Cálculo vetorial aplicado à biologia

Detalhes bibliográficos
Ano de defesa: 2025
Autor(a) principal: Cordeiro, Francisco Erivaldo
Orientador(a): Melo, Marcelo Ferreira de
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Área do conhecimento CNPq:
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
Link de acesso: http://repositorio.ufc.br/handle/riufc/81509
Resumo: This work presents the essential mathematical foundations for the study of vector calculus and its main applications to the study of biology. The initial chapters cover the basic concepts of vector theory, including the definition of vectors, operations with vectors, scalar product, cross product, as well as their properties, geometric interpretations and application of these concepts to biology. Subsequently, the study delves deeper into vector calculus, focusing on line and surface integrals, as well as vector operators, highlighting the definitions and applications of gradient, divergence and rotation. The following chapters explore Green's, Stokes' and Divergent (Gauss) Theorems, which are fundamental pillars in the study of vector calculus. The work concludes with applications of vector calculus to biology, demonstrating how mathematical concepts can be used to model and analyze complex biological phenomena, promoting an interdisciplinary understanding.
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spelling Cordeiro, Francisco ErivaldoMelo, Marcelo Ferreira de2025-07-09T14:06:52Z2025-07-09T14:06:52Z2025CORDEIRO, Francisco Erivaldo. Cálculo vetorial aplicado à biologia. 2025. 119 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Centro de Ciências, Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, 2025.http://repositorio.ufc.br/handle/riufc/81509This work presents the essential mathematical foundations for the study of vector calculus and its main applications to the study of biology. The initial chapters cover the basic concepts of vector theory, including the definition of vectors, operations with vectors, scalar product, cross product, as well as their properties, geometric interpretations and application of these concepts to biology. Subsequently, the study delves deeper into vector calculus, focusing on line and surface integrals, as well as vector operators, highlighting the definitions and applications of gradient, divergence and rotation. The following chapters explore Green's, Stokes' and Divergent (Gauss) Theorems, which are fundamental pillars in the study of vector calculus. The work concludes with applications of vector calculus to biology, demonstrating how mathematical concepts can be used to model and analyze complex biological phenomena, promoting an interdisciplinary understanding.Este trabalho apresenta os fundamentos matemáticos essenciais para o estudo do cálculo vetorial e as principais aplicações ao estudo da biologia. Nos capítulos iniciais, abordam-se os conceitos básicos da teoria vetorial, incluindo a definição de vetores, operações com vetores, produto escalar, produto vetorial, bem como suas propriedades, interpretações geométricas e aplicação desses conceitos à biologia. Posteriormente, o estudo aprofunda-se no cálculo vetorial, com foco nas integrais de linha e de superfície, bem como nos operadores vetoriais, destacando as definições e aplicações de gradiente, divergente e rotacional. Os capítulos seguintes exploram os Teoremas de Green, Stokes e Divergente(Gauss), que são pilares fundamentais no estudo do cálculo vetorial. O trabalho é concluído com aplicações do cálculo vetorial à biologia, demonstrando como conceitos matemáticos podem ser utilizados para modelar e analisar fenômenos biológicos complexos, promovendo uma compreensão interdisciplinar.Cálculo vetorial aplicado à biologiaVector calculus applied to biologyinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisBiologia - MatemáticaVetoresCálculo vetorialBiology - MathematicsVectorsVector calculusCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAinfo:eu-repo/semantics/openAccessporreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFChttp://lattes.cnpq.br/2047269418121164http://lattes.cnpq.br/5064883781827911ORIGINAL2025_dis_fecordeiro.pdf2025_dis_fecordeiro.pdfapplication/pdf2735917http://repositorio.ufc.br/bitstream/riufc/81509/3/2025_dis_fecordeiro.pdf7d6ac8abb22d8b6e94b260ed75faf883MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.ufc.br/bitstream/riufc/81509/4/license.txt8a4605be74aa9ea9d79846c1fba20a33MD54riufc/815092025-07-09 11:06:59.891oai:repositorio.ufc.br:riufc/81509Tk9URTogUExBQ0UgWU9VUiBPV04gTElDRU5TRSBIRVJFClRoaXMgc2FtcGxlIGxpY2Vuc2UgaXMgcHJvdmlkZWQgZm9yIGluZm9ybWF0aW9uYWwgcHVycG9zZXMgb25seS4KCk5PTi1FWENMVVNJVkUgRElTVFJJQlVUSU9OIExJQ0VOU0UKCkJ5IHNpZ25pbmcgYW5kIHN1Ym1pdHRpbmcgdGhpcyBsaWNlbnNlLCB5b3UgKHRoZSBhdXRob3Iocykgb3IgY29weXJpZ2h0Cm93bmVyKSBncmFudHMgdG8gRFNwYWNlIFVuaXZlcnNpdHkgKERTVSkgdGhlIG5vbi1leGNsdXNpdmUgcmlnaHQgdG8gcmVwcm9kdWNlLAp0cmFuc2xhdGUgKGFzIGRlZmluZWQgYmVsb3cpLCBhbmQvb3IgZGlzdHJpYnV0ZSB5b3VyIHN1Ym1pc3Npb24gKGluY2x1ZGluZwp0aGUgYWJzdHJhY3QpIHdvcmxkd2lkZSBpbiBwcmludCBhbmQgZWxlY3Ryb25pYyBmb3JtYXQgYW5kIGluIGFueSBtZWRpdW0sCmluY2x1ZGluZyBidXQgbm90IGxpbWl0ZWQgdG8gYXVkaW8gb3IgdmlkZW8uCgpZb3UgYWdyZWUgdGhhdCBEU1UgbWF5LCB3aXRob3V0IGNoYW5naW5nIHRoZSBjb250ZW50LCB0cmFuc2xhdGUgdGhlCnN1Ym1pc3Npb24gdG8gYW55IG1lZGl1bSBvciBmb3JtYXQgZm9yIHRoZSBwdXJwb3NlIG9mIHByZXNlcnZhdGlvbi4KCllvdSBhbHNvIGFncmVlIHRoYXQgRFNVIG1heSBrZWVwIG1vcmUgdGhhbiBvbmUgY29weSBvZiB0aGlzIHN1Ym1pc3Npb24gZm9yCnB1cnBvc2VzIG9mIHNlY3VyaXR5LCBiYWNrLXVwIGFuZCBwcmVzZXJ2YXRpb24uCgpZb3UgcmVwcmVzZW50IHRoYXQgdGhlIHN1Ym1pc3Npb24gaXMgeW91ciBvcmlnaW5hbCB3b3JrLCBhbmQgdGhhdCB5b3UgaGF2ZQp0aGUgcmlnaHQgdG8gZ3JhbnQgdGhlIHJpZ2h0cyBjb250YWluZWQgaW4gdGhpcyBsaWNlbnNlLiBZb3UgYWxzbyByZXByZXNlbnQKdGhhdCB5b3VyIHN1Ym1pc3Npb24gZG9lcyBub3QsIHRvIHRoZSBiZXN0IG9mIHlvdXIga25vd2xlZGdlLCBpbmZyaW5nZSB1cG9uCmFueW9uZSdzIGNvcHlyaWdodC4KCklmIHRoZSBzdWJtaXNzaW9uIGNvbnRhaW5zIG1hdGVyaWFsIGZvciB3aGljaCB5b3UgZG8gbm90IGhvbGQgY29weXJpZ2h0LAp5b3UgcmVwcmVzZW50IHRoYXQgeW91IGhhdmUgb2J0YWluZWQgdGhlIHVucmVzdHJpY3RlZCBwZXJtaXNzaW9uIG9mIHRoZQpjb3B5cmlnaHQgb3duZXIgdG8gZ3JhbnQgRFNVIHRoZSByaWdodHMgcmVxdWlyZWQgYnkgdGhpcyBsaWNlbnNlLCBhbmQgdGhhdApzdWNoIHRoaXJkLXBhcnR5IG93bmVkIG1hdGVyaWFsIGlzIGNsZWFybHkgaWRlbnRpZmllZCBhbmQgYWNrbm93bGVkZ2VkCndpdGhpbiB0aGUgdGV4dCBvciBjb250ZW50IG9mIHRoZSBzdWJtaXNzaW9uLgoKSUYgVEhFIFNVQk1JU1NJT04gSVMgQkFTRUQgVVBPTiBXT1JLIFRIQVQgSEFTIEJFRU4gU1BPTlNPUkVEIE9SIFNVUFBPUlRFRApCWSBBTiBBR0VOQ1kgT1IgT1JHQU5JWkFUSU9OIE9USEVSIFRIQU4gRFNVLCBZT1UgUkVQUkVTRU5UIFRIQVQgWU9VIEhBVkUKRlVMRklMTEVEIEFOWSBSSUdIVCBPRiBSRVZJRVcgT1IgT1RIRVIgT0JMSUdBVElPTlMgUkVRVUlSRUQgQlkgU1VDSApDT05UUkFDVCBPUiBBR1JFRU1FTlQuCgpEU1Ugd2lsbCBjbGVhcmx5IGlkZW50aWZ5IHlvdXIgbmFtZShzKSBhcyB0aGUgYXV0aG9yKHMpIG9yIG93bmVyKHMpIG9mIHRoZQpzdWJtaXNzaW9uLCBhbmQgd2lsbCBub3QgbWFrZSBhbnkgYWx0ZXJhdGlvbiwgb3RoZXIgdGhhbiBhcyBhbGxvd2VkIGJ5IHRoaXMKbGljZW5zZSwgdG8geW91ciBzdWJtaXNzaW9uLgo=Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2025-07-09T14:06:59Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.pt_BR.fl_str_mv Cálculo vetorial aplicado à biologia
dc.title.en.pt_BR.fl_str_mv Vector calculus applied to biology
title Cálculo vetorial aplicado à biologia
spellingShingle Cálculo vetorial aplicado à biologia
Cordeiro, Francisco Erivaldo
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
Biologia - Matemática
Vetores
Cálculo vetorial
Biology - Mathematics
Vectors
Vector calculus
title_short Cálculo vetorial aplicado à biologia
title_full Cálculo vetorial aplicado à biologia
title_fullStr Cálculo vetorial aplicado à biologia
title_full_unstemmed Cálculo vetorial aplicado à biologia
title_sort Cálculo vetorial aplicado à biologia
author Cordeiro, Francisco Erivaldo
author_facet Cordeiro, Francisco Erivaldo
author_role author
dc.contributor.author.fl_str_mv Cordeiro, Francisco Erivaldo
dc.contributor.advisor1.fl_str_mv Melo, Marcelo Ferreira de
contributor_str_mv Melo, Marcelo Ferreira de
dc.subject.cnpq.fl_str_mv CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
topic CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
Biologia - Matemática
Vetores
Cálculo vetorial
Biology - Mathematics
Vectors
Vector calculus
dc.subject.ptbr.pt_BR.fl_str_mv Biologia - Matemática
Vetores
Cálculo vetorial
dc.subject.en.pt_BR.fl_str_mv Biology - Mathematics
Vectors
Vector calculus
description This work presents the essential mathematical foundations for the study of vector calculus and its main applications to the study of biology. The initial chapters cover the basic concepts of vector theory, including the definition of vectors, operations with vectors, scalar product, cross product, as well as their properties, geometric interpretations and application of these concepts to biology. Subsequently, the study delves deeper into vector calculus, focusing on line and surface integrals, as well as vector operators, highlighting the definitions and applications of gradient, divergence and rotation. The following chapters explore Green's, Stokes' and Divergent (Gauss) Theorems, which are fundamental pillars in the study of vector calculus. The work concludes with applications of vector calculus to biology, demonstrating how mathematical concepts can be used to model and analyze complex biological phenomena, promoting an interdisciplinary understanding.
publishDate 2025
dc.date.accessioned.fl_str_mv 2025-07-09T14:06:52Z
dc.date.available.fl_str_mv 2025-07-09T14:06:52Z
dc.date.issued.fl_str_mv 2025
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 CORDEIRO, Francisco Erivaldo. Cálculo vetorial aplicado à biologia. 2025. 119 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Centro de Ciências, Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, 2025.
dc.identifier.uri.fl_str_mv http://repositorio.ufc.br/handle/riufc/81509
identifier_str_mv CORDEIRO, Francisco Erivaldo. Cálculo vetorial aplicado à biologia. 2025. 119 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Centro de Ciências, Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, 2025.
url http://repositorio.ufc.br/handle/riufc/81509
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Federal do Ceará (UFC)
instname:Universidade Federal do Ceará (UFC)
instacron:UFC
instname_str Universidade Federal do Ceará (UFC)
instacron_str UFC
institution UFC
reponame_str Repositório Institucional da Universidade Federal do Ceará (UFC)
collection Repositório Institucional da Universidade Federal do Ceará (UFC)
bitstream.url.fl_str_mv http://repositorio.ufc.br/bitstream/riufc/81509/3/2025_dis_fecordeiro.pdf
http://repositorio.ufc.br/bitstream/riufc/81509/4/license.txt
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repository.name.fl_str_mv Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)
repository.mail.fl_str_mv bu@ufc.br || repositorio@ufc.br
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