Differential Equations and the Calculus of Variations

Author: Lev Elsgolts

Publisher: N.A

ISBN: 9781410210678

Category: Mathematics

Page: 444

View: 4157

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.
Posted in Mathematics

Calculus of Variations and Differential Equations

Author: Alexander Ioffe,Simeon Reich,I Shafrir

Publisher: CRC Press

ISBN: 9780849306051

Category: Mathematics

Page: 272

View: 1887

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.
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Calculus of Variations and Partial Differential Equations

Topics on Geometrical Evolution Problems and Degree Theory

Author: Luigi Ambrosio,Norman Dancer

Publisher: Springer Science & Business Media

ISBN: 3642571867

Category: Mathematics

Page: 348

View: 8670

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.
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Partial Differential Equations and Calculus of Variations

Author: Stefan Hildebrandt,Rolf Leis

Publisher: Springer

ISBN: 3540460241

Category: Mathematics

Page: 428

View: 3598

This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.
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Ordinary Differential Equations and Calculus of Variations

Author: M V Makarets,V Yu Reshetnyak

Publisher: World Scientific

ISBN: 9814500763

Category: Mathematics

Page: 384

View: 5999

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
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Calculus of Variations and Partial Differential Equations

Proceedings of a Conference, held in Trento, Italy, June 16-21, 1986

Author: Stefan Hildebrandt,David Kinderlehrer,Mario Miranda

Publisher: Springer

ISBN: 3540459324

Category: Mathematics

Page: 308

View: 2108

Posted in Mathematics

Calculus of Variations and Nonlinear Partial Differential Equations

Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, June 27 - July 2, 2005

Author: Centro internazionale matematico estivo. Summer School,Luigi Ambrosio,Luis A. Caffarelli,Michael G. Crandall,Lawrence C. Evans,Nicola Fusco

Publisher: Springer Science & Business Media

ISBN: 3540759131

Category: Mathematics

Page: 196

View: 6648

With a historical overview by Elvira Mascolo
Posted in Mathematics

Calculus of Variations and Optimal Control/Differential Equations Set

Author: Alexander Ioffe,Simeon Reich,I Shafrir

Publisher: CRC Press

ISBN: 1584881402

Category: Mathematics

Page: 280

View: 701

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.
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Calculus of Variations and Partial Differential Equations of the First Order

Author: Constantin Carathéodory

Publisher: Courier Corporation

ISBN: 9780821819999

Category: Mathematics

Page: 402

View: 5286

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.
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The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations

Author: Ian Anderson,Gerard Thompson

Publisher: American Mathematical Soc.

ISBN: 9780821861967

Category: Mathematics

Page: 110

View: 6858

This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centres on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coicides with a given system of ordinary differential equations. The authors rederive the basic necessary and sufficient conditions of Douglas for second order equations and extend them to equations of higher order using methods of the variational bicomplex of Tulcyjew, Vinogradov, and Tsujishita. The authors present an algorithm, based upon exterior differential systems techniques, for solving the inverse problem for second order equations. a number of new examples illustrate the effectiveness of this approach.
Posted in Mathematics

Direct Methods in the Calculus of Variations

Author: Enrico Giusti

Publisher: World Scientific

ISBN: 9814488291

Category: Mathematics

Page: 412

View: 7730

This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory. Contents:Semi-Classical TheoryMeasurable FunctionsSobolev SpacesConvexity and SemicontinuityQuasi-Convex FunctionalsQuasi-MinimaHölder ContinuityFirst DerivativesPartial RegularityHigher Derivatives Readership: Graduate students, academics and researchers in the field of analysis and differential equations. Keywords:Reviews:“This book must be recommended both to beginners in variational calculus and to more confirmed specialists in regularity theory of elliptic problems. It will become a reference in the calculus of variations and it contains in one volume of a reasonable size a very clear presentation of deep results.”Zentralblatt MATH “It can be recommended for graduate courses or post-graduate courses in the calculus of variations, or as reference text.”Studia Universitatis Babes-Bolyai, Series Mathematica “The exposition is always clear and self-contained … therefore this book may serve well as a textbook for a graduate course on the subject. Each chapter is complemented with detailed historical notes and interesting results which may be difficult to find elsewhere.”Mathematical Reviews
Posted in Mathematics

Introduction to the Calculus of Variations

Author: U. Brechteken-Mandersch

Publisher: CRC Press

ISBN: 9780412366901

Category: Mathematics

Page: 208

View: 7937

This text provides a clear, concise introduction to the calculus of variations. The introductory chapter provides a general sense of the subject through a discussion of several classical and contemporary examples of the subject's use.
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Introduction to the Calculus of Variations

Third Edition

Author: Bernard Dacorogna

Publisher: World Scientific Publishing Company

ISBN: 178326554X

Category: Mathematics

Page: 324

View: 7713

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.
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Mathematical Problems in Image Processing

Partial Differential Equations and the Calculus of Variations

Author: Gilles Aubert,Pierre Kornprobst

Publisher: Springer Science & Business Media

ISBN: 0387217665

Category: Mathematics

Page: 288

View: 5152

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.
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Linear Integral Equations

Author: William Vernon Lovitt

Publisher: Courier Corporation

ISBN: 0486442853

Category: Mathematics

Page: 253

View: 994

Not only general theory of linear equations but also differential equations, calculus of variations, and special areas in mathematical physics. Discusses Fredholm's equation, Hilbert-Schmidt theory, and auxiliary theorems on harmonic functions. 1924 edition.
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Calculus of Variations, Applications and Computations

Author: C Bandle,Michel Chipot,J Saint Jean Paulin,Josef Bemelmans,I Shafrir

Publisher: CRC Press

ISBN: 9780582239623

Category: Mathematics

Page: 296

View: 1117

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.
Posted in Mathematics