Introduction To The Variational Calculus
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Introduction To The Variational Calculus
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Author : J. H. Heinbockel
language : en
Publisher: Trafford Publishing
Release Date : 2007-01-04
Introduction To The Variational Calculus written by J. H. Heinbockel and has been published by Trafford Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-04 with Mathematics categories.
A textbook that is suitable for engineers, physicists, and scientist desiring an introduction to the basic concepts associated with the calculus of variations subject area with numerous worked examples.
An Introduction To The Calculus Of Variations
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Author : L.A. Pars
language : en
Publisher: Courier Corporation
Release Date : 2013-12-10
An Introduction To The Calculus Of Variations written by L.A. Pars and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-10 with Mathematics categories.
Clear, rigorous introductory treatment covers applications to geometry, dynamics, and physics. It focuses upon problems with one independent variable, connecting abstract theory with its use in concrete problems. 1962 edition.
Introduction To The Calculus Of Variations
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Author : Hans Sagan
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Introduction To The Calculus Of Variations written by Hans Sagan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
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.
Introduction To The Calculus Of Variations And Control With Modern Applications
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Author : John A. Burns
language : en
Publisher: CRC Press
Release Date : 2013-08-28
Introduction To The Calculus Of Variations And Control With Modern Applications written by John A. Burns and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-28 with Mathematics categories.
Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions a
Introduction To The Calculus Of Variations
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Author : Bernard Dacorogna
language : en
Publisher: World Scientific Publishing Company
Release Date : 2008-12-10
Introduction To The Calculus Of Variations written by Bernard Dacorogna and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.
The calculus of variations is one of the oldest subjects in mathematics, yet is very much alive and is still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology. This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist — mathematicians, physicists, engineers, students or researchers — in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions. In this new edition, the chapter on regularity has been significantly expanded and 27 new exercises have been added. The book, containing a total of 103 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels. Request Inspection Copy Contents:PreliminariesClassical MethodsDirect Methods: ExistenceDirect Methods: RegularityMinimal SurfacesIsoperimetric InequalitySolutions to the Exercises Readership: Graduate and undergraduate students in analysis and differential equations.
Introduction To The Fractional Calculus Of Variations
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Author : Delfim F M Torres
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-09-14
Introduction To The Fractional Calculus Of Variations written by Delfim F M Torres and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.
This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler-Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV.The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature./a
Classical Mechanics With Calculus Of Variations And Optimal Control
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Author : Mark Levi
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-03-07
Classical Mechanics With Calculus Of Variations And Optimal Control written by Mark Levi 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 2014-03-07 with Mathematics categories.
This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.
Calculus Of Variations And Optimal Control Theory
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Author : Daniel Liberzon
language : en
Publisher: Princeton University Press
Release Date : 2012
Calculus Of Variations And Optimal Control Theory written by Daniel Liberzon and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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
Calculus Of Variations
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Author : I. M. Gelfand
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Calculus Of Variations written by I. M. Gelfand and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
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.
Variational Calculus And Optimal Control
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Author : John L. Troutman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Variational Calculus And Optimal Control written by John L. Troutman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Although the calculus of variations has ancient origins in questions of Ar istotle and Zenodoros, its mathematical principles first emerged in the post calculus investigations of Newton, the Bernoullis, Euler, and Lagrange. Its results now supply fundamental tools of exploration to both mathematicians and those in the applied sciences. (Indeed, the macroscopic statements ob tained through variational principles may provide the only valid mathemati cal formulations of many physical laws. ) Because of its classical origins, variational calculus retains the spirit of natural philosophy common to most mathematical investigations prior to this century. The original applications, including the Bernoulli problem of finding the brachistochrone, require opti mizing (maximizing or minimizing) the mass, force, time, or energy of some physical system under various constraints. The solutions to these problems satisfy related differential equations discovered by Euler and Lagrange, and the variational principles of mechanics (especially that of Hamilton from the last century) show the importance of also considering solutions that just provide stationary behavior for some measure of performance of the system. However, many recent applications do involve optimization, in particular, those concerned with problems in optimal control. Optimal control is the rapidly expanding field developed during the last half-century to analyze optimal behavior of a constrained process that evolves in time according to prescribed laws. Its applications now embrace a variety of new disciplines, including economics and production planning.