• Mathematics

Differential Equations and the Calculus of Variations


Author: Lev Elsgolts
Publisher: N.A
ISBN: 9781410210678
Category: Mathematics
Page: 444
View: 9579
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.

    • Mathematics

Ordinary Differential Equations and Calculus of Variations

Book of Problems
Author: M. V. Makarets,V. Yu Reshetnyak
Publisher: World Scientific
ISBN: 9810221916
Category: Mathematics
Page: 372
View: 7964
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.

    • Mathematics

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: 5749
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.

    • Mathematics

Calculus of Variations and Differential Equations


Author: Alexander Ioffe,Simeon Reich,I Shafrir
Publisher: CRC Press
ISBN: 9780849306051
Category: Mathematics
Page: 272
View: 469
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.

    • 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: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 3540759131
Category: Mathematics
Page: 196
View: 6272
With a historical overview by Elvira Mascolo


    • Mathematics

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: 5776

    • Mathematics

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: 446
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.

    • Mathematics

Calculus of Variations and Partial Differential Equations of the First Order


Author: Constantin Carathéodory
Publisher: Courier Corporation
ISBN: 9780821819999
Category: Mathematics
Page: 402
View: 623
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.

    • 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: 5991
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.

    • Mathematics

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


Author: Ian Anderson,Gerard Thompson
Publisher: American Mathematical Soc.
ISBN: 082182533X
Category: Mathematics
Page: 110
View: 3632
This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centers on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coincides 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. What emerges is a fundamental dichotomy between second and higher order systems: the most general Lagrangian for any higher order system can depend only upon finitely many constants. 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. The monograph also contains a study of the inverse problem for a pair of geodesic equations arising from a two dimensional symmetric affine connection. The various possible solutions to the inverse problem for these equations are distinguished by geometric properties of the Ricci tensor.

    • Mathematics

The Inverse Problem of the Calculus of Variations

Local and Global Theory
Author: Dmitry V. Zenkov
Publisher: Springer
ISBN: 9462391092
Category: Mathematics
Page: 289
View: 4803
The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).

    • Science

Modern Methods in the Calculus of Variations

L^p Spaces
Author: Irene Fonseca,Giovanni Leoni
Publisher: Springer Science & Business Media
ISBN: 0387690069
Category: Science
Page: 600
View: 1789
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.

    • Mathematics

Calculus of Variations


Author: I. M. Gelfand,S. V. Fomin
Publisher: Courier Corporation
ISBN: 0486135012
Category: Mathematics
Page: 240
View: 8702
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.

    • Mathematics

Calculus of Variations

With Applications to Physics and Engineering
Author: Robert Weinstock
Publisher: Courier Corporation
ISBN: 9780486630694
Category: Mathematics
Page: 326
View: 8215
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.

    • Mathematics

Calculus of Variations


Author: L. E. Elsgolc
Publisher: Elsevier
ISBN: 1483137562
Category: Mathematics
Page: 178
View: 2815
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.

    • Mathematics

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: 6972
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.

    • Mathematics

Partial Differential Equations and Calculus of Variations


Author: Stefan Hildebrandt,Rolf Leis
Publisher: Springer
ISBN: 3540460241
Category: Mathematics
Page: 428
View: 9337
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.

    • Mathematics

Directions in Partial Differential Equations

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 28—30, 1985
Author: Michael G. Crandall,Paul H. Rabinowitz,E. L. Turner
Publisher: Academic Press
ISBN: 1483269248
Category: Mathematics
Page: 258
View: 9183
Directions in Partial Differential Equations covers the proceedings of the 1985 Symposium by the same title, conducted by the Mathematics Research Center, held at the University of Wisconsin, Madison. This book is composed of 13 chapters and begins with reviews of the calculus of variations and differential geometry. The subsequent chapters deal with the study of development of singularities, regularity theory, hydrodynamics, mathematical physics, asymptotic behavior, and critical point theory. Other chapters discuss the use of probabilistic methods, the modern theory of Hamilton-Jacobi equations, the interaction between theory and numerical methods for partial differential equations. The remaining chapters explore attempts to understand oscillatory phenomena in solutions of nonlinear equations. This book will be of great value to mathematicians and engineers.