Calculus Of Variations Classical And Modern
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Introduction To The Calculus Of Variations And Control With Modern Applications
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Author : John A. Burns
language : en
Publisher: CRC Press
Release Date : 2013-08-28
Introduction To The Calculus Of Variations And Control With Modern Applications written by John A. Burns and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-28 with Mathematics categories.
Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions a
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
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Author : Filip Rindler
language : en
Publisher: Springer
Release Date : 2018-06-20
Calculus Of Variations written by Filip Rindler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-20 with Mathematics categories.
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.
Calculus Of Variations Classical And Modern
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Author : Roberto Conti
language : en
Publisher:
Release Date : 1967
Calculus Of Variations Classical And Modern written by Roberto Conti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Calculus of variations categories.
The Calculus Of Variations And Functional Analysis
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Author : L. P. Lebedev
language : en
Publisher: World Scientific
Release Date : 2003
The Calculus Of Variations And Functional Analysis written by L. P. Lebedev 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 with Mathematics categories.
In this book, Sam helps his goose sisters fly to safety to looking for familiar landforms.
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.
Calculus Of Variations
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Author : I. M. Gelfand
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Calculus Of Variations written by I. M. Gelfand 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.
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.
Calculus Of Variations Classical And Modern
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Author :
language : it
Publisher:
Release Date : 1966
Calculus Of Variations Classical And Modern written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.
Classical And Modern Optimization
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Author : Guillaume Carlier
language : en
Publisher: World Scientific
Release Date : 2022-03-16
Classical And Modern Optimization written by Guillaume Carlier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-16 with Mathematics categories.
The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning.Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications.Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class.
Introduction To The Fractional Calculus Of Variations
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Author : Delfim F M Torres
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-09-14
Introduction To The Fractional Calculus Of Variations written by Delfim F M Torres and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.
This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler-Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV.The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature./a