Calculus Of Variations

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A First Course in the Calculus of Variations

Author : Mark Kot
Publisher : American Mathematical Society
ISBN 13 : 1470414953
Total Pages : 298 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A First Course in the Calculus of Variations by : Mark Kot

Download or read book A First Course in the Calculus of Variations written by Mark Kot and published by American Mathematical Society. This book was released on 2014-10-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields. The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics. Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.

Calculus of Variations

Author : I. M. Gelfand
Publisher : Courier Corporation
ISBN 13 : 0486135012
Total Pages : 240 pages
Book Rating : 4.4/5 (861 download)

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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.

The Calculus of Variations

Author : Bruce van Brunt
Publisher : Springer Science & Business Media
ISBN 13 : 0387216979
Total Pages : 292 pages
Book Rating : 4.3/5 (872 download)

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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.

Calculus of Variations

Author : Charles R. MacCluer
Publisher : Courier Corporation
ISBN 13 : 0486278301
Total Pages : 272 pages
Book Rating : 4.4/5 (862 download)

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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.

A Primer on the Calculus of Variations and Optimal Control Theory

Author : Mike Mesterton-Gibbons
Publisher : American Mathematical Soc.
ISBN 13 : 0821847724
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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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.

An Introduction to the Calculus of Variations

Author : L.A. Pars
Publisher : Courier Corporation
ISBN 13 : 0486165957
Total Pages : 368 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis An Introduction to the Calculus of Variations by : L.A. Pars

Download or read book An Introduction to the Calculus of Variations written by L.A. Pars and published by Courier Corporation. This book was released on 2013-12-10 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Calculus of Variations

Author : Filip Rindler
Publisher : Springer
ISBN 13 : 3319776371
Total Pages : 444 pages
Book Rating : 4.3/5 (197 download)

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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 444 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.

Applied Calculus of Variations for Engineers

Author : Louis Komzsik
Publisher : CRC Press
ISBN 13 : 1482253607
Total Pages : 234 pages
Book Rating : 4.4/5 (822 download)

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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.

Modern Methods in the Calculus of Variations

Author : Irene Fonseca
Publisher : Springer Science & Business Media
ISBN 13 : 0387690069
Total Pages : 600 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis Modern Methods in the Calculus of Variations by : Irene Fonseca

Download or read book Modern Methods in the Calculus of Variations written by Irene Fonseca and published by Springer Science & Business Media. This book was released on 2007-08-22 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

Classical Mechanics with Calculus of Variations and Optimal Control

Author : Mark Levi
Publisher : American Mathematical Soc.
ISBN 13 : 0821891383
Total Pages : 299 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Classical Mechanics with Calculus of Variations and Optimal Control by : Mark Levi

Download or read book Classical Mechanics with Calculus of Variations and Optimal Control written by Mark Levi and published by American Mathematical Soc.. This book was released on 2014-03-07 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Hansjörg Kielhöfer
Publisher : Springer
ISBN 13 : 3319711237
Total Pages : 227 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Calculus of Variations by : Hansjörg Kielhöfer

Download or read book Calculus of Variations written by Hansjörg Kielhöfer and published by Springer. This book was released on 2018-01-25 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous theoretical background.

The Calculus of Variations in the Large

Author : Marston Morse
Publisher : American Mathematical Soc.
ISBN 13 : 0821810189
Total Pages : 368 pages
Book Rating : 4.8/5 (218 download)

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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.

Introduction to the Calculus of Variations

Author : Hans Sagan
Publisher : Courier Corporation
ISBN 13 : 048613802X
Total Pages : 484 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to the Calculus of Variations by : Hans Sagan

Download or read book Introduction to the Calculus of Variations written by Hans Sagan and published by Courier Corporation. This book was released on 2012-04-26 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Bernard Dacorogna
Publisher : Imperial College Press
ISBN 13 : 1848163339
Total Pages : 241 pages
Book Rating : 4.8/5 (481 download)

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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.

Emmy Noether's Wonderful Theorem

Author : Dwight E. Neuenschwander
Publisher : JHU Press
ISBN 13 : 1421422689
Total Pages : 338 pages
Book Rating : 4.4/5 (214 download)

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Book Synopsis Emmy Noether's Wonderful Theorem by : Dwight E. Neuenschwander

Download or read book Emmy Noether's Wonderful Theorem written by Dwight E. Neuenschwander and published by JHU Press. This book was released on 2017-04-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important—and beautiful—mathematical solutions ever devised, Noether’s theorem touches on every aspect of physics. "In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."—Albert Einstein The year was 1915, and the young mathematician Emmy Noether had just settled into Göttingen University when Albert Einstein visited to lecture on his nearly finished general theory of relativity. Two leading mathematicians of the day, David Hilbert and Felix Klein, dug into the new theory with gusto, but had difficulty reconciling it with what was known about the conservation of energy. Knowing of her expertise in invariance theory, they requested Noether’s help. To solve the problem, she developed a novel theorem, applicable across all of physics, which relates conservation laws to continuous symmetries—one of the most important pieces of mathematical reasoning ever developed. Noether’s “first” and “second” theorem was published in 1918. The first theorem relates symmetries under global spacetime transformations to the conservation of energy and momentum, and symmetry under global gauge transformations to charge conservation. In continuum mechanics and field theories, these conservation laws are expressed as equations of continuity. The second theorem, an extension of the first, allows transformations with local gauge invariance, and the equations of continuity acquire the covariant derivative characteristic of coupled matter-field systems. General relativity, it turns out, exhibits local gauge invariance. Noether’s theorem also laid the foundation for later generations to apply local gauge invariance to theories of elementary particle interactions. In Dwight E. Neuenschwander’s new edition of Emmy Noether’s Wonderful Theorem, readers will encounter an updated explanation of Noether’s “first” theorem. The discussion of local gauge invariance has been expanded into a detailed presentation of the motivation, proof, and applications of the “second” theorem, including Noether’s resolution of concerns about general relativity. Other refinements in the new edition include an enlarged biography of Emmy Noether’s life and work, parallels drawn between the present approach and Noether’s original 1918 paper, and a summary of the logic behind Noether’s theorem.

Direct Methods in the Calculus of Variations

Author : Bernard Dacorogna
Publisher : Springer Science & Business Media
ISBN 13 : 3642514405
Total Pages : 312 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Direct Methods in the Calculus of Variations by : Bernard Dacorogna

Download or read book Direct Methods in the Calculus of Variations written by Bernard Dacorogna and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a considerable renewal of interest in the clas sical problems of the calculus of variations, both from the point of view of mathematics and of applications. Some of the most powerful tools for proving existence of minima for such problems are known as direct methods. They are often the only available ones, particularly for vectorial problems. It is the aim of this book to present them. These methods were introduced by Tonelli, following earlier work of Hilbert and Lebesgue. Although there are excellent books on calculus of variations and on direct methods, there are recent important developments which cannot be found in these books; in particular, those dealing with vector valued functions and relaxation of non convex problems. These two last ones are important in appli cations to nonlinear elasticity, optimal design . . . . In these fields the variational methods are particularly effective. Part of the mathematical developments and of the renewal of interest in these methods finds its motivations in nonlinear elasticity. Moreover, one of the recent important contributions to nonlinear analysis has been the study of the behaviour of nonlinear functionals un der various types of convergence, particularly the weak convergence. Two well studied theories have now been developed, namely f-convergence and compen sated compactness. They both include as a particular case the direct methods of the calculus of variations, but they are also, both, inspired and have as main examples these direct methods.

Calculus of Variations with Applications

Author : George McNaught Ewing
Publisher : Courier Corporation
ISBN 13 : 0486648567
Total Pages : 355 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis Calculus of Variations with Applications by : George McNaught Ewing

Download or read book Calculus of Variations with Applications written by George McNaught Ewing and published by Courier Corporation. This book was released on 1985-01-01 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications-oriented introduction to variational theory develops insight and promotes understanding of specialized books and research papers. Suitable for advanced undergraduate and graduate students as a primary or supplementary text. 1969 edition.