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Differential Equations and the Calculus of Variations

Differential Equations and the Calculus of Variations Author Lev Elsgolts
ISBN-10 1410210677
Release 2003-12-01
Pages 444
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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.



Ordinary Differential Equations and Calculus of Variations

Ordinary Differential Equations and Calculus of Variations Author M V Makarets
ISBN-10 9789814500760
Release 1995-06-30
Pages 384
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This problem book contains exercises for courses in differential equations and calculus of variations at universities and technical institutes. It is designed for non-mathematics students and also for scientists and practicing engineers who feel a need to refresh their knowledge. The book contains more than 260 examples and about 1400 problems to be solved by the students — much of which have been composed by the authors themselves. Numerous references are given at the end of the book to furnish sources for detailed theoretical approaches, and expanded treatment of applications. Contents:First Order Differential EquationsN-th Order Differential EquationsLinear Second Order EquationsSystems of Differential EquationsPartial Equations of the First OrderNonlinear Equations and StabilityCalculus of VariationsAnswers to Problems Readership: Mathematicians and engineers. keywords:Examples;Differential Equations;Calculus of Variations “… the book can be successfully used both by students and practising engineers.” Mathematics Abstracts



Calculus of Variations and Partial Differential Equations

Calculus of Variations and Partial Differential Equations Author Luigi Ambrosio
ISBN-10 9783642571862
Release 2012-12-06
Pages 348
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At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.



Calculus of Variations and Nonlinear Partial Differential Equations

Calculus of Variations and Nonlinear Partial Differential Equations Author Luigi Ambrosio
ISBN-10 9783540759133
Release 2008
Pages 196
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With a historical overview by Elvira Mascolo



Calculus of Variations and Partial Differential Equations of the First Order

Calculus of Variations and Partial Differential Equations of the First Order Author Constantin Carathéodory
ISBN-10 0821819992
Release 1999-01
Pages 402
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From the Preface: The book consists of two parts. In the first part, I have made an attempt to simplify the presentation of the theory of partial differential equations to the first order so that its study will require little time and also be accessible to the average student of mathematics ... The second part, which contains the Calculus of Variations, can also be read independently if one refers back to earlier sections in Part I ... I have never lost sight of the fact that the Calculus of Variations, as it is presented in Part II, should above all be a servant of Mechanics. Therefore, I have in particular prepared everything from the very outset for treatment in multidimensional spaces. In this second English edition of Caratheodory's famous work, the two volumes of the first edition have been combined into one (with a combination of the two indexes into a single index). There is a deep and fundamental relationship between the differential equations that occur in the calculus of variations and partial differential equations of the first order: in particular, to each such partial differential equation there correspond variational problems. This basic fact forms the rationale for Caratheodory's masterpiece.



Partial Differential Equations and the Calculus of Variations

Partial Differential Equations and the Calculus of Variations Author COLOMBINI
ISBN-10 9781461598312
Release 2013-11-11
Pages 1019
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Partial Differential Equations and the Calculus of Variations has been writing in one form or another for most of life. You can find so many inspiration from Partial Differential Equations and the Calculus of Variations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Partial Differential Equations and the Calculus of Variations book for free.



Mathematical Problems in Image Processing

Mathematical Problems in Image Processing Author Gilles Aubert
ISBN-10 9780387217666
Release 2008-04-06
Pages 288
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Partial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then. The main goal of this work is to present the variety of image analysis applications and the precise mathematics involved. It is intended for two audiences. The first is the mathematical community, to show the contribution of mathematics to this domain and to highlight some unresolved theoretical questions. The second is the computer vision community, to present a clear, self-contained, and global overview of the mathematics involved in image processing problems. The book is divided into five main parts. Chapter 1 is a detailed overview. Chapter 2 describes and illustrates most of the mathematical notions found throughout the work. Chapters 3 and 4 examine how PDEs and variational methods can be successfully applied in image restoration and segmentation processes. Chapter 5, which is more applied, describes some challenging computer vision problems, such as sequence analysis or classification. This book will be useful to researchers and graduate students in mathematics and computer vision.



Calculus of Variations and Differential Equations

Calculus of Variations and Differential Equations Author Alexander Ioffe
ISBN-10 0849306051
Release 1999-07-15
Pages 272
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The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the refereed proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts. The papers in the first volume focus on critical point theory and differential equations. The other volume deals with variational aspects of optimal control. Together they provide a unique opportunity to review the state-of-the-art of the calculus of variations, as presented by an international panel of masters in the field.



A Primer on the Calculus of Variations and Optimal Control Theory

A Primer on the Calculus of Variations and Optimal Control Theory Author Mike Mesterton-Gibbons
ISBN-10 9780821847725
Release 2009
Pages 252
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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.



Calculus of Variations

Calculus of Variations Author I. M. Gelfand
ISBN-10 9780486135014
Release 2012-04-26
Pages 240
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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.



Calculus of Variations and Optimal Control Differential Equations Set

Calculus of Variations and Optimal Control Differential Equations Set Author Alexander Ioffe
ISBN-10 9781584881407
Release 1999-07-16
Pages 280
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The calculus of variations is a classical area of mathematical analysis yet its myriad applications in science and technology continue to keep it an active area of research. Encompassing two volumes, this set brings together leading experts who focus on critical point theory, differential equations, and the variational aspects of optimal control. The books cover monotonicity, nonlinear optimization, the impossible pilot wave, the Lavrentiev phenomenon, and elliptic problems.



Calculus of Variations Applications and Computations

Calculus of Variations  Applications and Computations Author C Bandle
ISBN-10 0582239621
Release 1995-04-26
Pages 296
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This research presents some important domains of partial differential equations and applied mathematics including calculus of variations, control theory, modelling, numerical analysis and various applications in physics, mechanics and engineering. These topics are now part of many areas of science and have experienced tremendous development during the last decades.



Calculus of Variations

Calculus of Variations Author Robert Weinstock
ISBN-10 0486630692
Release 1974
Pages 326
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This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topics. Exercises in each chapter. 1952 edition.



Modern Methods in the Calculus of Variations

Modern Methods in the Calculus of Variations Author Irene Fonseca
ISBN-10 9780387690063
Release 2007-08-22
Pages 600
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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.



Differential Equations and the Calculus of Variations

Differential Equations and the Calculus of Variations Author L. Elsgolts
ISBN-10 OCLC:901445245
Release 1973
Pages
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Differential Equations and the Calculus of Variations has been writing in one form or another for most of life. You can find so many inspiration from Differential Equations and the Calculus of Variations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Differential Equations and the Calculus of Variations book for free.



Calculus of Variations

Calculus of Variations Author L. E. Elsgolc
ISBN-10 9781483137568
Release 2014-07-10
Pages 178
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Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter is illustrated by a large number of problems some of which are taken from existing textbooks. The solutions to the problems in each chapter are provided at the end of the book.



Multiple Integrals in the Calculus of Variations

Multiple Integrals in the Calculus of Variations Author Charles Bradfield Morrey Jr.
ISBN-10 354069952X
Release 2009-11-03
Pages 506
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From the reviews: "...the book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields. The book undoubtedly will become a standard reference for researchers in these areas. ...The book is addressed mainly to mature mathematical analysts. However, any student of analysis will be greatly rewarded by a careful study of this book." M. R. Hestenes in Journal of Optimization Theory and Applications "The work intertwines in masterly fashion results of classical analysis, topology, and the theory of manifolds and thus presents a comprehensive treatise of the theory of multiple integral variational problems." L. Schmetterer in Monatshefte für Mathematik "The book is very clearly exposed and contains the last modern theory in this domain. A comprehensive bibliography ends the book." M. Coroi-Nedeleu in Revue Roumaine de Mathématiques Pures et Appliquées