Modern Methods in the Calculus of Variations, Fonseca
Автор: Chapra, Steven C. Название: Numerical methods for engineers ISBN: 007126759X ISBN-13(EAN): 9780071267595 Издательство: McGraw-Hill Рейтинг: Цена: 5642 р. Наличие на складе: Поставка под заказ.
Автор: Fuente, Angel de la. Название: Mathematical methods and models for economists ISBN: 0521585295 ISBN-13(EAN): 9780521585293 Издательство: Cambridge Academ Рейтинг: Цена: 4891 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is intended as a textbook for a first-year PhD course in mathematics for economists and as a reference for graduate students in economics. It provides a self-contained, rigorous treatment of most of the concepts and techniques required to follow the standard first-year theory sequence in micro and macroeconomics. The topics covered include an introduction to analysis in metric spaces, differential calculus, comparative statics, convexity, static optimization, dynamical systems and dynamic optimization. The book includes a large number of applications to standard economic models and over two hundred fully worked-out problems.
Автор: Dacorogna Название: Direct Methods in the Calculus of Variations ISBN: 0387357793 ISBN-13(EAN): 9780387357799 Издательство: Springer Рейтинг: Цена: 11219 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is a new edition of the authors previous book entitled Direct Methods in the Calculus of Variations, 1989. It is devoted to the study of vectorial problems in the calculus of variations. The book has been updated significantly and a number of additional examples have been included. The book will appeal researchers and graduate students in mathematics and engineering.
Название: Direct methods in the calculus of variations ISBN: 9812380434 ISBN-13(EAN): 9789812380432 Издательство: World Scientific Publishing Рейтинг: Цена: 15664 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A self-contained discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. The work only requires a knowledge of the elements of Lebesgue integration theory.
Описание: This manuscript describes some mathematical problems arising in image analysis and computer vision. The authors consider both variational and pde approaches. The description focuses on theoretical- mathematical aspects of the problems, as well as on their applications and numerical descretiziations. This book is intended to be a reference and a basis for advanced courses in the fields of applied mathematics and computer vision.
Автор: Brunt Bruce van Название: The Calculus of Variations ISBN: 0387402470 ISBN-13(EAN): 9780387402475 Издательство: Springer Рейтинг: Цена: 7012 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The calculus of variations has a long history of interaction with other branches of mathematics, such as geometry and differential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations.This book is an introductory account of the calculus of variations suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering. The mathematical background assumed of the reader is a course in multivariable calculus, and some familiarity with the elements of real analysis and ordinary differential equations. The book focuses on variational problems that involve one independent variable. The fixed endpoint problem and problems with constraints are discussed in detail. In addition, more advanced topics such as the inverse problem, eigenvalue problems, separability conditions for the Hamilton-Jacobi equation, and Noether's theorem are discussed. The text contains numerous examples to illustrate key concepts along with problems to help the student consolidate the material. The book can be used as a textbook for a one semester course on the calculus of variations, or as a book to supplement a course on applied mathematics or classical mechanics. Bruce van Brunt is Senior Lecturer at Massey University, New Zealand. He is the author of The Lebesgue-Stieltjes Integral, with Michael Carter, and has been teaching the calculus of variations to undergraduate and graduate students for several years.
Описание: Calculus of variations is a major branch of analysis, and partial differential equations are used to model natural phenomena and are used in all of the physical sciences. Using degree theory and the geometric problem of evolution of a surface, this text brings these two fields together.
Автор: Introduction To The Calculus Of Variations(2Nd Edition) Название: Introduction To The Calculus Of Variations(2Nd Edition) ISBN: 1848163347 ISBN-13(EAN): 9781848163348 Издательство: World Scientific Publishing Рейтинг: Цена: 5464 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The calculus of variations is one of the oldest subjects in mathematics, yet is very much alive and is 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, the chapter on regularity has been significantly expanded and 27 new exercises have been added. The book, containing a
total of 103 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Описание: This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields.The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics.Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.
Описание: A. Blaqui?re: Quelques aspects g?om?triques des processus optimaux.- C. Castaing: Quelques probl?mes de mesurabilit? li?s ? la th?orie des commandes.- L. Cesari: Existence theorems for Lagrange and Pontryagin problems of the calculus of variations and optimal control of more-dimensional extensions in Sobolev space.- H. Halkin: Optimal control as programming in infinite dimensional spaces.- C. Olech: The range of integrals of a certain class vector-valued functions.- E. Rothe: Weak topology and calculus of variations.- E.O. Roxin: Problems about the set of attainability.
Описание: 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 and discusses the importance of distinguishing between the necessary and sufficient conditions. In the first part of the text, the author develops the calculus of variations and provides complete proofs of the main results. He explains how the ideas behind the proofs are essential to the development of modern optimization and control theory. Focusing on optimal control problems, the second part shows how optimal control is a natural extension of the classical calculus of variations to more complex problems. By emphasizing the basic ideas and their mathematical development, this book gives you the foundation to use these mathematical tools to then tackle new problems. The text moves from simple to more complex problems, allowing you to see how the fundamental theory can be modified to address more difficult and advanced challenges. This approach helps you understand how to deal with future problems and applications in a realistic work environment.
Описание: This book is devoted to the recent progress on the turnpike theory. The turnpike property was discovered by Paul A. Samuelson, who applied it to problems in mathematical economics in 1949. These properties were studied for optimal trajectories of models of economic dynamics determined by convex processes. In this monograph the author, a leading expert in modern turnpike theory, presents a number of results concerning the turnpike properties in the calculus of variations and optimal control which were obtained in the last ten years. These results show that the turnpike properties form a general phenomenon which holds for various classes of variational problems and optimal control problems. The book should help to correct the misapprehension that turnpike properties are only special features of some narrow classes of convex problems of mathematical economics.
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