Lectures On The Calculus Of Variations
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Lecture Notes On Calculus Of Variations
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Author : Kung-ching Chang
language : en
Publisher: World Scientific
Release Date : 2016-09-16
Lecture Notes On Calculus Of Variations written by Kung-ching Chang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-16 with Mathematics categories.
This is based on the course 'Calculus of Variations' taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics. The book contains 20 lectures covering both the theoretical background material as well as an abundant collection of applications. Lectures 1-8 focus on the classical theory of calculus of variations. Lectures 9-14 introduce direct methods along with their theoretical foundations. Lectures 15-20 showcase a broad collection of applications. The book offers a panoramic view of the very important topic on calculus of variations. This is a valuable resource not only to mathematicians, but also to those students in engineering, economics, and management, etc.
Lectures On The Calculus Of Variations And Optimal Control Theory
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Author : Laurence Chisholm Young
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Lectures On The Calculus Of Variations And Optimal Control Theory written by Laurence Chisholm Young and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is divided into two parts. The first addresses the simpler variational problems in parametric and nonparametric form. The second covers extensions to optimal control theory. The author opens with the study of three classical problems whose solutions led to the theory of calculus of variations. They are the problem of geodesics, the brachistochrone, and the minimal surface of revolution. He gives a detailed discussion of the Hamilton-Jacobi theory, both in the parametric and nonparametric forms. This leads to the development of sufficiency theories describing properties of minimizing extremal arcs. Next, the author addresses existence theorems. He first develops Hilbert's basic existence theorem for parametric problems and studies some of its consequences. Finally, he develops the theory of generalized curves and "automatic" existence theorems. In the second part of the book, the author discusses optimal control problems. He notes that originally these problems were formulated as problems of Lagrange and Mayer in terms of differential constraints. In the control formulation, these constraints are expressed in a more convenient form in terms of control functions. After pointing out the new phenomenon that may arise, namely, the lack of controllability, the author develops the maximum principle and illustrates this principle by standard examples that show the switching phenomena that may occur. He extends the theory of geodesic coverings to optimal control problems. Finally, he extends the problem to generalized optimal control problems and obtains the corresponding existence theorems.
Lectures On The Calculus Of Variations
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Author : Oskar Bolza
language : en
Publisher: Courier Dover Publications
Release Date : 2018-02-01
Lectures On The Calculus Of Variations written by Oskar Bolza and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-01 with Mathematics categories.
Pioneering modern treatise studies the development of the subject from Euler to Hilbert, addressing basic problems with sufficient generality and rigor to provide a sound introduction for serious study. 1904 edition.
Lectures On The Calculus Of Variations
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Author : O. (Oskar) Bolza
language : en
Publisher: Hardpress Publishing
Release Date : 2012-08
Lectures On The Calculus Of Variations written by O. (Oskar) Bolza and has been published by Hardpress Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08 with categories.
Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.
Lectures On The Calculus Of Variations
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Author : Harris Hancock
language : en
Publisher:
Release Date : 1904
Lectures On The Calculus Of Variations written by Harris Hancock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1904 with Calculus of variations categories.
Lectures On The Calculus Of Variations The Weierstrassian Theory Classic Reprint
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Author : Harris Hancock
language : en
Publisher: Forgotten Books
Release Date : 2016-10-08
Lectures On The Calculus Of Variations The Weierstrassian Theory Classic Reprint written by Harris Hancock and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-08 with Mathematics categories.
Excerpt from Lectures on the Calculus of Variations (the Weierstrassian Theory) Through the courtesy of Professor Ormond Stone abstracts of this theory were published in Volumes IX, X, XI and XII of the Annals of Mathematics, and from time to time the Calculus of Variations has been included in my University lecture courses. 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.
Lectures On The Calculus Of Variations
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Author : Gilbert Ames Bliss
language : en
Publisher:
Release Date : 1916
Lectures On The Calculus Of Variations written by Gilbert Ames Bliss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1916 with Calculus of variations categories.
Lectures Of The Calculus Of Variations
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Author : Oskar Bolza
language : en
Publisher: Franklin Classics Trade Press
Release Date : 2018-10-29
Lectures Of The Calculus Of Variations written by Oskar Bolza and has been published by Franklin Classics Trade Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-29 with categories.
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Lectures In Magnetohydrodynamics
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Author : Dalton D. Schnack
language : en
Publisher: Springer
Release Date : 2009-08-11
Lectures In Magnetohydrodynamics written by Dalton D. Schnack and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-11 with Science categories.
Magnetohydrodynamics, or MHD, is a theoretical way of describing the statics and dynamics of electrically conducting uids. The most important of these uids occurring in both nature and the laboratory are ionized gases, called plasmas. These have the simultaneous properties of conducting electricity and being electrically charge neutral on almost all length scales. The study of these gases is called plasma physics. MHD is the poor cousin of plasma physics. It is the simplest theory of plasma dynamics. In most introductory courses, it is usually afforded a short chapter or lecture at most: Alfven ́ waves, the kink mode, and that is it. (Now, on to Landau damping!) In advanced plasma courses, such as those dealing with waves or kinetic theory, it is given an even more cursory treatment, a brief mention on the way to things more profound and interesting. (It is just MHD! Besides, real plasma phy- cists do kinetic theory!) Nonetheless, MHD is an indispensable tool in all applications of plasma physics.
Lectures On The Calculus Of Variations And Optimal Control Theory
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Author : L. C. Young
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-30
Lectures On The Calculus Of Variations And Optimal Control Theory written by L. C. Young 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 2024-10-30 with Mathematics categories.
This book is divided into two parts. The first addresses the simpler variational problems in parametric and nonparametric form. The second covers extensions to optimal control theory. The author opens with the study of three classical problems whose solutions led to the theory of calculus of variations. They are the problem of geodesics, the brachistochrone, and the minimal surface of revolution. He gives a detailed discussion of the Hamilton-Jacobi theory, both in the parametric and nonparametric forms. This leads to the development of sufficiency theories describing properties of minimizing extremal arcs. Next, the author addresses existence theorems. He first develops Hilbert's basic existence theorem for parametric problems and studies some of its consequences. Finally, he develops the theory of generalized curves and ?automatic? existence theorems. In the second part of the book, the author discusses optimal control problems. He notes that originally these problems were formulated as problems of Lagrange and Mayer in terms of differential constraints. In the control formulation, these constraints are expressed in a more convenient form in terms of control functions. After pointing out the new phenomenon that may arise, namely, the lack of controllability, the author develops the maximum principle and illustrates this principle by standard examples that show the switching phenomena that may occur. He extends the theory of geodesic coverings to optimal control problems. Finally, he extends the problem to generalized optimal control problems and obtains the corresponding existence theorems.