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Author : Hans Sagan
Publisher : Courier Corporation
Page : 484 pages
File Size : 43,7 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486138022
Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.
Author : Charles Fox
Publisher : Courier Corporation
Page : 308 pages
File Size : 47,8 Mb
Release : 1987-01-01
Category : Mathematics
ISBN : 0486654990
In this highly regarded text for advanced undergraduate and graduate students, the author develops the calculus of variations both for its intrinsic interest and for its powerful applications to modern mathematical physics. Topics include first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.
Author : Frederic Wan
Publisher : CRC Press
Page : 660 pages
File Size : 44,7 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 0412051419
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.
Author : Charles Fox
Publisher : Unknown
Page : 290 pages
File Size : 45,6 Mb
Release : 1950
Category : Calculus of variations
ISBN : UOM:39015064426979
Author : Bernard Dacorogna
Publisher : Imperial College Press
Page : 241 pages
File Size : 42,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9781848163331
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.
Author : Hansjörg Kielhöfer
Publisher : Springer
Page : 227 pages
File Size : 43,5 Mb
Release : 2018-01-25
Category : Mathematics
ISBN : 9783319711232
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.
Author : Bernard Dacorogna
Publisher : World Scientific Publishing Company
Page : 324 pages
File Size : 45,9 Mb
Release : 2014-08-13
Category : Mathematics
ISBN : 9781783265541
The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and 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, several new exercises have been added. The book, containing a total of 119 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Author : John A. Burns
Publisher : CRC Press
Page : 562 pages
File Size : 54,5 Mb
Release : 2013-08-28
Category : Mathematics
ISBN : 9781466571402
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
Author : L.A. Pars
Publisher : Courier Corporation
Page : 368 pages
File Size : 49,5 Mb
Release : 2013-12-10
Category : Mathematics
ISBN : 9780486165950
Clear, rigorous introductory treatment covers applications to geometry, dynamics, and physics. It focuses upon problems with one independent variable, connecting abstract theory with its use in concrete problems. 1962 edition.
Author : Anonim
Publisher : Unknown
Page : 271 pages
File Size : 52,5 Mb
Release : 1950
Category : Calculus of variations
ISBN : LCCN:51003039
Author : Bruce van Brunt
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 54,6 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387216973
Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.
Author : Frederic Wan
Publisher : Routledge
Page : 381 pages
File Size : 45,5 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351436519
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.
Author : I. M. Gelfand,S. V. Fomin
Publisher : Courier Corporation
Page : 240 pages
File Size : 47,9 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486135014
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.
Author : Filip Rindler
Publisher : Springer
Page : 444 pages
File Size : 49,6 Mb
Release : 2018-06-20
Category : Mathematics
ISBN : 9783319776378
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.
Author : Mark Kot
Publisher : American Mathematical Society
Page : 298 pages
File Size : 53,8 Mb
Release : 2014-10-06
Category : Mathematics
ISBN : 9781470414955
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.