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A History Of The Calculus Of Variations In The Eighteenth Century
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Book Synopsis A History of the Calculus of Variations in the Eighteenth Century by : Robert Woodhouse
Download or read book A History of the Calculus of Variations in the Eighteenth Century written by Robert Woodhouse and published by American Mathematical Society. This book was released on 2004-04-13 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A History of the Calculus of Variations from the 17th through the 19th Century by : H. H. Goldstine
Download or read book A History of the Calculus of Variations from the 17th through the 19th Century written by H. H. Goldstine and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A History of the Calculus of Variations in the Eighteenth Century by : Robert Whoodhouse
Download or read book A History of the Calculus of Variations in the Eighteenth Century written by Robert Whoodhouse and published by . This book was released on 1900 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences by : Ivor Grattan-Guiness
Download or read book Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences written by Ivor Grattan-Guiness and published by Routledge. This book was released on 2004-11-11 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.
Book Synopsis Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences by : I. Grattan-Guinness
Download or read book Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences written by I. Grattan-Guinness and published by JHU Press. This book was released on 2003 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second book of a two-volume encyclopaedia which makes the vast and varied history of mathematics available in a reasonably compact format. The book offers in-depth accounts of the principal areas of activity up to the 1930s and touches on related topics, including ethnomathematics.
Download or read book Mathematical monthly written by and published by . This book was released on 1861 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematical Monthly written by and published by . This book was released on 1859 with total page 1266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Mathematical Monthly by : John Daniel Runkle
Download or read book The Mathematical Monthly written by John Daniel Runkle and published by . This book was released on 1861 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A complete catalogue of the writings of Sir John Herschel": v. 3, p. 220-227.
Book Synopsis Proceedings of the Royal Society of London by : Royal Society (Great Britain)
Download or read book Proceedings of the Royal Society of London written by Royal Society (Great Britain) and published by . This book was released on 1884 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Early Period of the Calculus of Variations by : Paolo Freguglia
Download or read book The Early Period of the Calculus of Variations written by Paolo Freguglia and published by Birkhäuser. This book was released on 2016-06-27 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores the early development of the calculus of variations in continental Europe during the Eighteenth Century by illustrating the mathematics of its founders. Closely following the original papers and correspondences of Euler, Lagrange, the Bernoullis, and others, the reader is immersed in the challenge of theory building. We see what the founders were doing, the difficulties they faced, the mistakes they made, and their triumphs. The authors guide the reader through these works with instructive commentaries and complements to the original proofs, as well as offering a modern perspective where useful. The authors begin in 1697 with Johann Bernoulli’s work on the brachystochrone problem and the events leading up to it, marking the dawn of the calculus of variations. From there, they cover key advances in the theory up to the development of Lagrange’s δ-calculus, including: • The isoperimetrical problems • Shortest lines and geodesics • Euler’s Methodus Inveniendi and the two Additamenta Finally, the authors give the readers a sense of how vast the calculus of variations has become in centuries hence, providing some idea of what lies outside the scope of the book as well as the current state of affairs in the field. This book will be of interest to anyone studying the calculus of variations who wants a deeper intuition for the techniques and ideas that are used, as well as historians of science and mathematics interested in the development and evolution of modern calculus and analysis.
Book Synopsis A Historian Looks Back by : Judith V. Grabiner
Download or read book A Historian Looks Back written by Judith V. Grabiner and published by MAA. This book was released on 2010-10-14 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: An inspiring collection of a historian's work on the history of mathematics.
Book Synopsis A History of Analysis by : Hans Niels Jahnke
Download or read book A History of Analysis written by Hans Niels Jahnke and published by American Mathematical Soc.. This book was released on 2003 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Anachronisms in the History of Mathematics by : Niccol- Guicciardini
Download or read book Anachronisms in the History of Mathematics written by Niccol- Guicciardini and published by Cambridge University Press. This book was released on 2021-07-22 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.
Book Synopsis The Optics of Rays, Wavefronts, and Caustics by : O Stavroudis
Download or read book The Optics of Rays, Wavefronts, and Caustics written by O Stavroudis and published by Elsevier. This book was released on 2012-12-02 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Optics of Rays, Wavefronts, and Caustics presents the fundamental principles of geometrical optics and its unique role in modern technology. It also discusses the procedures used in optical design, which are based on geometrical optics. Organized into 16 chapters, this volume begins with an overview of the underlying general mathematical facts, which constitute the substance of geometrical optics. It then presents the various techniques used to solve the ray and wavefront problems in general inhomogeneous medium. Other chapters consider the concept of ray tracing as a tool for calculating the principal curvatures of a wavefront as it propagates through a lens. In addition, the book tackles several topics, including the aspects of lens design, as well as a system of equations that are similar to the Maxwell equations. The last chapter deals with orthotomic systems of rays. Optical designers, optical physicists, theoretical physicists, and mathematicians will find the information and methods in this book extremely useful.
Book Synopsis A History of Science Technology and Philosophy in the 18th Century by : Abraham Wolf
Download or read book A History of Science Technology and Philosophy in the 18th Century written by Abraham Wolf and published by Routledge. This book was released on 2019-04-23 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published in 1938: The new volume presents a full and profusely illustrated account of progress made during the eighteenth century in Mathematics, Mechanics, Astronomy, Physics, Meteorology, Geography, Chemistry, Biology, Medicine, Psychology, Demography, Economics, Philosophy, and Technology.
Book Synopsis Variational Methods in Mathematical Physics by : Philippe Blanchard
Download or read book Variational Methods in Mathematical Physics written by Philippe Blanchard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition (in German) had the prevailing character of a textbook owing to the choice of material and the manner of its presentation. This second (translated, revised, and extended) edition, however, includes in its new parts considerably more recent and advanced results and thus goes partially beyond the textbook level. We should emphasize here that the primary intentions of this book are to provide (so far as possible given the restrictions of space) a selfcontained presentation of some modern developments in the direct methods of the cal culus of variations in applied mathematics and mathematical physics from a unified point of view and to link it to the traditional approach. These modern developments are, according to our background and interests: (i) Thomas-Fermi theory and related theories, and (ii) global systems of semilinear elliptic partial-differential equations and the existence of weak solutions and their regularity. Although the direct method in the calculus of variations can naturally be considered part of nonlinear functional analysis, we have not tried to present our material in this way. Some recent books on nonlinear functional analysis in this spirit are those by K. Deimling (Nonlinear Functional Analysis, Springer, Berlin Heidelberg 1985) and E. Zeidler (Nonlinear Functional Analysis and Its Applications, Vols. 1-4; Springer, New York 1986-1990).
Book Synopsis Mathematics Applied to Continuum Mechanics by : Lee A. Segel
Download or read book Mathematics Applied to Continuum Mechanics written by Lee A. Segel and published by SIAM. This book was released on 1977-01-01 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the fundamental ideas of continuum mechanics by analyzing models of fluid flow and solid deformation and examining problems in elasticity, water waves, and extremum principles. Mathematics Applied to Continuum Mechanics gives an excellent overview of the subject, with an emphasis on clarity, explanation, and motivation. Audience: upper-level undergraduate and graduate students in the fields of applied mathematics, science, and engineering.
