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Calculus of Variations I, Mariano Giaquinta; Stefan Hildebrandt


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Автор: Mariano Giaquinta; Stefan Hildebrandt
Название:  Calculus of Variations I
ISBN: 9783642080746
Издательство: Springer
Классификация:



ISBN-10: 364208074X
Обложка/Формат: Paperback
Страницы: 474
Вес: 0.70 кг.
Дата издания: 04.12.2010
Серия: Grundlehren der mathematischen Wissenschaften
Язык: English
Размер: 234 x 156 x 26
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for- mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as well as Hamilton- Jacobi theory and the classical theory of partial differential equations of first ordel;. In a subsequent treatise we shall describe developments arising from Hilberts 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus we have particularly emphasized the often neglected theory of inner variations, i. e. of variations of the independent variables, which is a source of useful information such as mono tonicity for- mulas, conformality relations and conservation laws. The combined variation of dependent and independent variables leads to the general conservation laws of Emmy Noether, an important tool in exploiting symmetries. Other parts of this volume deal with Legendre-Jacobi theory and with field theories. In particular we give a detailed presentation of one-dimensional field theory for nonpara- metric and parametric integrals and its relations to Hamilton-Jacobi theory, geometrical optics and point mechanics. Moreover we discuss various ways of exploiting the notion of convexity in the calculus of variations, and field theory is certainly the most subtle method to make use of convexity. We also stress the usefulness of the concept of a null Lagrangian which plays an important role in we give an exposition of Hamilton-Jacobi several instances.


Introduction to the Fractional Calculus of Variations

Автор: Torres Delfim F. M.
Название: Introduction to the Fractional Calculus of Variations
ISBN: 1848169663 ISBN-13(EAN): 9781848169661
Издательство: World Scientific Publishing
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Цена: 10454.00 р.
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Описание: Suitable for graduate students and ambitious undergraduates in mathematics and mechanics, this title offers an introduction to the subject of Fractional Calculus of Variations (FCV). It describes non-conservative systems in mechanics.

Computational Methods in the Fractional Calculus of Variations

Автор: Almeida Ricardo, Pooseh Shakoor, Torres Delfim F.
Название: Computational Methods in the Fractional Calculus of Variations
ISBN: 1783266406 ISBN-13(EAN): 9781783266401
Издательство: World Scientific Publishing
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Цена: 10296.00 р.
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Описание: This book fills a gap in the literature by introducing numerical techniques to solve problems of the 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 Early Period of the Calculus of Variations

Автор: Freguglia
Название: The Early Period of the Calculus of Variations
ISBN: 3319389440 ISBN-13(EAN): 9783319389448
Издательство: Springer
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Цена: 13275.00 р.
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Описание: This monograph explores the early development of the calculus of variations in continental Europe during the Eighteenth Century by illustrating the mathematics of its founders. Closely following the original papers and correspondences of Euler, Lagrange, the Bernoullis, and others, the reader is immersed in the challenge of theory building. We see what the founders were doing, the difficulties they faced, the mistakes they made, and their triumphs. The authors guide the reader through these works with instructive commentaries and complements to the original proofs, as well as offering a modern perspective where useful. The authors begin in 1697 with Johann Bernoulli’s work on the brachystochrone problem and the events leading up to it, marking the dawn of the calculus of variations. From there, they cover key advances in the theory up to the development of Lagrange’s ?-calculus, including: • The isoperimetrical problems• Shortest lines and geodesics• Euler’s Methodus Inveniendi and the two AdditamentaFinally, the authors give the readers a sense of how vast the calculus of variations has become in centuries hence, providing some idea of what lies outside the scope of the book as well as the current state of affairs in the field. This book will be of interest to anyone studying the calculus of variations who wants a deeper intuition for the techniques and ideas that are used, as well as historians of science and mathematics interested in the development and evolution of modern calculus and analysis.

Functional Analysis, Calculus of Variations and Optimal Cont

Автор: Clarke Francis
Название: Functional Analysis, Calculus of Variations and Optimal Cont
ISBN: 1447148193 ISBN-13(EAN): 9781447148197
Издательство: Springer
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Цена: 9776.00 р.
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Описание: This book provides a thorough introduction to optimal control, offering many substantial examples, and more than 300 exercises covering viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory.

Direct Methods in the Calculus of Variations

Автор: Bernard Dacorogna
Название: Direct Methods in the Calculus of Variations
ISBN: 1441922598 ISBN-13(EAN): 9781441922595
Издательство: Springer
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Цена: 15372.00 р.
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Описание: This book is developed for the study of vectorial problems in the calculus of variations. It is a new edition of the earlier book published in 1989. Almost half of the book consists of new material and there are added examples.

Plateau`s Problem and the Calculus of Variations. (MN-35):

Автор: Struwe Michael
Название: Plateau`s Problem and the Calculus of Variations. (MN-35):
ISBN: 0691607753 ISBN-13(EAN): 9780691607757
Издательство: Wiley
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Цена: 4752.00 р.
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Описание: This book is meant to give an account of recent developments in the theory of Plateau`s problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is given and re

Functional Analysis, Calculus of Variations and Optimal Control

Автор: Francis Clarke
Название: Functional Analysis, Calculus of Variations and Optimal Control
ISBN: 1447162102 ISBN-13(EAN): 9781447162100
Издательство: Springer
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Цена: 9776.00 р.
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Описание: This book provides a thorough introduction to optimal control, offering many substantial examples, and more than 300 exercises covering viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory.

Turnpike Properties in the Calculus of Variations and Optimal Control

Автор: Alexander Zaslavski
Название: Turnpike Properties in the Calculus of Variations and Optimal Control
ISBN: 1441939245 ISBN-13(EAN): 9781441939241
Издательство: Springer
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Цена: 20263.00 р.
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Описание: Infinite Horizon Variational Problems.- Extremals of Nonautonomous Problems.- Extremals of Autonomous Problems.- Infinite Horizon Autonomous Problems.- Turnpike for Autonomous Problems.- Linear Periodic Control Systems.- Linear Systems with Nonperiodic Integrands.- Discrete-Time Control Systems.- Control Problems in Hilbert Spaces.- A Class of Differential Inclusions.- Convex Processes.- A Dynamic Zero-Sum Game.

Introduction to the Calculus of Variations

Название: Introduction to the Calculus of Variations
ISBN: 1783265523 ISBN-13(EAN): 9781783265527
Издательство: World Scientific Publishing
Цена: 8870.00 р.
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Описание: The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and still evolving.


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