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An Introduction To The Calculus Of Variations

An Introduction to the Calculus of Variations PDF
Author: Charles Fox
Publisher: Courier Corporation
Release: 1987-01-01
Size: 59.92 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 271
View: 4474

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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.

Introduction To The Calculus Of Variations

Introduction to the Calculus of Variations PDF
Author: Hans Sagan
Publisher: Courier Corporation
Release: 2012-04-26
Size: 60.65 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 480
View: 2458

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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.

Introduction To The Calculus Of Variations

Introduction to the Calculus of Variations PDF
Author: Bernard Dacorogna
Publisher: Imperial College Press
Release: 2004
Size: 69.39 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 228
View: 3672

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- Serves as an excellent introduction to the calculus of variations - Useful to researchers in different fields of mathematics who want to get a concise but broad introduction to the subject - Includes more than 70 exercises with solutions

Introduction To The Calculus Of Variations

Introduction to the Calculus of Variations PDF
Author: Bernard Dacorogna
Publisher: World Scientific Publishing Company
Release: 2014-08-13
Size: 22.84 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 324
View: 812

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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.

An Introduction To The Calculus Of Variations

An Introduction to the Calculus of Variations PDF
Author: L.A. Pars
Publisher: Courier Corporation
Release: 2013-12-10
Size: 66.64 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 368
View: 5085

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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.

Calculus Of Variations

Calculus of Variations PDF
Author: Robert Weinstock
Publisher: Courier Corporation
Release: 1974-01-01
Size: 29.25 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 326
View: 5473

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This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topics. Exercises in each chapter. 1952 edition.

Calculus Of Variations

Calculus of Variations PDF
Author: Lev D. Elsgolc
Publisher: Courier Corporation
Release: 2007-01-15
Size: 61.96 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 178
View: 1502

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This concise text offers both professionals and students an introduction to the fundamentals and standard methods of the calculus of variations. In addition to surveys of problems with fixed and movable boundaries, it explores highly practical direct methods for the solution of variational problems. Topics include the method of variation in problems with fixed boundaries; variational problems with movable boundaries and other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter features numerous illustrative problems, and solutions appear at the end.

The Calculus Of Variations And Optimal Control

The Calculus of Variations and Optimal Control PDF
Author: George Leitmann
Publisher: Springer Science & Business Media
Release: 1981-05-31
Size: 77.28 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 311
View: 1283

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When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching the rope into the shape of a circular arc and thereby maximized the area of the land upon which she was to found Carthage. This story of the founding of Carthage is apocryphal. Nonetheless it is probably the first account of a problem of the kind that inspired an entire mathematical discipline, the calculus of variations and its extensions such as the theory of optimal control. This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. The discussion in Part I is restricted to the simplest problem of the calculus of variations. The topic is entirely classical; all of the basic theory had been developed before the turn of the century. Consequently the material comes from many sources; however, those most useful to me have been the books of Oskar Bolza and of George M. Ewing. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

Calculus Of Variations And Optimal Control Theory

Calculus of Variations and Optimal Control Theory PDF
Author: Daniel Liberzon
Publisher: Princeton University Press
Release: 2012
Size: 47.52 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 235
View: 2519

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This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control