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Lectures On The Calculus Of Variations Illustrated
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Book Synopsis Lectures on the Calculus of Variations - Illustrated by : Oskar Bolza
Download or read book Lectures on the Calculus of Variations - Illustrated written by Oskar Bolza and published by Merchant Books. This book was released on 2007-01-01 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrated To Include 48 Figures - Chapters Include: Agreements Concerning Notation And Terminology - Vanishing Of The First Variation - The Fundamental Lemma And Euler's Differential Equation - Weirstrass's Lemma And The E-Function - Discontinuous Solutions - Boundary Conditions - Legendre's Condition - Jacobi's Theorem - Jacobi's Criterion - Geometrical Interpretation Of The Conjugate Points - Necessity Of Jacobi's Condition - Sufficient Conditions For An Extremum Of The Integral - Weirstrass's Theory Of The Problem In Parameter Representation - Formulation Of The Problem - Kneser's Theory: Gauss's Theorems On Geodesics - Construction Of A Field - Kneser's Curvilinear Coordinates -Sufficient Conditions For A Minimum In The Case Of One Moveable Endpoint - The Focal Point - Weierstrass's Theory Of The Isoperimetric Problems - Euler's Rule - The Second Necessary Condition - The Third Necessary Condition And The Conjugate Point - Hilbert's Existence Theorem - Hilbert's Construction - Properties Of Hilbert's Curve, Etc., Etc. - Addenda - Index
Book Synopsis Lectures on the Calculus of Variations by : Oskar Bolza
Download or read book Lectures on the Calculus of Variations written by Oskar Bolza and published by University of Michigan Library. This book was released on 1904 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Calculus of Variations by : Filip Rindler
Download or read book Calculus of Variations written by Filip Rindler and published by Springer. This book was released on 2018-06-20 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.
Book Synopsis Calculus of Variations and Optimal Control Theory by : Daniel Liberzon
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
Book Synopsis Lectures on the Calculus of Variations by : G.A. Bliss
Download or read book Lectures on the Calculus of Variations written by G.A. Bliss and published by . This book was released on 1951 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topics in the Calculus of Variations by : Martin Fuchs
Download or read book Topics in the Calculus of Variations written by Martin Fuchs and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates two basic principles in the calculus of variations which are the question of existence of solutions and closely related the problem of regularity of minimizers. Chapter one studies variational problems for nonquadratic energy functionals defined on suitable classes of vectorvalued functions where also nonlinear constraints are incorporated. Problems of this type arise for mappings between Riemannian manifolds or in nonlinear elasticity. Using direct methods the existence of generalized minimizers is rather easy to establish and it is then shown that regularity holds up to a set of small measure. Chapter two contains a short introduction into Geometric Measure Theory which serves as a basis for developing an existence theory for (generalized) manifolds with prescribed mean curvature form and boundary in arbitrary dimensions and codimensions. One major aspect of the book is to concentrate on techniques and to present methods which turn out to be useful for applications in regularity theorems as well as for existence problems.
Book Synopsis Calculus of Variations by : I. M. Gelfand
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.
Book Synopsis A Primer on the Calculus of Variations and Optimal Control Theory by : Mike Mesterton-Gibbons
Download or read book A Primer on the Calculus of Variations and Optimal Control Theory written by Mike Mesterton-Gibbons and published by American Mathematical Soc.. This book was released on 2009 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical software. It is suitable for an undergraduate or beginning graduate course, or for self study. It provides excellent preparation for more advanced books and courses on the calculus of variations and optimal control theory.
Book Synopsis Lectures on the Calculus of Variations by : Oskar Bolza
Download or read book Lectures on the Calculus of Variations written by Oskar Bolza and published by Courier Dover Publications. This book was released on 2018-02-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on the Calculus of Variations and Optimal Control Theory by : Laurence Chisholm Young
Download or read book Lectures on the Calculus of Variations and Optimal Control Theory written by Laurence Chisholm Young and published by American Mathematical Soc.. This book was released on 2000 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on the Calculus of Variations by : Gilbert Ames Bliss
Download or read book Lectures on the Calculus of Variations written by Gilbert Ames Bliss and published by . This book was released on 1961 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on the Calculus of Variations by : Oskar Bolza
Download or read book Lectures on the Calculus of Variations written by Oskar Bolza and published by . This book was released on 1904 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on the Calculus of Variations (the Weierstrassian Theory) (Classic Reprint) by : Harris Hancock
Download or read book Lectures on the Calculus of Variations (the Weierstrassian Theory) (Classic Reprint) written by Harris Hancock and published by Forgotten Books. This book was released on 2016-10-08 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topics in Calculus of Variations by : Mariano Giaquinta
Download or read book Topics in Calculus of Variations written by Mariano Giaquinta and published by Springer. This book was released on 2006-11-14 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lecture Notes On Calculus Of Variations by : Kung-ching Chang
Download or read book Lecture Notes On Calculus Of Variations written by Kung-ching Chang and published by World Scientific. This book was released on 2016-09-16 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on the Calculus of Variations by : Bliss
Download or read book Lectures on the Calculus of Variations written by Bliss and published by . This book was released on 1986-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on the Calculus of Variations by : Harris Hancock
Download or read book Lectures on the Calculus of Variations written by Harris Hancock and published by . This book was released on 1904 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
