The Development of Newtonian Calculus in Britain, 1700-1800Cambridge University Press, 13 de nov. 2003 - 244 pàgines Guicciardini presents a comprehensive survey of both the research and teaching of Newtonian calculus, the calculus of "fluxions", over the period between 1700 and 1810. Although Newton was one of the inventors of calculus, the developments in Britain remained separate from the rest of Europe for over a century. While it is usually maintained that after Newton there was a period of decline in British mathematics, the author's research demonstrates that the methods used by researchers of the period yielded considerable success in laying the foundations and investigating the applications of the calculus. Even when "decline" set in, in mid century, the foundations of the reform were being laid, which were to change the direction and nature of the mathematics community. The book considers the importance of Isaac Newton, Roger Cotes, Brook Taylor, James Stirling, Abraham de Moivre, Colin Maclaurin, Thomas Bayes, John Landen and Edward Waring. This will be a useful book for students and researchers in the history of science, philosophers of science and undergraduates studying the history of mathematics. |
Continguts
THE DIFFUSION OF THE CALCULUS 170030 | 11 |
11 Early initiates | 12 |
12 Textbook writers | 13 |
13 The teaching of the calculus in the universities | 18 |
DEVELOPMENTS IN THE CALCULUS OF FLUXIONS 171433 | 28 |
21 Methods of integration | 29 |
22 The Methodus differentialis | 31 |
23 Geometry | 36 |
83 Olynthus Gregory and Peter Barlow | 112 |
84 The Royal Military College at Sandhurst | 114 |
85 The Ladles Diary and the Mathematical Repository | 115 |
86 Ivorys breakthrough | 117 |
87 Other journals and the encyclopaedias | 118 |
88 The Royal Naval Academy at Portsmouth | 121 |
CAMBRIDGE AND DUBLIN 17901820 | 124 |
92 Robert Woodhouse | 126 |
THE CONTROVERSY ON THE FOUNDATIONS OF THE CALCULUS 173442 | 38 |
32 The definitions of the basic terms of the calculus in the works of the early fluxionists | 41 |
33 The doctrine of prime and ultimate ratios | 43 |
34 The foundations of the calculus in Maclaurins Treatise of Fluxions | 47 |
THE MIDDLE PERIOD | 53 |
THE TEXTBOOKS ON FLUXIONS 173658 | 55 |
42 Textbooks on fluxions and the science books trade | 60 |
SOME APPLICATIONS OF THE CALCULUS 17403 | 68 |
51 Maclaurins study of the attraction of ellipsoids | 69 |
52 Simpsons study of the attraction of ellipsoids | 73 |
53 Remarks on the use of partial differentials in Clairauts Theorie de la Figure de la Terre | 79 |
THE ANALYTIC ART 175585 | 82 |
61 Simpsons methodology | 83 |
62 Landens Residual Analysis | 85 |
63 Warings work on partial fluxional equations | 89 |
THE REFORM | 93 |
SCOTLAND 17851809 | 95 |
72 John Playfair | 99 |
73 Wallace and Ivory | 103 |
74 Glenie and Spence | 104 |
THE MILITARY SCHOOLS 17731819 | 108 |
81 The Royal Military Academy at Woolwich | 109 |
82 Charles Hutton | 111 |
93 Ireland in the eighteenth century | 131 |
94 The reform of mathematics at the University of Dublin | 132 |
95 The Analytical Society | 135 |
CONCLUSION | 139 |
TABLE OF CONTENTS OF FLUXIONARY TEXTBOOKS | 143 |
A2 Table of contents of Thomas Simpsons The Doctrine and Application of Fluxions 1750c | 146 |
A3 Table of contents of John Howes An Introduction to the Doctrine of Fluxions 1751 | 147 |
PRICE LIST OF MATHEMATICAL BOOKS PRINTED FOR JOHN NOURSE | 148 |
CHAIRS IN THE UNIVERSITIES | 150 |
C3 University of Oxford | 151 |
C4 University of Edinburgh | 152 |
C6 University of St Andrews | 153 |
C8 University of Dublin | 155 |
MILITARY ACADEMIES | 156 |
D2 Royal Military College Sandhurst masters and professors of mathematics | 157 |
D3 Royal Naval Academy at Portsmouth headmasters | 158 |
SUBJECT INDEX OF PRIMARY LITERATURE | 159 |
MANUSCRIPT SOURCES | 165 |
Notes | 167 |
Bibliography | 183 |
222 | |
Altres edicions - Mostra-ho tot
The Development of Newtonian Calculus in Britain, 1700-1800 Niccol- Guicciardini Previsualització no disponible - 1989 |
Frases i termes més freqüents
2nd edn Academy algebraical analysis Analytical Society appointed astronomy attraction Berkeley Brinkley Britain British mathematicians British mathematics calculus of fluxions calculus of variations Cambridge Chair of Mathematics chapter Clairaut Colin Maclaurin College continental Cotes Cotes's Craig(e curves differential notation Dublin Edinburgh edition eighteenth century ellipsoids Emerson employed Euler fluents fluxional calculus fluxionists foundations functions geometry Gregory Hutton Increments infinitesimals integration Ivory James John John Colson John Playfair Jurin Keill kinematical Lagrange Lagrangian Landen lectures Leibniz London Maclaurin 1742 mathematicians mathematics mechanics Method of Fluxions Moivre motion Natural Philosophy Newtonian partial differential Phil Philosophical Transactions Playfair Principia Principles problems Professor of Mathematics published quadratura quantities reform Robert Simson Robert Woodhouse Royal Military Royal Society Sandhurst Saunderson Simpson Spence Stewart Stirling Taylor teaching textbooks theorem theory Thomas Trans translation Treatise of Fluxions treatises on fluxions University variable velocity W.D. Jones Wallace Waring William Woodhouse Woolwich
Referències a aquest llibre
Mr Hopkins' Men: Cambridge Reform and British Mathematics in the 19th Century A.D.D. Craik Previsualització limitada - 2008 |
Teaching and Learning in Nineteenth-century Cambridge Jonathan Smith,Christopher Stray Previsualització limitada - 2001 |