Problemas e modelos que contribu?ram com o desenvolvimento do c?lculo diferencial e integral: dos gregos ? Newton

• Main Author: Silva, Maria Deusa Ferreira da
• Other Authors: CPF:12432962249
• Format: Others
• Language: Portuguese
• Published: Universidade Federal do Rio Grande do Norte 2014
• Subjects: Hist?ria da matem?tica; Hist?ria do c?lculo; Modelagem matem?tica; Ensino de c?lculo; CNPQ::CIENCIAS HUMANAS::EDUCACAO
• Online Access: http://repositorio.ufrn.br:8080/jspui/handle/123456789/14317

Made available in DSpace on 2014-12-17T14:36:15Z (GMT). No. of bitstreams: 1 MariaDFS_TESE_1-129.pdf: 4033430 bytes, checksum: adb4bfc3ed31e11090efa86c94de906a (MD5) Previous issue date: 2010-06-25 === This article refers to a research which tries to historically (re)construct the conceptual development of the Integral and Differential calculus, taking into account its constructing model feature, since the Greeks to Newton. These models were created by the problems that have been proposed by the history and were being modified by the time the new problems were put and the mathematics known advanced. In this perspective, I also show how a number of nature philosophers and mathematicians got involved by this process. Starting with the speculations over scientific and philosophical natures done by the ancient Greeks, it culminates with Newton s work in the 17th century. Moreover, I present and analyze the problems proposed (open questions), models generated (questions answered) as well as the religious, political, economic and social conditions involved. This work is divided into 6 chapters plus the final considerations. Chapter 1 shows how the research came about, given my motivation and experience. I outline the ways I have gone trough to refine the main question and present the subject of and the objectives of the research, ending the chapter showing the theoretical bases by which the research was carried out, naming such bases as Investigation Theoretical Fields (ITF). Chapter 2 presents each one of the theoretical bases, which was introduced in the chapter 1 s end. In this discuss, I try to connect the ITF to the research. The Chapter 3 discusses the methodological choices done considering the theoretical fields considered. So, the Chapters 4, 5 and 6 present the main corpus of the research, i.e., they reconstruct the calculus history under a perspective of model building (questions answered) from the problems given (open questions), analyzing since the ancient Greeks contribution (Chapter 4), pos- Greek, especially, the Romans contribution, Hindus, Arabian, and the contribution on the Medium Age (Chapter 5). I relate the European reborn and the contribution of the philosophers and scientists until culminate with the Newton s work (Chapter 6). In the final considerations, it finally gives an account on my impressions about the development of the research as well as the results reached here. By the end, I plan out a propose of curse of Differential and Integral Calculus, having by basis the last three chapters of the article === Esta tese de Doutorado teve como objetivo fazer uma (re)constru??o hist?rica do desenvolvimento Conceitual do C?lculo Diferencial e Integral olhando-o como uma constru??o de modelos, dos gregos a Newton. Tais modelos eram gerados a partir de problemas que foram sendo propostos ao longo da hist?ria e iam sendo modificados ? medida que novos problemas eram postos e o conhecimento matem?tico avan?ava. Nessa perspectiva, busco tamb?m mostrar que esse processo envolveu uma legi?o de matem?ticos/fil?sofos da natureza, tendo in?cio com as especula??es de natureza cient?fica e filos?fica dos antigos gregos e culmina com o trabalho de Newton, no s?culo XVII. Al?m disso, nesse processo de reconstru??o do desenvolvimento conceitual do c?lculo apresento e analiso os problemas propostos (quest?es em aberto), modelos gerados (quest?es respondidas) bem como as condi??es sociais, econ?micas, pol?ticas e religiosas envolvidas no processo. O trabalho est? dividido em seis cap?tulos mais as considera??es finais. No cap?tulo 1 apresento como a pesquisa se configurou a partir das minhas motiva??es e experi?ncias. Delineio os caminhos percorridos para o refinamento da pergunta diretriz e apresento o objeto de e os objetivos da pesquisa e fecho o cap?tulo apresentando os campos te?ricos em que a pesquisa se fundamenta, os quais denominei de Campos Te?ricos de Investiga??o (CTI). No cap?tulo 2 discorro sobre cada um dos Campos Te?ricos de Investiga??o, introduzidos no final do primeiro cap?tulo. Nessa discuss?o procuro ligar os CTI com a pesquisa. No cap?tulo 3 delimito e discuto as escolhas metodol?gicas com base nos campos te?ricos em que a pesquisa se assenta. Ent?o, nos cap?tulos 4,5 e 6, apresento o corpus principal da pesquisa, ou seja, reconstruo a hist?ria do c?lculo numa perspectiva de constru??o de modelos (quest?es respondidas) a partir a dos problemas geradores (quest?es e aberto), analisando as contribui??es dos gregos antigos ( cap?tulo 4), p?s-gregos, especialmente, a contribui??o dos romanos, indus, ?rabes e as contribui??es na Idade M?dia (cap?tulo 5). Retomo o renascimento europeu e as contribui??es dos fil?sofos/cientistas at? culminar com o trabalho de Newton (cap?tulo 6). Finalmente, nas considera??es finais, relato minhas impress?es sobre o desenvolvimento da pesquisa e de como asseguro que a pergunta diretriz e os objetivos foram alcan?ados. Por ?ltimo, delineio uma proposta de curso de C?lculo Diferencial e Integral tendo como eixo os tr?s ?ltimos cap?tulos da tese