A History of Numerical Analysis from the 16th Through the 19th CenturyIn this book I have attempted to trace the development of numerical analysis during the period in which the foundations of the modern theory were being laid. To do this I have had to exercise a certain amount of selectivity in choosing and in rejecting both authors and papers. I have rather arbitrarily chosen, in the main, the most famous mathematicians of the period in question and have concentrated on their major works in numerical analysis at the expense, perhaps, of other lesser known but capable analysts. This selectivity results from the need to choose from a large body of literature, and from my feeling that almost by definition the great masters of mathematics were the ones responsible for the most significant accomplishments. In any event I must accept full responsibility for the choices. I would particularly like to acknowledge my thanks to Professor Otto Neugebauer for his help and inspiration in the preparation of this book. This consisted of many friendly discussions that I will always value. I should also like to express my deep appreciation to the International Business Machines Corporation of which I have the honor of being a Fellow and in particular to Dr. Ralph E. Gomory, its Vice-President for Research, for permitting me to undertake the writing of this book and for helping make it possible by his continuing encouragement and support. |
Contents
Euler and Lagrange | 119 |
Laplace Legendre and Gauss | 185 |
Other Nineteenth Century Figures | 261 |
Copyright | |
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A History of Numerical Analysis from the 16th through the 19th Century H. H. Goldstine Limited preview - 2012 |
A History of Numerical Analysis from the 16th through the 19th Century H. H. Goldstine No preview available - 2012 |
Common terms and phrases
a₁ Acad approximation arbitrary Arithmetica Bernoulli numbers Bernoulli polynomials Briggs calculation Cauchy coefficients column considers constant convergence cotan D₁ derivatives difference equations differential equations discussion error Euler Euler-Maclaurin Euler-Maclaurin formula expansion expression finite differences Fluxions function Gauss given gives Goldstine Gregory hence Hermite infinite interpolation formula Jacobi Jour Kutta Lagrange Lagrange's Laplace Laplace VII 1820 Laplace's Legendre Leibniz Lindelöf linear logarithms Maclaurin Math mathematics Mém Mémoire method Moreover Napier Newton Nörlund notation notes numerical integration Oeuvres ordinates paper Paris polynomial problem quantities relation remarks result roots sequence shows Simpson's Rule sine solution solving Stirling Suppose theorem Theoria Theoria Eng theory transl trigonometric interpolation values variables Vieta Werke Whiteside writes wrote μα