A History of the Calculus of Variations in the Eighteenth Century PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download A History of the Calculus of Variations in the Eighteenth Century PDF full book. Access full book title A History of the Calculus of Variations in the Eighteenth Century by Robert Woodhouse. Download full books in PDF and EPUB format.
Author: Robert Woodhouse
Publisher: American Mathematical Society
ISBN: 0821836471
Category : Mathematics
Languages : en
Pages : 170
Get Book Here
Book Description
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.
Author: Robert Woodhouse
Publisher: American Mathematical Society
ISBN: 0821836471
Category : Mathematics
Languages : en
Pages : 170
Get Book Here
Book Description
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.
Author: Robert Woodhouse
Publisher: American Mathematical Society
ISBN: 9780821836477
Category : Mathematics
Languages : en
Pages : 172
Get Book Here
Book Description
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.
Author: H. H. Goldstine
Publisher: Springer Science & Business Media
ISBN: 1461381061
Category : Mathematics
Languages : en
Pages : 427
Get Book Here
Book Description
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.
Author: Hans Niels Jahnke
Publisher: American Mathematical Soc.
ISBN: 0821826239
Category : Mathematics
Languages : en
Pages : 434
Get Book Here
Book Description
Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general trends and an examination of the specific problems. This volume is designed as a collective work of authors who are proven experts in the history of mathematics. It clarifies the conceptual change that analysis underwent during its development while elucidating the influence of specific applications and describing the relevance of biographical and philosophical backgrounds. The first ten chapters of the book outline chronological development and the last three chapters survey the history of differential equations, the calculus of variations, and functional analysis. Special features are a separate chapter on the development of the theory of complex functions in the nineteenth century and two chapters on the influence of physics on analysis. One is about the origins of analytical mechanics, and one treats the development of boundary-value problems of mathematical physics (especially potential theory) in the nineteenth century. The book presents an accurate and very readable account of the history of analysis. Each chapter provides a comprehensive bibliography. Mathematical examples have been carefully chosen so that readers with a modest background in mathematics can follow them. It is suitable for mathematical historians and a general mathematical audience.
Author: Robert Whoodhouse
Publisher:
ISBN:
Category :
Languages : en
Pages : 154
Get Book Here
Book Description
Author: Thomas L. Hankins
Publisher: Cambridge University Press
ISBN: 1316284034
Category : Technology & Engineering
Languages : en
Pages : 261
Get Book Here
Book Description
Science and the Enlightenment is a general history of eighteenth-century science covering both the physical and life sciences. It places the scientific developments of the century in the cultural context of the Enlightenment and reveals the extent to which scientific ideas permeated the thought of the age. The book takes advantage of topical scholarship, which is rapidly changing our understanding of science during the eighteenth century. In particular it describes how science was organized into fields that were quite different from those we know today. Professor Hankins's work is a much needed addition to the literature on eighteenth-century science. His study is not technical; it will be of interest to all students of the Enlightenment and the history of science, as well as to the general reader with some background in science.
Author: David C. Lindberg
Publisher: Cambridge University Press
ISBN: 9780521572439
Category : Science
Languages : en
Pages : 956
Get Book Here
Book Description
The fullest and most complete survey of the development of science in the eighteenth century.
Author: Ivor Grattan-Guiness
Publisher: Routledge
ISBN: 1134887558
Category : History
Languages : en
Pages : 578
Get Book Here
Book Description
First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.
Author: Judith V. Grabiner
Publisher: MAA
ISBN: 0883855720
Category : Mathematics
Languages : en
Pages : 307
Get Book Here
Book Description
An inspiring collection of a historian's work on the history of mathematics.
Author: photographer and broadcaster Foreword by Dr Adam Hart-Davis
Publisher: OUP Oxford
ISBN: 0191627941
Category : Mathematics
Languages : en
Pages : 738
Get Book Here
Book Description
During the Victorian era, industrial and economic growth led to a phenomenal rise in productivity and invention. That spirit of creativity and ingenuity was reflected in the massive expansion in scope and complexity of many scientific disciplines during this time, with subjects evolving rapidly and the creation of many new disciplines. The subject of mathematics was no exception and many of the advances made by mathematicians during the Victorian period are still familiar today; matrices, vectors, Boolean algebra, histograms, and standard deviation were just some of the innovations pioneered by these mathematicians. This book constitutes perhaps the first general survey of the mathematics of the Victorian period. It assembles in a single source research on the history of Victorian mathematics that would otherwise be out of the reach of the general reader. It charts the growth and institutional development of mathematics as a profession through the course of the 19th century in England, Scotland, Ireland, and across the British Empire. It then focuses on developments in specific mathematical areas, with chapters ranging from developments in pure mathematical topics (such as geometry, algebra, and logic) to Victorian work in the applied side of the subject (including statistics, calculating machines, and astronomy). Along the way, we encounter a host of mathematical scholars, some very well known (such as Charles Babbage, James Clerk Maxwell, Florence Nightingale, and Lewis Carroll), others largely forgotten, but who all contributed to the development of Victorian mathematics.
