Ordinary Differential Equations And Calculus Of Variations

Author : M V Makarets,V Yu Reshetnyak
Publisher : World Scientific
Page : 384 pages
File Size : 52,7 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 : Richard S. Palais,Robert Andrew Palais
Publisher : American Mathematical Soc.
Page : 329 pages
File Size : 41,6 Mb
Release : 2009-11-13
Category : Mathematics
ISBN : 9780821821381

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Differential Equations, Mechanics, and Computation by Richard S. Palais,Robert Andrew Palais Pdf

This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.

Author : Ian Anderson,Gerard Thompson
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 48,6 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825334

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The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations by Ian Anderson,Gerard Thompson Pdf

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.

Author : Luigi Ambrosio,Norman Dancer
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 47,5 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 : Lev Elsgolts
Publisher : Unknown
Page : 444 pages
File Size : 53,9 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 : Vasile Staicu
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 40,9 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 : Dreyfus
Publisher : Academic Press
Page : 247 pages
File Size : 42,8 Mb
Release : 1965-01-01
Category : Computers
ISBN : 9780080955278

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Dynamic Programming and the Calculus of Variations by Dreyfus Pdf

Dynamic Programming and the Calculus of Variations

Author : I. M. Gelfand,S. V. Fomin
Publisher : Courier Corporation
Page : 240 pages
File Size : 47,7 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 : Ricardo Almeida,Shakoor Pooseh,Delfim F M Torres
Publisher : World Scientific Publishing Company
Page : 280 pages
File Size : 53,5 Mb
Release : 2015-03-19
Category : Mathematics
ISBN : 9781783266425

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Computational Methods In The Fractional Calculus Of Variations by Ricardo Almeida,Shakoor Pooseh,Delfim F M Torres Pdf

This book fills a gap in the literature by introducing numerical techniques to solve problems of fractional calculus of variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.The authors are well-known researchers in the area of FCV and the book contains some of their recent results, serving as a companion volume to Introduction to the Fractional Calculus of Variations by A B Malinowska and D F M Torres, where analytical methods are presented to solve FCV problems. After some preliminaries on the subject, different techniques are presented in detail with numerous examples to help the reader to better understand the methods. The techniques presented may be used not only to deal with FCV problems but also in other contexts of fractional calculus, such as fractional differential equations and fractional optimal control. It is suitable as an advanced book for graduate students in mathematics, physics and engineering, as well as for researchers interested in fractional calculus.

Author : Robert Weinstock
Publisher : Courier Corporation
Page : 354 pages
File Size : 43,5 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486141060

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Calculus of Variations by Robert Weinstock Pdf

This book by Robert Weinstock was written to fill the need for a basic introduction to the calculus of variations. Simply and easily written, with an emphasis on the applications of this calculus, it has long been a standard reference of physicists, engineers, and applied mathematicians. The author begins slowly, introducing the reader to the calculus of variations, and supplying lists of essential formulae and derivations. Later chapters cover isoperimetric problems, geometrical optics, Fermat's principle, dynamics of particles, the Sturm-Liouville eigenvalue-eigenfunction problem, the theory of elasticity, quantum mechanics, and electrostatics. Each chapter ends with a series of exercises which should prove very useful in determining whether the material in that chapter has been thoroughly grasped. The clarity of exposition makes this book easily accessible to anyone who has mastered first-year calculus with some exposure to ordinary differential equations. Physicists and engineers who find variational methods evasive at times will find this book particularly helpful. "I regard this as a very useful book which I shall refer to frequently in the future." J. L. Synge, Bulletin of the American Mathematical Society.

Author : L. Cesari
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461381655

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Optimization—Theory and Applications by L. Cesari Pdf

This book has grown out of lectures and courses in calculus of variations and optimization taught for many years at the University of Michigan to graduate students at various stages of their careers, and always to a mixed audience of students in mathematics and engineering. It attempts to present a balanced view of the subject, giving some emphasis to its connections with the classical theory and to a number of those problems of economics and engineering which have motivated so many of the present developments, as well as presenting aspects of the current theory, particularly value theory and existence theorems. However, the presentation ofthe theory is connected to and accompanied by many concrete problems of optimization, classical and modern, some more technical and some less so, some discussed in detail and some only sketched or proposed as exercises. No single part of the subject (such as the existence theorems, or the more traditional approach based on necessary conditions and on sufficient conditions, or the more recent one based on value function theory) can give a sufficient representation of the whole subject. This holds particularly for the existence theorems, some of which have been conceived to apply to certain large classes of problems of optimization. For all these reasons it is essential to present many examples (Chapters 3 and 6) before the existence theorems (Chapters 9 and 11-16), and to investigate these examples by means of the usual necessary conditions, sufficient conditions, and value function theory.

Author : Bruce van Brunt
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 44,9 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 : A.N. Kolmogorov,A.P. Yushkevich
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 52,5 Mb
Release : 1998-03-24
Category : Mathematics
ISBN : 3764358459

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Mathematics of the 19th Century by A.N. Kolmogorov,A.P. Yushkevich Pdf

The editors of the present series had originally intended to publish an integrated work on the history of mathematics in the nineteenth century, passing systemati cally from one discipline to another in some natural order. Circumstances beyond their control, mainly difficulties in choosing authors, led to the abandonment of this plan by the time the second volume appeared. Instead of a unified mono graph we now present to the reader a series of books intended to encompass all the mathematics of the nineteenth century, but not in the order of the accepted classification of the component disciplines. In contrast to the first two books of The Mathematics of the Nineteenth Century, which were divided into chapters, this third volume consists of four parts, more in keeping with the nature of the publication. 1 We recall that the first book contained essays on the history of mathemati 2 cal logic, algebra, number theory, and probability, while the second covered the history of geometry and analytic function theory. In the present third volume the reader will find: 1. An essay on the development of Chebyshev's theory of approximation of functions, later called "constructive function theory" by S. N. Bernshtein. This highly original essay is due to the late N. I. Akhiezer (1901-1980), the author of fundamental discoveries in this area. Akhiezer's text will no doubt attract attention not only from historians of mathematics, but also from many specialists in constructive function theory.

Author : Lev Ėrnestovich Ėlʹsgolʹt︠s︡
Publisher : Unknown
Page : 448 pages
File Size : 52,9 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 : P.A. Griffiths
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 50,7 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.