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Applied Calculus of Variations for Engineers

Author: Louis Komzsik

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 234

ISBN-13: 1482253607

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.

Applied Calculus of Variations for Engineers, Second Edition

Author: Louis Komzsik

Publisher:

Published: 2014-01-01

Total Pages: 234

ISBN-13: 9781306866118

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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."

Applied Calculus of Variations for Engineers, Third edition

Author: Louis Komzsik

Publisher: CRC Press

Published: 2019-11-22

Total Pages: 293

ISBN-13: 1000764370

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Calculus of variations has a long history. Its fundamentals were laid down by icons of mathematics like Euler and Lagrange. It was once heralded as the panacea for all engineering optimization problems by suggesting that all one needed to do was to state a variational problem, apply the appropriate Euler-Lagrange equation and solve the resulting differential equation. This, as most all encompassing solutions, turned out to be not always true and the resulting differential equations are not necessarily easy to solve. On the other hand, many of the differential equations commonly used in various fields of engineering are derived from a variational problem. Hence it is an extremely important topic justifying the new edition of this book. This third edition extends the focus of the book to academia and supports both variational calculus and mathematical modeling classes. The newly added sections, extended explanations, numerous examples and exercises aid the students in learning, the professors in teaching, and the engineers in applying variational concepts.

CALCULUS OF VARIATIONS WITH APPLICATIONS

Author: A. S. GUPTA

Publisher: PHI Learning Pvt. Ltd.

Published: 1996-01-01

Total Pages: 256

ISBN-13: 8120311205

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Calculus of variations is one of the most important mathematical tools of great scientific significance used by scientistis and engineers. Unfortunately, a few books that are available are written at a level which is not easily comprehensible for postgraduate students.This book, written by a highly respected academic, presents the materials in a lucid manner so as to be within the easy grasp of the students with some background in calculus, differential equations and functional analysis. The aim is to give a thorough and systematic analysis of various aspects of calculus of variations.

Calculus of Variations

Author: Charles R. MacCluer

Publisher: Courier Corporation

Published: 2013-05-20

Total Pages: 272

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 - With Applications to Physics and Engineering

Author: Robert Weinstock

Publisher: Weinstock Press

Published: 2007-03

Total Pages: 340

ISBN-13: 1406756652

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This text is in two sections. the first part dealing with, background material, basic theorems and isoperimetric problems. The second part devoted to applications, geometrical optics, particle dynamics, he theory of elasticity, electrostatics, quantum mechanics and much more. Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

A First Course in the Calculus of Variations

Author: Mark Kot

Publisher: American Mathematical Society

Published: 2014-10-06

Total Pages: 311

ISBN-13: 1470414953

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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.

Variational Methods with Applications in Science and Engineering

Author: Kevin W. Cassel

Publisher: Cambridge University Press

Published: 2013-07-22

Total Pages: 433

ISBN-13: 1107022584

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This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.

Calculus of Variations, Applications and Computations

Author: C Bandle

Publisher: CRC Press

Published: 1995-04-26

Total Pages: 300

ISBN-13: 9780582239623

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This research presents some important domains of partial differential equations and applied mathematics including calculus of variations, control theory, modelling, numerical analysis and various applications in physics, mechanics and engineering. These topics are now part of many areas of science and have experienced tremendous development during the last decades.

Applied Calculus of Variations for Engineers

Author: Louis Komzsik

Publisher: CRC Press

Published: 2008-10-27

Total Pages: 185

ISBN-13: 1420086650

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The subject of calculus of variations is to find optimal solutions to engineering problems where the optimum may be a certain quantity, a shape, or a function. Applied Calculus of Variations for Engineers addresses this very important mathematical area applicable to many engineering disciplines. Its unique, application-oriented approach sets it apa