Calculus of Variations
Calculus of Variations

Author: Hansjörg Kielhöfer

Publisher: Springer

Published: 2018-01-25

Total Pages: 242

ISBN-13: 3319711237

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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.

Introduction To The Calculus Of Variations (3rd Edition)
Introduction To The Calculus Of Variations (3rd Edition)

Author: Bernard Dacorogna

Publisher: World Scientific Publishing Company

Published: 2014-08-13

Total Pages: 322

ISBN-13: 178326554X

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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.

Applied Calculus of Variations for Engineers
Applied Calculus of Variations for Engineers

Author: Louis Komzsik

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 234

ISBN-13: 1482253607

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The purpose of the calculus of variations is to find optimal solutions to engineering problems whose optimum may be a certain quantity, shape, or function. Applied Calculus of Variations for Engineers addresses this important mathematical area applicable to many engineering disciplines. Its unique, application-oriented approach sets it apart from the theoretical treatises of most texts, as it is aimed at enhancing the engineer’s understanding of the topic. This Second Edition text: Contains new chapters discussing analytic solutions of variational problems and Lagrange-Hamilton equations of motion in depth Provides new sections detailing the boundary integral and finite element methods and their calculation techniques Includes enlightening new examples, such as the compression of a beam, the optimal cross section of beam under bending force, the solution of Laplace’s equation, and Poisson’s equation with various methods Applied Calculus of Variations for Engineers, Second Edition extends the collection of techniques aiding the engineer in the application of the concepts of the calculus of variations.

Introduction to the Calculus of Variations and Control with Modern Applications
Introduction to the Calculus of Variations and Control with Modern Applications

Author: John A. Burns

Publisher: CRC Press

Published: 2013-08-28

Total Pages: 562

ISBN-13: 1466571403

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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

Introduction to the Calculus of Variations
Introduction to the Calculus of Variations

Author: Hans Sagan

Publisher: Courier Corporation

Published: 2012-04-26

Total Pages: 484

ISBN-13: 048613802X

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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.

The Calculus of Variations
The Calculus of Variations

Author: Bruce van Brunt

Publisher: Springer Science & Business Media

Published: 2006-04-18

Total Pages: 295

ISBN-13: 0387216979

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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.

Calculus of Variations
Calculus of Variations

Author: Charles R. MacCluer

Publisher: Courier Corporation

Published: 2013-05-20

Total Pages: 274

ISBN-13: 0486278301

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First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.

Calculus of Variations
Calculus of Variations

Author: I. M. Gelfand

Publisher: Courier Corporation

Published: 2012-04-26

Total Pages: 260

ISBN-13: 0486135012

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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.

An Introduction to the Calculus of Variations
An Introduction to the Calculus of Variations

Author: Charles Fox

Publisher: Courier Corporation

Published: 1987-01-01

Total Pages: 308

ISBN-13: 9780486654997

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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.

The Calculus of Variations and Optimal Control
The Calculus of Variations and Optimal Control

Author: George Leitmann

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 313

ISBN-13: 148990333X

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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.