A History Of The Calculus Of Variations
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A History Of The Calculus Of Variations In The Eighteenth Century
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Author : Robert Woodhouse
language : en
Publisher: American Mathematical Society
Release Date : 2004-04-13
A History Of The Calculus Of Variations In The Eighteenth Century written by Robert Woodhouse and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-13 with Mathematics categories.
Shortly after the invention of differential and integral calculus, the calculus of variations was developed. The new calculus looks for functions that minimize or maximize some quantity, such as the brachistochrone problem, which was solved by Johann Bernoulli, Leibniz, Newton, Jacob Bernoulli and l'Hopital and is sometimes considered as the starting point of the calculus of variations. In Woodhouse's book, first published in 1810, he has interwoven the historical progress with the scientific development of the subject. The reader will have the opportunity to see how calculus, during its first one hundred years, developed by seemingly tiny increments to become the highly polished subject that we know today. Here, Woodhouse's interweaving of history and science gives his special point of view on the mathematics. As he states in his preface: ""Indeed the authors who write near the beginnings of science are, in general, the most instructive; they take the reader more along with them, show him the real difficulties and, which is the main point, teach him the subject, the way they themselves learned it.
A History Of The Calculus Of Variations From The 17th Through The 19th Century
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Author : H. H. Goldstine
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A History Of The Calculus Of Variations From The 17th Through The 19th Century written by H. H. Goldstine and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The calculus of variations is a subject whose beginning can be precisely dated. It might be said to begin at the moment that Euler coined the name calculus of variations but this is, of course, not the true moment of inception of the subject. It would not have been unreasonable if I had gone back to the set of isoperimetric problems considered by Greek mathemati cians such as Zenodorus (c. 200 B. C. ) and preserved by Pappus (c. 300 A. D. ). I have not done this since these problems were solved by geometric means. Instead I have arbitrarily chosen to begin with Fermat's elegant principle of least time. He used this principle in 1662 to show how a light ray was refracted at the interface between two optical media of different densities. This analysis of Fermat seems to me especially appropriate as a starting point: He used the methods of the calculus to minimize the time of passage cif a light ray through the two media, and his method was adapted by John Bernoulli to solve the brachystochrone problem. There have been several other histories of the subject, but they are now hopelessly archaic. One by Robert Woodhouse appeared in 1810 and another by Isaac Todhunter in 1861.
A History Of The Calculus Of Variations
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Author : I. Todhunter
language : en
Publisher: BoD – Books on Demand
Release Date : 2022-06-12
A History Of The Calculus Of Variations written by I. Todhunter and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-12 with Fiction categories.
Reprint of the original, first published in 1861.
A History Of The Calculus Of Variations From The 17th Through The 19th Century
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Author : Herman Heine Goldstine
language : en
Publisher:
Release Date : 1995
A History Of The Calculus Of Variations From The 17th Through The 19th Century written by Herman Heine Goldstine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
A History Of The Progress Of The Calculus Of Variations During The Nineteenth Century By I Todhunter
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Author : Isaac Todhunter
language : en
Publisher:
Release Date : 1861
A History Of The Progress Of The Calculus Of Variations During The Nineteenth Century By I Todhunter written by Isaac Todhunter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1861 with Calculus of variations categories.
History Of Calculus Of Variations
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Author : Isaac Todhunter
language : en
Publisher:
Release Date : 1861
History Of Calculus Of Variations written by Isaac Todhunter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1861 with categories.
Change And Variations
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Author : Jeremy Gray
language : en
Publisher: Springer Nature
Release Date : 2021-06-03
Change And Variations written by Jeremy Gray and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-03 with Mathematics categories.
This book presents a history of differential equations, both ordinary and partial, as well as the calculus of variations, from the origins of the subjects to around 1900. Topics treated include the wave equation in the hands of d’Alembert and Euler; Fourier’s solutions to the heat equation and the contribution of Kovalevskaya; the work of Euler, Gauss, Kummer, Riemann, and Poincaré on the hypergeometric equation; Green’s functions, the Dirichlet principle, and Schwarz’s solution of the Dirichlet problem; minimal surfaces; the telegraphists’ equation and Thomson’s successful design of the trans-Atlantic cable; Riemann’s paper on shock waves; the geometrical interpretation of mechanics; and aspects of the study of the calculus of variations from the problems of the catenary and the brachistochrone to attempts at a rigorous theory by Weierstrass, Kneser, and Hilbert. Three final chapters look at how the theory of partial differential equations stood around 1900, as they were treated by Picard and Hadamard. There are also extensive, new translations of original papers by Cauchy, Riemann, Schwarz, Darboux, and Picard. The first book to cover the history of differential equations and the calculus of variations in such breadth and detail, it will appeal to anyone with an interest in the field. Beyond secondary school mathematics and physics, a course in mathematical analysis is the only prerequisite to fully appreciate its contents. Based on a course for third-year university students, the book contains numerous historical and mathematical exercises, offers extensive advice to the student on how to write essays, and can easily be used in whole or in part as a course in the history of mathematics. Several appendices help make the book self-contained and suitable for self-study.
A History Of The Calculus Of Variations In The Eighteenth Century
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Author : Robert Whoodhouse
language : en
Publisher:
Release Date : 1900
A History Of The Calculus Of Variations In The Eighteenth Century written by Robert Whoodhouse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1900 with categories.
A History Of The Calculus Of Variations During The Nineteenth Century
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Author : I. Todhunter
language : en
Publisher:
Release Date : 1964
A History Of The Calculus Of Variations During The Nineteenth Century written by I. Todhunter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with categories.
A History Of The Progress Of The Calculus Of Variations During The Nineteenth Century Classic Reprint
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Author : Isaac Todhunter
language : en
Publisher: Forgotten Books
Release Date : 2018-01-06
A History Of The Progress Of The Calculus Of Variations During The Nineteenth Century Classic Reprint written by Isaac Todhunter and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-06 with Mathematics categories.
Excerpt from A History of the Progress of the Calculus of Variations During the Nineteenth Century Caias College, Cambridge. This work details the history of the Calculus of Variations from its origin until the close of the eighteenth century, and has obtained a high reputation for accuracy and clearness. During the present century some of the most eminent mathematicians have endeavoured to enlarge the boundaries of the subject, and it seemed probable that a survey of What had been accomplished would not be destitute of interest and value. Accord ingly the present work has been undertaken, and a short account will now be given of its plan. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.