A History Of The Calculus Of Variations From The Seventeenth Through The Nineteenth Century

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A History of the Calculus of Variations from the 17th through the 19th Century

Author : H. H. Goldstine
Publisher : Springer Science & Business Media
ISBN 13 : 1461381061
Total Pages : 427 pages
Book Rating : 4.4/5 (613 download)

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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.

Mathematics of the 19th Century

Author : A.N. Kolmogorov
Publisher : Springer Science & Business Media
ISBN 13 : 9783764358457
Total Pages : 376 pages
Book Rating : 4.3/5 (584 download)

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Book Synopsis Mathematics of the 19th Century by : A.N. Kolmogorov

Download or read book Mathematics of the 19th Century written by A.N. Kolmogorov and published by Springer Science & Business Media. This book was released on 1998-03-24 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The editors of the present series had originally intended to publish an integrated work on the history of mathematics in the nineteenth century, passing systemati cally from one discipline to another in some natural order. Circumstances beyond their control, mainly difficulties in choosing authors, led to the abandonment of this plan by the time the second volume appeared. Instead of a unified mono graph we now present to the reader a series of books intended to encompass all the mathematics of the nineteenth century, but not in the order of the accepted classification of the component disciplines. In contrast to the first two books of The Mathematics of the Nineteenth Century, which were divided into chapters, this third volume consists of four parts, more in keeping with the nature of the publication. 1 We recall that the first book contained essays on the history of mathemati 2 cal logic, algebra, number theory, and probability, while the second covered the history of geometry and analytic function theory. In the present third volume the reader will find: 1. An essay on the development of Chebyshev's theory of approximation of functions, later called "constructive function theory" by S. N. Bernshtein. This highly original essay is due to the late N. I. Akhiezer (1901-1980), the author of fundamental discoveries in this area. Akhiezer's text will no doubt attract attention not only from historians of mathematics, but also from many specialists in constructive function theory.

A Historian Looks Back

Author : Judith V. Grabiner
Publisher : MAA
ISBN 13 : 0883855720
Total Pages : 307 pages
Book Rating : 4.8/5 (838 download)

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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.

The Lazy Universe

Author : Jennifer Coopersmith
Publisher : Oxford University Press
ISBN 13 : 0198743041
Total Pages : 280 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis The Lazy Universe by : Jennifer Coopersmith

Download or read book The Lazy Universe written by Jennifer Coopersmith and published by Oxford University Press. This book was released on 2017 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Principle of Least Action underlies all physics and leads into quantum mechanics and Einstein's Relativity. There are some textbooks that do the calculations, and one book with nice pictures, but no book (before this one) that explains what 'action' is, and why nature follows this principle.

A History of Analysis

Author : Hans Niels Jahnke
Publisher : American Mathematical Soc.
ISBN 13 : 0821826239
Total Pages : 434 pages
Book Rating : 4.8/5 (218 download)

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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.

A History of the Progress of the Calculus of Variations During the Nineteenth Century

Author : Isaac Todhunter
Publisher :
ISBN 13 :
Total Pages : 572 pages
Book Rating : 4.A/5 ( download)

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Book Synopsis A History of the Progress of the Calculus of Variations During the Nineteenth Century by : Isaac Todhunter

Download or read book A History of the Progress of the Calculus of Variations During the Nineteenth Century written by Isaac Todhunter and published by . This book was released on 1861 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Science and the Enlightenment

Author : Thomas L. Hankins
Publisher : Cambridge University Press
ISBN 13 : 1316284034
Total Pages : 261 pages
Book Rating : 4.3/5 (162 download)

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Book Synopsis Science and the Enlightenment by : Thomas L. Hankins

Download or read book Science and the Enlightenment written by Thomas L. Hankins and published by Cambridge University Press. This book was released on 1985-04-26 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mechanics Day

Author : W. F. Shadwick
Publisher : American Mathematical Soc.
ISBN 13 : 0821802615
Total Pages : 271 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mechanics Day by : W. F. Shadwick

Download or read book Mechanics Day written by W. F. Shadwick and published by American Mathematical Soc.. This book was released on 1996 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of a workshop held at The Fields Institute in June 1992 both as a commemoration of the 25th anniversary of the publication of "Foundations of Mechanics" by Ralph Abraham and Jerrold Marsden and as a celebration of Marsden's 50th birthday. The publication of that first edition marked a period of remarkable resurgence in all aspects of mechanics, which has continued through the publication of the second edition in 1978, deeply nourished by contacts with a variety of areas of mathematics, including topology, differential geometry, Lie theory, and partial diffe.

Variational Calculus with Engineering Applications

Author : Constantin Udriste
Publisher : John Wiley & Sons
ISBN 13 : 1119944368
Total Pages : 228 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis Variational Calculus with Engineering Applications by : Constantin Udriste

Download or read book Variational Calculus with Engineering Applications written by Constantin Udriste and published by John Wiley & Sons. This book was released on 2023-02-13 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of foundational variational methods for problems in engineering Variational calculus is a field in which small alterations in functions and functionals are used to find their relevant maxima and minima. It is a potent tool for addressing a range of dynamic problems with otherwise counter-intuitive solutions, particularly ones incorporating multiple confounding variables. Its value in engineering fields, where materials and geometric configurations can produce highly specific problems with unconventional or unintuitive solutions, is considerable. Variational Calculus with Engineering Applications provides a comprehensive survey of this toolkit and its engineering applications. Balancing theory and practice, it offers a thorough and accessible introduction to the field pioneered by Euler, Lagrange and Hamilton, offering tools that can be every bit as powerful as the better-known Newtonian mechanics. It is an indispensable resource for those looking for engineering-oriented overview of a subject whose capacity to provide engineering solutions is only increasing. Variational Calculus with Engineering Applications readers will also find: Discussion of subjects including variational principles, levitation, geometric dynamics, and more Examples and instructional problems in every Chapter, along with MAPLE codes for performing the simulations described in each Engineering applications based on simple, curvilinear, and multiple integral functionals Variational Calculus with Engineering Applications is ideal for advanced students, researchers, and instructors in engineering and materials science.

Variational Methods in Shape Optimization Problems

Author : Dorin Bucur
Publisher : Springer Science & Business Media
ISBN 13 : 9780817643591
Total Pages : 232 pages
Book Rating : 4.6/5 (435 download)

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Book Synopsis Variational Methods in Shape Optimization Problems by : Dorin Bucur

Download or read book Variational Methods in Shape Optimization Problems written by Dorin Bucur and published by Springer Science & Business Media. This book was released on 2005-07-01 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.

Variational Calculus and Optimal Control

Author : John L. Troutman
Publisher : Springer Science & Business Media
ISBN 13 : 1461207371
Total Pages : 471 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Variational Calculus and Optimal Control by : John L. Troutman

Download or read book Variational Calculus and Optimal Control written by John L. Troutman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the variational methods used to formulate and solve mathematical and physical problems, allowing the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency, laying as it does the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, as well as computer science.

Duality Principles in Nonconvex Systems

Author : David Yang Gao
Publisher : Springer Science & Business Media
ISBN 13 : 1475731760
Total Pages : 463 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Duality Principles in Nonconvex Systems by : David Yang Gao

Download or read book Duality Principles in Nonconvex Systems written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Jacques Hadamard

Author : Vladimir Gilelevič Mazʹâ
Publisher : American Mathematical Soc.
ISBN 13 : 9780821819234
Total Pages : 604 pages
Book Rating : 4.8/5 (192 download)

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Book Synopsis Jacques Hadamard by : Vladimir Gilelevič Mazʹâ

Download or read book Jacques Hadamard written by Vladimir Gilelevič Mazʹâ and published by American Mathematical Soc.. This book was released on 1999 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a fascinating story of the long life and great accomplishments of Jacques Hadamard (1865-1963), who was once called 'the living legend of mathematics'. As one of the last universal mathematicians, Hadamard's contributions to mathematics are landmarks in various fields. His life is linked with world history of the 20th century in a dramatic way. This work provides an inspiring view of the development of various branches of mathematics during the 19th and 20th centuries.Part I of the book portrays Hadamard's family, childhood and student years, scientific triumphs, and his personal life and trials during the first two world wars. The story is told of his involvement in the Dreyfus affair and his subsequent fight for justice and human rights. Also recounted are Hadamard's worldwide travels, his famous seminar, his passion for botany, his home orchestra, where he played the violin with Einstein, and his interest in the psychology of mathematical creativity. Hadamard's life is described in a readable and inviting way.The authors humorously weave throughout the text his jokes and the myths about him. They also movingly recount the tragic side of his life. Stories about his relatives and friends, and old letters and documents create an authentic and colorful picture. The book contains over 300 photographs and illustrations. Part II of the book includes a lucid overview of Hadamard's enormous work, spanning over six decades. The authors do an excellent job of connecting his results to current concerns.While the book is accessible to beginners, it also provides rich information of interest to experts. Vladimir Mazya and Tatyana Shaposhnikova were the 2003 laureates of the Insitut de France's Prix Alfred Verdaguer. One or more prizes are awarded each year, based on suggestions from the Academie francaise, the Academie de sciences, and the Academie de beaux-arts, for the most remarkable work in the arts, literature, and the sciences. In 2003, the award for excellence was granted in recognition of Mazya and Shaposhnikova's book, ""Jacques Hadamard, A Universal Mathematician"", which is both an historical book about a great citizen and a scientific book about a great mathematician.

Variational Principles and Methods in Theoretical Physics and Chemistry

Author : Robert K. Nesbet
Publisher : Cambridge University Press
ISBN 13 : 1139435698
Total Pages : 245 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Variational Principles and Methods in Theoretical Physics and Chemistry by : Robert K. Nesbet

Download or read book Variational Principles and Methods in Theoretical Physics and Chemistry written by Robert K. Nesbet and published by Cambridge University Press. This book was released on 2002-11-14 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the essential ideas and methods behind applications of variational theory in theoretical physics and chemistry. The emphasis is on understanding physical and computational applications of variational methodology rather than on rigorous mathematical formalism. The text begins with an historical survey of familiar variational principles in classical mechanics and optimization theory, then proceeds to develop the variational principles and formalism behind current computational methodology for bound and continuum quantum states of interacting electrons in atoms, molecules, and condensed matter. It covers multiple-scattering theory, including a detailed presentation of contemporary methodology for electron-impact rotational and vibrational excitation of molecules. The book ends with an introduction to the variational theory of relativistic fields. Ideal for graduate students and researchers in any field that uses variational methodology, this book is particularly suitable as a backup reference for lecture courses in mathematical methods in physics and theoretical chemistry.

A History of the Calculus of Variations from the Seventeenth Through the Nineteenth Century

Author : Herman Heine Goldstine
Publisher :
ISBN 13 :
Total Pages : 410 pages
Book Rating : 4.:/5 (8 download)

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Book Synopsis A History of the Calculus of Variations from the Seventeenth Through the Nineteenth Century by : Herman Heine Goldstine

Download or read book A History of the Calculus of Variations from the Seventeenth Through the Nineteenth Century written by Herman Heine Goldstine and published by . This book was released on 1980 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lagrangian and Hamiltonian Dynamics

Author : Peter Mann
Publisher : Oxford University Press
ISBN 13 : 0198822375
Total Pages : 553 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis Lagrangian and Hamiltonian Dynamics by : Peter Mann

Download or read book Lagrangian and Hamiltonian Dynamics written by Peter Mann and published by Oxford University Press. This book was released on 2018 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.

Encyclopedia of Operations Research and Management Science

Author : Saul I. Gass
Publisher : Springer Science & Business Media
ISBN 13 : 1461304598
Total Pages : 774 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Encyclopedia of Operations Research and Management Science by : Saul I. Gass

Download or read book Encyclopedia of Operations Research and Management Science written by Saul I. Gass and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operations Research: 1934-1941," 35, 1, 143-152; "British The goal of the Encyclopedia of Operations Research and Operational Research in World War II," 35, 3, 453-470; Management Science is to provide to decision makers and "U. S. Operations Research in World War II," 35, 6, 910-925; problem solvers in business, industry, government and and the 1984 article by Harold Lardner that appeared in academia a comprehensive overview of the wide range of Operations Research: "The Origin of Operational Research," ideas, methodologies, and synergistic forces that combine to 32, 2, 465-475. form the preeminent decision-aiding fields of operations re search and management science (OR/MS). To this end, we The Encyclopedia contains no entries that define the fields enlisted a distinguished international group of academics of operations research and management science. OR and MS and practitioners to contribute articles on subjects for are often equated to one another. If one defines them by the which they are renowned. methodologies they employ, the equation would probably The editors, working with the Encyclopedia's Editorial stand inspection. If one defines them by their historical Advisory Board, surveyed and divided OR/MS into specific developments and the classes of problems they encompass, topics that collectively encompass the foundations, applica the equation becomes fuzzy. The formalism OR grew out of tions, and emerging elements of this ever-changing field. We the operational problems of the British and U. s. military also wanted to establish the close associations that OR/MS efforts in World War II.