Differential Equations And The Calculus Of Variations

Author : Lev Elsgolts
Publisher : Unknown
Page : 444 pages
File Size : 54,8 Mb
Release : 2003-12-01
Category : Mathematics
ISBN : 1410210677

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Differential Equations and the Calculus of Variations by Lev Elsgolts Pdf

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.

Author : Alexander Ioffe,Simeon Reich,I Shafrir
Publisher : CRC Press
Page : 276 pages
File Size : 53,5 Mb
Release : 1999-07-15
Category : Mathematics
ISBN : 0849306051

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Calculus of Variations and Differential Equations by Alexander Ioffe,Simeon Reich,I Shafrir Pdf

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.

Author : M. V. Makarets,V. Yu Reshetnyak
Publisher : World Scientific
Page : 385 pages
File Size : 52,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9789810221911

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Ordinary Differential Equations and Calculus of Variations by M. V. Makarets,V. Yu Reshetnyak Pdf

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.

Author : Mariano Giaquinta,Stefan Hildebrandt
Publisher : Springer Science & Business Media
Page : 512 pages
File Size : 52,7 Mb
Release : 2004-06-23
Category : Mathematics
ISBN : 354050625X

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Calculus of Variations I by Mariano Giaquinta,Stefan Hildebrandt Pdf

This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems—such as those of geometric optics—of parts of the theory. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.

Author : Luigi Ambrosio,Norman Dancer
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642571862

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Calculus of Variations and Partial Differential Equations by Luigi Ambrosio,Norman Dancer Pdf

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.

Author : M V Makarets,V Yu Reshetnyak
Publisher : World Scientific
Page : 384 pages
File Size : 51,5 Mb
Release : 1995-06-30
Category : Mathematics
ISBN : 9789814500760

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Ordinary Differential Equations and Calculus of Variations by M V Makarets,V Yu Reshetnyak Pdf

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

Author : Izrail Moiseevitch Gelfand,Serge? Vasil?evich Fomin,Richard A. Silverman
Publisher : Courier Corporation
Page : 260 pages
File Size : 46,6 Mb
Release : 2000-01-01
Category : Mathematics
ISBN : 0486414485

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Calculus of Variations by Izrail Moiseevitch Gelfand,Serge? Vasil?evich Fomin,Richard A. Silverman Pdf

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.

Author : Lev Ėrnestovich Ėlʹsgolʹt︠s︡
Publisher : Unknown
Page : 448 pages
File Size : 49,8 Mb
Release : 1970
Category : Calculus of variations
ISBN : UOM:39015017329825

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Differential Equations and the Calculus of Variations by Lev Ėrnestovich Ėlʹsgolʹt︠s︡ Pdf

Author : Bruce van Brunt
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 55,5 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387216973

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The Calculus of Variations by Bruce van Brunt Pdf

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.

Author : Vasile Staicu
Publisher : Springer Science & Business Media
Page : 435 pages
File Size : 41,7 Mb
Release : 2008-03-12
Category : Mathematics
ISBN : 9783764384821

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Differential Equations, Chaos and Variational Problems by Vasile Staicu Pdf

This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.

Author : I. M. Gelfand,S. V. Fomin
Publisher : Courier Corporation
Page : 240 pages
File Size : 52,6 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486135014

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Calculus of Variations by I. M. Gelfand,S. V. Fomin Pdf

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.

Author : Charles Fox
Publisher : Courier Corporation
Page : 308 pages
File Size : 51,8 Mb
Release : 1987-01-01
Category : Mathematics
ISBN : 0486654990

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An Introduction to the Calculus of Variations by Charles Fox Pdf

In this highly regarded text for advanced undergraduate and graduate students, the author develops the calculus of variations both for its intrinsic interest and for its powerful applications to modern mathematical physics. Topics include first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.

Author : Filip Rindler
Publisher : Springer
Page : 444 pages
File Size : 50,6 Mb
Release : 2018-06-20
Category : Mathematics
ISBN : 9783319776378

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Calculus of Variations by Filip Rindler Pdf

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.

Author : Louis Komzsik
Publisher : CRC Press
Page : 234 pages
File Size : 54,6 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781482253603

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Applied Calculus of Variations for Engineers by Louis Komzsik Pdf

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.

Author : P.A. Griffiths
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 46,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781461581666

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Exterior Differential Systems and the Calculus of Variations by P.A. Griffiths Pdf

15 0. PRELIMINARIES a) Notations from Manifold Theory b) The Language of Jet Manifolds c) Frame Manifolds d) Differentia! Ideals e) Exterior Differential Systems EULER-LAGRANGE EQUATIONS FOR DIFFERENTIAL SYSTEMS ~liTH ONE I. 32 INDEPENDENT VARIABLE a) Setting up the Problem; Classical Examples b) Variational Equations for Integral Manifolds of Differential Systems c) Differential Systems in Good Form; the Derived Flag, Cauchy Characteristics, and Prolongation of Exterior Differential Systems d) Derivation of the Euler-Lagrange Equations; Examples e) The Euler-Lagrange Differential System; Non-Degenerate Variational Problems; Examples FIRST INTEGRALS OF THE EULER-LAGRANGE SYSTEM; NOETHER'S II. 1D7 THEOREM AND EXAMPLES a) First Integrals and Noether's Theorem; Some Classical Examples; Variational Problems Algebraically Integrable by Quadratures b) Investigation of the Euler-Lagrange System for Some Differential-Geometric Variational Pro~lems: 2 i) ( K ds for Plane Curves; i i) Affine Arclength; 2 iii) f K ds for Space Curves; and iv) Delauney Problem. II I. EULER EQUATIONS FOR VARIATIONAL PROBLEfiJS IN HOMOGENEOUS SPACES 161 a) Derivation of the Equations: i) Motivation; i i) Review of the Classical Case; iii) the Genera 1 Euler Equations 2 K /2 ds b) Examples: i) the Euler Equations Associated to f for lEn; but for Curves in i i) Some Problems as in i) sn; Non- Curves in iii) Euler Equations Associated to degenerate Ruled Surfaces IV.