Introduction To The Variational Calculus With Elementary Convexity
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Introduction To The Variational Calculus With Elementary Convexity
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Author : John L. Troutman
language : en
Publisher:
Release Date : 1983
Introduction To The Variational Calculus With Elementary Convexity written by John L. Troutman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Calculus of variations categories.
Variational Calculus With Elementary Convexity
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Author : J.L. Troutman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Variational Calculus With Elementary Convexity written by J.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.
The calculus of variations, whose origins can be traced to the works of Aristotle and Zenodoros, is now Ii vast repository supplying fundamental tools of exploration not only to the mathematician, but-as evidenced by current literature-also to those in most branches of science in which mathematics is applied. (Indeed, the macroscopic statements afforded by variational principles may provide the only valid mathematical formulation of many physical laws. ) As such, it retains the spirit of natural philosophy common to most mathematical investigations prior to this century. How ever, it is a discipline in which a single symbol (b) has at times been assigned almost mystical powers of operation and discernment, not readily subsumed into the formal structures of modern mathematics. And it is a field for which it is generally supposed that most questions motivating interest in the subject will probably not be answerable at the introductory level of their formulation. In earlier articles,1,2 it was shown through several examples that a complete characterization of the solution of optimization problems may be available by elementary methods, and it is the purpose of this work to explore further the convexity which underlay these individual successes in the context of a full introductory treatment of the theory of the variational calculus. The required convexity is that determined through Gateaux variations, which can be defined in any real linear space and which provide an unambiguous foundation for the theory.
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.
An Introduction To Variational Calculus
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Author : Hebert Montegranario
language : en
Publisher: Springer Nature
Release Date : 2024-12-23
An Introduction To Variational Calculus written by Hebert Montegranario and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-23 with Computers categories.
This textbook introduces variational calculus and regularization methods for inverse problems, seamlessly blending classical concepts with contemporary computational applications, particularly in the field of image processing. The classical perspective draws upon foundational topics explored by pioneers such as Euler and Lagrange, establishing a solid theoretical groundwork. In recent decades, the advent of disciplines such as computer vision has expanded the horizons of variational calculus, showcasing its effectiveness in addressing complex problems that necessitate computational solutions. Consequently, this book places a strong emphasis on the synergy between mathematical theory, practical applications, and algorithmic development. To ensure the text is comprehensive and accessible, essential principles of functional analysis and Fourier analysis are incorporated, facilitating a deeper and more nuanced understanding of the applications presented. Covering both classic and more recent aspects of variational calculus, this book suggests that many topics of modern technology such as computer vision, robotics and especially digital image processing can be formulated in terms of variational problems.
Introduction To The Calculus Of Variations 4th Edition
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Author : Bernard Dacorogna
language : en
Publisher: World Scientific
Release Date : 2024-08-27
Introduction To The Calculus Of Variations 4th Edition written by Bernard Dacorogna and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-27 with Mathematics categories.
The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and 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.This new edition offers an entirely new chapter, as well as the addition of several new exercises. The book, containing a total of 147 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Introduction To The Calculus Of Variations And Its Applications
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Author : Frederic Wan
language : en
Publisher: Routledge
Release Date : 2017-10-19
Introduction To The Calculus Of Variations And Its Applications written by Frederic Wan and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, including sufficient conditions for optimality, the theory and techniques are extended to problems with a free end point, a free boundary, auxiliary and inequality constraints, leading to a study of optimal control theory.
Introduction To The Calculus Of Variations
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Author : Bernard Dacorogna
language : en
Publisher: Imperial College Press
Release Date : 2004
Introduction To The Calculus Of Variations written by Bernard Dacorogna and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
- Serves as an excellent introduction to the calculus of variations - Useful to researchers in different fields of mathematics who want to get a concise but broad introduction to the subject - Includes more than 70 exercises with solutions
Introduction To The Calculus Of Variations 3rd Edition
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Author : Bernard Dacorogna
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-08-13
Introduction To The Calculus Of Variations 3rd Edition 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 2014-08-13 with Mathematics categories.
The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and 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, several new exercises have been added. The book, containing a total of 119 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Variational Calculus With Elementary Convexity
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Author : John L. Troutman
language : en
Publisher:
Release Date : 1996
Variational Calculus With Elementary Convexity written by John L. Troutman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Introduction To Optimal Control Theory
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Author : Jack Macki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Optimal Control Theory written by Jack Macki 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 Science categories.
This monograph is an introduction to optimal control theory for systems governed by vector ordinary differential equations. It is not intended as a state-of-the-art handbook for researchers. We have tried to keep two types of reader in mind: (1) mathematicians, graduate students, and advanced undergraduates in mathematics who want a concise introduction to a field which contains nontrivial interesting applications of mathematics (for example, weak convergence, convexity, and the theory of ordinary differential equations); (2) economists, applied scientists, and engineers who want to understand some of the mathematical foundations. of optimal control theory. In general, we have emphasized motivation and explanation, avoiding the "definition-axiom-theorem-proof" approach. We make use of a large number of examples, especially one simple canonical example which we carry through the entire book. In proving theorems, we often just prove the simplest case, then state the more general results which can be proved. Many of the more difficult topics are discussed in the "Notes" sections at the end of chapters and several major proofs are in the Appendices. We feel that a solid understanding of basic facts is best attained by at first avoiding excessive generality. We have not tried to give an exhaustive list of references, preferring to refer the reader to existing books or papers with extensive bibliographies. References are given by author's name and the year of publication, e.g., Waltman [1974].