Topics In Calculus Of Variations
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Calculus Of Variations And Partial Differential Equations
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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Calculus Of Variations And Partial Differential Equations written by Luigi Ambrosio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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 With Applications To Physics And Engineering
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Author : Robert Weinstock
language : en
Publisher: READ BOOKS
Release Date : 2008-11
Calculus Of Variations With Applications To Physics And Engineering written by Robert Weinstock and has been published by READ BOOKS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11 with Mathematics categories.
International Series in Pure and Applied Mathematics WILLIAM TED MARTIN. CALCULUS OF VARIATIONS. PREFACE: There seems to have been published, up to the present time, no English language volume in which an elementary introduction to the calculus of variations is followed by extensive application of the subject to problems of physics and theoretical engineering. The present volume is offered as partial fulfillment of the need for such a book. Thus its chief purpose is twofold: ( i) To provide for the senior or first-year graduate student in mathe matics, science, or engineering an introduction to the ideas and techniques of the calculus of variations. ( The material of the first seven chapters with selected topics from the later chapters has been used several times as the subject matter of a 10-week course in the Mathematics Department at Stanford University.) ( ii) To illustrate the application of the calculus of variations in several fields outside the realm of pure mathematics. ( By far the greater emphasis is placed upon this second aspect of the book's purpose.) The range of topics considered may be determined at a glance in the table of contents. Mention here of some of the more significant omis sions may be pertinent: The vague, mechanical d method is avoided throughout. Thus, while no advantage is taken of a sometimes convenient shorthand tactic, there is eliminated a source of confusion which often grips the careful student when confronted with its use. No attempt is made to treat problems of sufficiency or existence: no consideration is taken of the second variation or of the conditions of Legendrc, Jacobi, and Weicrstrass. Besides being outside the scope of the chief aim of this book, these matters are excellently treated in the volumes of Bolza and Bliss listed in the Bibliography. Expansion theorems for the eigenfunctions associated with certain boundary-value problems are stated without proof. The proofs, beyond the scope of this volume, can be constructed, in most instances, on the basis of the theory of integral equations. Space limitations prevent inclusion of such topics as perturbation theory, heat flow, hydrodynamics, torsion and buckling of bars, Schwingcr's treatment of atomic scattering, and others. However, the reader who has mastered the essence of the material included should have little difficulty in applying the calculus of variations to most of the subjects which have been squeezed out.
Topics In Calculus Of Variations
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Author : Mariano Giaquinta
language : en
Publisher: Springer
Release Date : 2006-11-14
Topics In Calculus Of Variations written by Mariano Giaquinta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Science categories.
Topics In The Calculus Of Variations
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Author : Martin Fuchs
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topics In The Calculus Of Variations written by Martin Fuchs and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
This book illustrates two basic principles in the calculus of variations which are the question of existence of solutions and closely related the problem of regularity of minimizers. Chapter one studies variational problems for nonquadratic energy functionals defined on suitable classes of vectorvalued functions where also nonlinear constraints are incorporated. Problems of this type arise for mappings between Riemannian manifolds or in nonlinear elasticity. Using direct methods the existence of generalized minimizers is rather easy to establish and it is then shown that regularity holds up to a set of small measure. Chapter two contains a short introduction into Geometric Measure Theory which serves as a basis for developing an existence theory for (generalized) manifolds with prescribed mean curvature form and boundary in arbitrary dimensions and codimensions. One major aspect of the book is to concentrate on techniques and to present methods which turn out to be useful for applications in regularity theorems as well as for existence problems.
Calculus Of Variations
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Author : Hansjörg Kielhöfer
language : en
Publisher: Springer
Release Date : 2018-01-25
Calculus Of Variations written by Hansjörg Kielhöfer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-25 with Mathematics categories.
This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous theoretical background.
Calculus Of Variations
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Author : Diego Pallara
language : en
Publisher:
Release Date : 2004
Calculus Of Variations written by Diego Pallara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Topics In Calculus Of Variations
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Author : Mariano Giaquinta
language : en
Publisher: Springer
Release Date : 2014-03-12
Topics In Calculus Of Variations written by Mariano Giaquinta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Science categories.
Calculus Of Variations And Functional Analysis The With Optimal Control And Applications In Mechanics
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Author : Lebedev Leonid P
language : en
Publisher: World Scientific
Release Date : 2003-12-23
Calculus Of Variations And Functional Analysis The With Optimal Control And Applications In Mechanics written by Lebedev Leonid P and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-23 with Technology & Engineering categories.
This is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of “the calculus of variations”) and more modern topics (under the heading of “optimal control”). It employs the language and terminology of functional analysis to discuss and justify the setup of problems that are of great importance in applications. The book is concise and self-contained, and should be suitable for readers with a standard undergraduate background in engineering mathematics.
Calculus Of Variations
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Author : Lev D. Elsgolc
language : en
Publisher: Courier Corporation
Release Date : 2007-01-15
Calculus Of Variations written by Lev D. Elsgolc and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-15 with Mathematics categories.
This concise text offers both professionals and students an introduction to the fundamentals and standard methods of the calculus of variations. In addition to surveys of problems with fixed and movable boundaries, it explores highly practical direct methods for the solution of variational problems. Topics include the method of variation in problems with fixed boundaries; variational problems with movable boundaries and other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter features numerous illustrative problems, and solutions appear at the end.
Functional Analysis Calculus Of Variations And Optimal Control
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Author : Francis Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-06
Functional Analysis Calculus Of Variations And Optimal Control written by Francis Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-06 with Mathematics categories.
Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.