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Author : Isaac Todhunter
Publisher :
ISBN 13 :
Total Pages : 572 pages
Book Rating : 4.A/5 ( download)
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:
Author : H. H. Goldstine
Publisher : Springer Science & Business Media
ISBN 13 : 1461381061
Total Pages : 427 pages
Book Rating : 4.4/5 (613 download)
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.
Author : Charles R. MacCluer
Publisher : Courier Corporation
ISBN 13 : 0486278301
Total Pages : 274 pages
Book Rating : 4.4/5 (862 download)
Download or read book Calculus of Variations written by Charles R. MacCluer and published by Courier Corporation. This book was released on 2013-05-20 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.
Author : Mark Kot
Publisher : American Mathematical Society
ISBN 13 : 1470414953
Total Pages : 311 pages
Book Rating : 4.4/5 (74 download)
Download or read book A First Course in the Calculus of Variations written by Mark Kot and published by American Mathematical Society. This book was released on 2014-10-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields. The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics. Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.
Author : Hans Sagan
Publisher : Courier Corporation
ISBN 13 : 048613802X
Total Pages : 484 pages
Book Rating : 4.4/5 (861 download)
Download or read book Introduction to the Calculus of Variations written by Hans Sagan and published by Courier Corporation. This book was released on 2012-04-26 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.
Author : Bruce van Brunt
Publisher : Springer Science & Business Media
ISBN 13 : 0387216979
Total Pages : 295 pages
Book Rating : 4.3/5 (872 download)
Download or read book The Calculus of Variations written by Bruce van Brunt and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.
Author :
Publisher :
ISBN 13 :
Total Pages : 610 pages
Book Rating : 4.A/5 ( download)
Download or read book The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science written by and published by . This book was released on 1861 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hans Niels Jahnke
Publisher : American Mathematical Soc.
ISBN 13 : 9780821890509
Total Pages : 436 pages
Book Rating : 4.8/5 (95 download)
Download or read book A History of Analysis written by Hans Niels Jahnke and published by American Mathematical Soc.. This book was released on with total page 436 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.
Author : I. M. Gelfand
Publisher : Courier Corporation
ISBN 13 : 0486135012
Total Pages : 260 pages
Book Rating : 4.4/5 (861 download)
Download or read book Calculus of Variations written by I. M. Gelfand and published by Courier Corporation. This book was released on 2012-04-26 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.
Author :
Publisher :
ISBN 13 :
Total Pages : 586 pages
Book Rating : 4.:/5 (319 download)
Download or read book Philosophical Magazine written by and published by . This book was released on 1861 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 271 pages
Book Rating : 4.:/5 (51 download)
Download or read book An Introduction to the Calculus of Variations written by and published by . This book was released on 1950 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Royal Society (Great Britain)
Publisher :
ISBN 13 :
Total Pages : 566 pages
Book Rating : 4.3/5 (21 download)
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:
Author : Daniel Liberzon
Publisher : Princeton University Press
ISBN 13 : 0691151873
Total Pages : 255 pages
Book Rating : 4.6/5 (911 download)
Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
Author : George McNaught Ewing
Publisher : Courier Corporation
ISBN 13 : 0486648567
Total Pages : 355 pages
Book Rating : 4.4/5 (866 download)
Download or read book Calculus of Variations with Applications written by George McNaught Ewing and published by Courier Corporation. This book was released on 1985-01-01 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications-oriented introduction to variational theory develops insight and promotes understanding of specialized books and research papers. Suitable for advanced undergraduate and graduate students as a primary or supplementary text. 1969 edition.
Author : Hans Niels Jahnke
Publisher : American Mathematical Soc.
ISBN 13 : 0821826239
Total Pages : 434 pages
Book Rating : 4.8/5 (218 download)
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.
Author :
Publisher :
ISBN 13 :
Total Pages : 420 pages
Book Rating : 4.B/5 (1 download)
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:
Author : Stefan Hildebrandt
Publisher : Springer Science & Business Media
ISBN 13 : 9780387979915
Total Pages : 370 pages
Book Rating : 4.9/5 (799 download)
Download or read book The Parsimonious Universe written by Stefan Hildebrandt and published by Springer Science & Business Media. This book was released on 1996-07-18 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why does nature prefer some shapes and not others? The variety of sizes, shapes, and irregularities in nature is endless. Skillfully integrating striking full-color illustrations, the authors describe the efforts by scientists and mathematicians since the Renaissance to identify and describe the principles underlying the shape of natural forms. But can one set of laws account for both the symmetry and irregularity as well as the infinite variety of nature's designs? A complete answer to this question is likely never to be discovered. Yet, it is fascinating to see how the search for some simple universal laws down through the ages has increased our understanding of nature. The Parsimonious Universe looks at examples from the world around us at a non-mathematical, non-technical level to show that nature achieves efficiency by being stingy with the energy it expends.
