
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UFG |
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Brasil |
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Instituto de Matemática e Estatística - IME (RG) |
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Universidade Federal de Goiás |
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