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The Calculus Of Variations In The Large
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Book Synopsis The Calculus of Variations in the Large by : Marston Morse
Download or read book The Calculus of Variations in the Large written by Marston Morse and published by American Mathematical Soc.. This book was released on 1934-12-31 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.
Book Synopsis Calculus of Variations by : Charles R. MacCluer
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 272 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.
Book Synopsis Introduction to the Calculus of Variations by : Bernard Dacorogna
Download or read book Introduction to the Calculus of Variations written by Bernard Dacorogna and published by Imperial College Press. This book was released on 2009 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamic Programming and the Calculus of Variations by : Dreyfus
Download or read book Dynamic Programming and the Calculus of Variations written by Dreyfus and published by Academic Press. This book was released on 1965-01-01 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic Programming and the Calculus of Variations
Book Synopsis Differential Equations and the Calculus of Variations by : Lev Elsgolts
Download or read book Differential Equations and the Calculus of Variations written by Lev Elsgolts and published by . This book was released on 2003-12-01 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in the Soviet Union, this text is meant for students of higher schools and deals with the most important sections of mathematics - differential equations and the calculus of variations. The first part describes the theory of differential equations and reviews the methods for integrating these equations and investigating their solutions. The second part gives an idea of the calculus of variations and surveys the methods for solving variational problems. The book contains a large number of examples and problems with solutions involving applications of mathematics to physics and mechanics. Apart from its main purpose the textbook is of interest to expert mathematicians. Lev Elsgolts (deceased) was a Doctor of Physico-Mathematical Sciences, Professor at the Patrice Lumumba University of Friendship of Peoples. His research work was dedicated to the calculus of variations and differential equations. He worked out the theory of differential equations with deviating arguments and supplied methods for their solution. Lev Elsgolts was the author of many printed works. Among others, he wrote the well-known books Qualitative Methods in Mathematical Analysis and Introduction to the Theory of Differential Equations with Deviating Arguments. In addition to his research work Lev Elsgolts taught at higher schools for over twenty years.
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 Functional Analysis, Calculus of Variations and Optimal Control by : Francis Clarke
Download or read book Functional Analysis, Calculus of Variations and Optimal Control written by Francis Clarke and published by Springer Science & Business Media. This book was released on 2013-02-06 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.
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 324 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 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 240 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 Calculus of Variations by : Robert Weinstock
Download or read book Calculus of Variations written by Robert Weinstock and published by Courier Corporation. This book was released on 2012-04-26 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book by Robert Weinstock was written to fill the need for a basic introduction to the calculus of variations. Simply and easily written, with an emphasis on the applications of this calculus, it has long been a standard reference of physicists, engineers, and applied mathematicians. The author begins slowly, introducing the reader to the calculus of variations, and supplying lists of essential formulae and derivations. Later chapters cover isoperimetric problems, geometrical optics, Fermat's principle, dynamics of particles, the Sturm-Liouville eigenvalue-eigenfunction problem, the theory of elasticity, quantum mechanics, and electrostatics. Each chapter ends with a series of exercises which should prove very useful in determining whether the material in that chapter has been thoroughly grasped. The clarity of exposition makes this book easily accessible to anyone who has mastered first-year calculus with some exposure to ordinary differential equations. Physicists and engineers who find variational methods evasive at times will find this book particularly helpful. "I regard this as a very useful book which I shall refer to frequently in the future." J. L. Synge, Bulletin of the American Mathematical Society.
Book Synopsis Applied Calculus of Variations for Engineers by : Louis Komzsik
Download or read book Applied Calculus of Variations for Engineers written by Louis Komzsik and published by CRC Press. This book was released on 2018-09-03 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the calculus of variations is to find optimal solutions to engineering problems whose optimum may be a certain quantity, shape, or function. Applied Calculus of Variations for Engineers addresses this important mathematical area applicable to many engineering disciplines. Its unique, application-oriented approach sets it apart from the theoretical treatises of most texts, as it is aimed at enhancing the engineer’s understanding of the topic. This Second Edition text: Contains new chapters discussing analytic solutions of variational problems and Lagrange-Hamilton equations of motion in depth Provides new sections detailing the boundary integral and finite element methods and their calculation techniques Includes enlightening new examples, such as the compression of a beam, the optimal cross section of beam under bending force, the solution of Laplace’s equation, and Poisson’s equation with various methods Applied Calculus of Variations for Engineers, Second Edition extends the collection of techniques aiding the engineer in the application of the concepts of the calculus of variations.
Book Synopsis Techniques of Variational Analysis by : Jonathan Borwein
Download or read book Techniques of Variational Analysis written by Jonathan Borwein and published by Springer Science & Business Media. This book was released on 2006-06-18 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Borwein is an authority in the area of mathematical optimization, and his book makes an important contribution to variational analysis Provides a good introduction to the topic
Book Synopsis Calculus of Variations by : Lev Ėrnestovich Ėlʹsgolʹt͡s
Download or read book Calculus of Variations written by Lev Ėrnestovich Ėlʹsgolʹt͡s and published by Pergamon. This book was released on 1962 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamic Optimization, Second Edition by : Morton I. Kamien
Download or read book Dynamic Optimization, Second Edition written by Morton I. Kamien and published by Courier Corporation. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.
Book Synopsis CALCULUS OF VARIATIONS WITH APPLICATIONS by : A. S. GUPTA
Download or read book CALCULUS OF VARIATIONS WITH APPLICATIONS written by A. S. GUPTA and published by PHI Learning Pvt. Ltd.. This book was released on 1996-01-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus of variations is one of the most important mathematical tools of great scientific significance used by scientistis and engineers. Unfortunately, a few books that are available are written at a level which is not easily comprehensible for postgraduate students.This book, written by a highly respected academic, presents the materials in a lucid manner so as to be within the easy grasp of the students with some background in calculus, differential equations and functional analysis. The aim is to give a thorough and systematic analysis of various aspects of calculus of variations.
Author :R. Tyrrell Rockafellar Publisher :Springer Science & Business Media ISBN 13 :3642024319 Total Pages :736 pages Book Rating :4.6/5 (42 download)
Book Synopsis Variational Analysis by : R. Tyrrell Rockafellar
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Book Synopsis The Calculus of Variations by : Bruce van Brunt
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 292 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.
