A historical survey of the contributions of Francois-Joseph Servois to the development of the rigorous calculus.

详细信息   

• 作者：Petrilli ; Salvatore John ; Jr.
• 学历：Doctor
• 年：2009
• 导师：Smith, J. Philip,eadvisor
• 毕业院校：Teachers College, Columbia University
• ISBN：9781109289190
• CBH：3367985
• Country：USA
• 语种：English
• FileSize：6134374
• Pages：177

文摘

Historians of mathematics considered the nineteenth century to be the Golden Age of mathematics. During this time period many areas of mathematics, such as algebra and geometry, were being placed on rigorous foundations. Another area of mathematics which experienced fundamental change was analysis. The drive for rigor in calculus began in 1797 with the publication of Fonctions analytiques, in which Joseph-Louis Lagrange argued for calculus to be placed on a foundation of algebraic analysis. Although the contributions of major mathematicians, such as Lagrange and Cauchy, providing rigor to analysis have been thoroughly researched, no comprehensive historical survey exists which examines the contributions of lesser known mathematicians of the period. Additionally, the fragmented research does not provide an easily accessible source for teachers of calculus and the history of mathematics to draw from in developing classroom materials. This thesis traced the role of one of the lesser known mathematicians, Francois --- Joseph Servois, in providing calculus with a rigorous foundation. The dissertation reviewed calculus before the time of Servois, looking at Archimedes, Fermat, Newton, Leibniz, Euler, Lagrange, and dAlembert. A brief biography of Servois life was presented. The main source for the biography chapter was Jacques Boyers 1895 work, "Pieces Justicatives et Notes Diverses," which was translated by the author. Finally, Servois primary work, "Essai sur un nouveau mode dexposition des principes du calcul differential," was analyzed to understand his contributions to the advancement of rigor in analysis. The analysis of Servois "Essai" was possible due to a translation conducted by Robert Bradley, President of the Euler Society, and by the author of this thesis. The initial movement towards rigor in analysis is clear in the works of Lagrange and Servois. In light of what we know today, neither of these mathematicians fully succeeded in putting calculus on a mathematically correct foundation. It was Cauchy, through his approach to calculus by means of limits and inequalities, who moved the subject into the modern age.