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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 3540648038
Release 2000-01-24
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 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.



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.



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



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.



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 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 and Partial Differential Equations

Calculus of Variations and Partial Differential Equations Author Stefan Hildebrandt
ISBN-10 9783540459323
Release 2006-11-14
Pages 308
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Calculus of Variations and Partial Differential Equations has been writing in one form or another for most of life. You can find so many inspiration from Calculus of Variations and Partial Differential Equations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Calculus of Variations and Partial Differential Equations book for free.



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.



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.



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.



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

The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations Author Ian Anderson
ISBN-10 9780821825334
Release 1992
Pages 110
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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.



Introduction to the Calculus of Variations

Introduction to the Calculus of Variations Author Hans Sagan
ISBN-10 9780486138022
Release 2012-04-26
Pages 480
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Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.



Introduction to the Calculus of Variations

Introduction to the Calculus of Variations Author Bernard Dacorogna
ISBN-10 9781783265541
Release 2014-08-13
Pages 324
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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.



Fundamental Math and Physics for Scientists and Engineers

Fundamental Math and Physics for Scientists and Engineers Author David Yevick
ISBN-10 9781118985595
Release 2014-11-24
Pages 462
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Provides a concise overview of the core undergraduate physics and applied mathematics curriculum for students and practitioners of science and engineering Fundamental Math and Physics for Scientists and Engineers summarizes college and university level physics together with the mathematics frequently encountered in engineering and physics calculations. The presentation provides straightforward, coherent explanations of underlying concepts emphasizing essential formulas, derivations, examples, and computer programs. Content that should be thoroughly mastered and memorized is clearly identified while unnecessary technical details are omitted. Fundamental Math and Physics for Scientists and Engineers is an ideal resource for undergraduate science and engineering students and practitioners, students reviewing for the GRE and graduate-level comprehensive exams, and general readers seeking to improve their comprehension of undergraduate physics. Covers topics frequently encountered in undergraduate physics, in particular those appearing in the Physics GRE subject examination Reviews relevant areas of undergraduate applied mathematics, with an overview chapter on scientific programming Provides simple, concise explanations and illustrations of underlying concepts Succinct yet comprehensive, Fundamental Math and Physics for Scientists and Engineers constitutes a reference for science and engineering students, practitioners and non-practitioners alike.