Fundamental Theories And Their Applications Of The Calculus Of Variations
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Fundamental Theories And Their Applications Of The Calculus Of Variations
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Author : Dazhong Lao
language : en
Publisher: Springer Nature
Release Date : 2020-09-02
Fundamental Theories And Their Applications Of The Calculus Of Variations written by Dazhong Lao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-02 with Technology & Engineering categories.
This book focuses on the calculus of variations, including fundamental theories and applications. This textbook is intended for graduate and higher-level college and university students, introducing them to the basic concepts and calculation methods used in the calculus of variations. It covers the preliminaries, variational problems with fixed boundaries, sufficient conditions of extrema of functionals, problems with undetermined boundaries, variational problems of conditional extrema, variational problems in parametric forms, variational principles, direct methods for variational problems, variational principles in mechanics and their applications, and variational problems of functionals with vector, tensor and Hamiltonian operators. Many of the contributions are based on the authors’ research, addressing topics such as the extension of the connotation of the Hilbert adjoint operator, definitions of the other three kinds of adjoint operators, the extremum function theorem of the complete functional, unified Euler equations in variational methods, variational theories of functionals with vectors, modulus of vectors, arbitrary order tensors, Hamiltonian operators and Hamiltonian operator strings, reconciling the Euler equations and the natural boundary conditions, and the application range of variational methods. The book is also a valuable reference resource for teachers as well as science and technology professionals.
Introduction To The Calculus Of Variations And Its Applications
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Author : Frederic Wan
language : en
Publisher: Routledge
Release Date : 2017-10-19
Introduction To The Calculus Of Variations And Its Applications written by Frederic Wan and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, including sufficient conditions for optimality, the theory and techniques are extended to problems with a free end point, a free boundary, auxiliary and inequality constraints, leading to a study of optimal control theory.
Calculus Of Variations
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Author : Robert Weinstock
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Calculus Of Variations written by Robert Weinstock and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
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.
Partial Differential Equations And The Calculus Of Variations
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Author : COLOMBINI
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Partial Differential Equations And The Calculus Of Variations written by COLOMBINI 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.
The Italian school of Mathematical Analysis has long and glo rious traditions. In the last thirty years it owes very much to the scientific pre-eminence of Ennio De Giorgi, Professor of Mathemati cal Analysis at the Scuola Normale Superiore di Pisa. His fundamental theorems in Calculus of Variations, in Minimal Surfaces Theory, in Partial Differential Equations, in Axiomatic Set Theory as well as the fertility of his mind to discover both general mathematical structures and techniques which frame many different problems, and profound and meaningful examples which show the limits of a theory and give origin to new results and theories, makes him an absolute reference point for all Italian mathematicians, and a well-known and valued personage in the international mathematical world. We have been students of Ennio de Giorgi. Now, we are glad to present to him, together with all his collegues, friends and former students, these Essays of Mathematical Analysis written in his hon our on the occasion of his sixtieth birthday (February 8th, 1988), with our best wishes and our thanks for all he gave in the past and will give us in the future. We have added to the research papers of this book the text of a conversation with Ennio De Giorgi about the diffusion and the communication of science and, in particular, of Mathematics.
Modern Methods In The Calculus Of Variations
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Author : Irene Fonseca
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-22
Modern Methods In The Calculus Of Variations written by Irene Fonseca 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 2007-08-22 with Science categories.
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.
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.
Partial Differential Equations And The Calculus Of Variations
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Author : COLOMBINI
language : en
Publisher: Birkhäuser
Release Date : 2014-09-12
Partial Differential Equations And The Calculus Of Variations written by COLOMBINI and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-12 with Mathematics categories.
The Italian school of Mathematical Analysis has long and glo rious traditions. In the last thirty years it owes very much to the scientific pre-eminence of Ennio De Giorgi, Professor of Mathemati cal Analysis at the Scuola Normale Superiore di Pisa. His fundamental theorems in Calculus of Variations, in Minimal Surfaces Theory, in Partial Differential Equations, in Axiomatic Set Theory as well as the fertility of his mind to discover both general mathematical structures and techniques which frame many different problems, and profound and meaningful examples which show the limits of a theory and give origin to new results and theories, makes him an absolute reference point for all Italian mathematicians, and a well-known and valued personage in the international mathematical world. We have been students of Ennio de Giorgi. Now, we are glad to present to him, together with all his collegues, friends and former students, these Essays of Mathematical Analysis written in his hon our on the occasion of his sixtieth birthday (February 8th, 1988), with our best wishes and our thanks for all he gave in the past and will give us in the future. We have added to the research papers of this book the text of a conversation with Ennio De Giorgi about the diffusion and the communication of science and, in particular, of Mathematics.
Partial Differential Equations And The Calculus Of Variations
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Author : COLOMBINI
language : en
Publisher: Birkhäuser
Release Date : 2012-12-01
Partial Differential Equations And The Calculus Of Variations written by COLOMBINI and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-01 with Mathematics categories.
The Italian school of Mathematical Analysis has long and glo rious traditions. In the last thirty years it owes very much to the scientific pre-eminence of Ennio De Giorgi, Professor of Mathemati cal Analysis at the Scuola Normale Superiore di Pisa. His fundamental theorems in Calculus of Variations, in Minimal Surfaces Theory, in Partial Differential Equations, in Axiomatic Set Theory as well as the fertility of his mind to discover both general mathematical structures and techniques which frame many different problems, and profound and meaningful examples which show the limits of a theory and give origin to new results and theories, makes him an absolute reference point for all Italian mathematicians, and a well-known and valued personage in the international mathematical world. We have been students of Ennio de Giorgi. Now, we are glad to present to him, together with all his collegues, friends and former students, these Essays of Mathematical Analysis written in his hon our on the occasion of his sixtieth birthday (February 8th, 1988), with our best wishes and our thanks for all he gave in the past and will give us in the future. We have added to the research papers of this book the text of a conversation with Ennio De Giorgi about the diffusion and the communication of science and, in particular, of Mathematics.
Differential Geometry Calculus Of Variations And Their Applications
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Author : George M. Rassias
language : en
Publisher: CRC Press
Release Date : 2023-05-31
Differential Geometry Calculus Of Variations And Their Applications written by George M. Rassias and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-31 with Mathematics categories.
This book contains a series of papers on some of the longstanding research problems of geometry, calculus of variations, and their applications. It is suitable for advanced graduate students, teachers, research mathematicians, and other professionals in mathematics.
Calculus Of Variations With Applications
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Author : George McNaught Ewing
language : en
Publisher: Courier Corporation
Release Date : 1985-01-01
Calculus Of Variations With Applications written by George McNaught Ewing and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.
Applications-oriented introduction to variational theory develops insight and promotes understanding of specialized books and research papers. Suitable for advanced undergraduate and graduate students as a primary or supplementary text. 1969 edition.