Download or read book Applied Calculus of Variations for Engineers Third edition written by Louis Komzsik and published by CRC Press. This book was released on 2019-11-22 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied Calculus of Variations for Engineers written by Louis Komzsik and published by CRC Press. This book was released on 2008-10-27 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Applied Calculus of Variations for Engineers Second Edition written by Louis Komzsik and published by CRC Press. This book was released on 2014-06-06 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Calculus of Variations written by Aamer Haque and published by . This book was released on 2019-08-28 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus of variations is an essential subject for classical mechanics and applied mechanics. Mathematical texts on this subject tend to focus on the intricate mathematical details of exceptional cases. The topic is rarely treated properly in physics and engineering texts. This book provides an introduction to calculus of variations. The goal is to provide the mathematical foundation for applications in physics and engineering. The book begins with a review of minimization of single and multivariable functions. The calculus of variations for functionals of single and multiple functions is developed. Finally, the results are applied to derive the major results of classical mechanics. This book is intended for students and researchers in applied mathematics, physics, and engineering. A background in advanced calculus is assumed. The necessary results from real and functional analysis are provided
Download or read book Calculus of Variations written by Robert Weinstock and published by Courier Corporation. This book was released on 2012-04-26 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book by Robert Weinstock was written to fill the need for a basic introduction to the calculus of variations. Simply and easily written, with an emphasis on the applications of this calculus, it has long been a standard reference of physicists, engineers, and applied mathematicians. The author begins slowly, introducing the reader to the calculus of variations, and supplying lists of essential formulae and derivations. Later chapters cover isoperimetric problems, geometrical optics, Fermat's principle, dynamics of particles, the Sturm-Liouville eigenvalue-eigenfunction problem, the theory of elasticity, quantum mechanics, and electrostatics. Each chapter ends with a series of exercises which should prove very useful in determining whether the material in that chapter has been thoroughly grasped. The clarity of exposition makes this book easily accessible to anyone who has mastered first-year calculus with some exposure to ordinary differential equations. Physicists and engineers who find variational methods evasive at times will find this book particularly helpful. "I regard this as a very useful book which I shall refer to frequently in the future." J. L. Synge, Bulletin of the American Mathematical Society.
Download or read book Calculus of Variations With Applications to Physics and Engineering written by Robert Weinstock and published by READ BOOKS. This book was released on 2008-11 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Series in Pure and Applied Mathematics WILLIAM TED MARTIN. CALCULUS OF VARIATIONS. PREFACE: There seems to have been published, up to the present time, no English language volume in which an elementary introduction to the calculus of variations is followed by extensive application of the subject to problems of physics and theoretical engineering. The present volume is offered as partial fulfillment of the need for such a book. Thus its chief purpose is twofold: ( i) To provide for the senior or first-year graduate student in mathe matics, science, or engineering an introduction to the ideas and techniques of the calculus of variations. ( The material of the first seven chapters with selected topics from the later chapters has been used several times as the subject matter of a 10-week course in the Mathematics Department at Stanford University.) ( ii) To illustrate the application of the calculus of variations in several fields outside the realm of pure mathematics. ( By far the greater emphasis is placed upon this second aspect of the book's purpose.) The range of topics considered may be determined at a glance in the table of contents. Mention here of some of the more significant omis sions may be pertinent: The vague, mechanical d method is avoided throughout. Thus, while no advantage is taken of a sometimes convenient shorthand tactic, there is eliminated a source of confusion which often grips the careful student when confronted with its use. No attempt is made to treat problems of sufficiency or existence: no consideration is taken of the second variation or of the conditions of Legendrc, Jacobi, and Weicrstrass. Besides being outside the scope of the chief aim of this book, these matters are excellently treated in the volumes of Bolza and Bliss listed in the Bibliography. Expansion theorems for the eigenfunctions associated with certain boundary-value problems are stated without proof. The proofs, beyond the scope of this volume, can be constructed, in most instances, on the basis of the theory of integral equations. Space limitations prevent inclusion of such topics as perturbation theory, heat flow, hydrodynamics, torsion and buckling of bars, Schwingcr's treatment of atomic scattering, and others. However, the reader who has mastered the essence of the material included should have little difficulty in applying the calculus of variations to most of the subjects which have been squeezed out.
Download or read book Introduction to the Mathematics of Variation written by Taha Sochi and published by Taha Sochi. This book was released on 2022-08-16 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the calculus of variations which is a subject concerned mainly with optimization of functionals. However, because part of it is based on using ordinary calculus in solving optimization problems, "Calculus of Variations" in its original title is modified to become “Mathematics of Variation”. In fact, the book is essentially a collection of solved problems with rather modest theoretical background and hence it is based on the method of "learning by example and practice" which in our view is the most effective way for learning mathematics and overcoming its difficulties. The main merit of the book is its clarity, intuitive structure and rather inclusiveness as it includes the main topics and applications of this subject. The materials in this book require decent background in general mathematics (mostly in single-variable and multi-variable differential and integral calculus). The book can be used as a text or as a reference for an introductory course on this subject as part of an undergraduate curriculum in physics or engineering or applied mathematics. The book can also be used as a source of supplementary pedagogical materials used in tutorial sessions associated with such a course.
Download or read book Introduction To The Calculus Of Variations 3rd Edition written by Bernard Dacorogna and published by World Scientific Publishing Company. This book was released on 2014-08-13 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Math Refresher for Scientists and Engineers written by John R. Fanchi and published by John Wiley & Sons. This book was released on 2006-06-12 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expanded coverage of essential math, including integral equations, calculus of variations, tensor analysis, and special integrals Math Refresher for Scientists and Engineers, Third Edition is specifically designed as a self-study guide to help busy professionals and students in science and engineering quickly refresh and improve the math skills needed to perform their jobs and advance their careers. The book focuses on practical applications and exercises that readers are likely to face in their professional environments. All the basic math skills needed to manage contemporary technology problems are addressed and presented in a clear, lucid style that readers familiar with previous editions have come to appreciate and value. The book begins with basic concepts in college algebra and trigonometry, and then moves on to explore more advanced concepts in calculus, linear algebra (including matrices), differential equations, probability, and statistics. This Third Edition has been greatly expanded to reflect the needs of today's professionals. New material includes: * A chapter on integral equations * A chapter on calculus of variations * A chapter on tensor analysis * A section on time series * A section on partial fractions * Many new exercises and solutions Collectively, the chapters teach most of the basic math skills needed by scientists and engineers. The wide range of topics covered in one title is unique. All chapters provide a review of important principles and methods. Examples, exercises, and applications are used liberally throughout to engage the readers and assist them in applying their new math skills to actual problems. Solutions to exercises are provided in an appendix. Whether to brush up on professional skills or prepare for exams, readers will find this self-study guide enables them to quickly master the math they need. It can additionally be used as a textbook for advanced-level undergraduates in physics and engineering.
Download or read book Calculus of Variations written by Charles R. MacCluer and published by Courier Corporation. This book was released on 2013-05-20 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied Mathematics for Engineers and Physicists written by Louis A. Pipes and published by Courier Corporation. This book was released on 2014-06-10 with total page 1043 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced courses in applied mathematics, this text covers analysis of lumped parameter systems, distributed parameter systems, and important areas of applied mathematics. Answers to selected problems. 1970 edition.
Download or read book Calculus of Variations With Applications to Physics and Engineering written by Robert Weinstock and published by Weinstock Press. This book was released on 2007-03 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of Mathematics for Engineers and Scientists written by Andrei D. Polyanin and published by CRC Press. This book was released on 2006-11-27 with total page 1542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific and engineering applications and present classical as well as newer solution methods for various mathematical equations. The book supplies numerous examples, graphs, figures, and diagrams and contains many results in tabular form, including finite sums and series and exact solutions of differential, integral, and functional equations.
Download or read book Methods of Applied Mathematics written by Francis B. Hildebrand and published by Courier Corporation. This book was released on 2012-06-08 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book offers engineers and physicists working knowledge of a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, but nevertheless extremely useful when applied to typical problems in many different fields. It deals principally with linear algebraic equations, quadratic and Hermitian forms, operations with vectors and matrices, the calculus of variations, and the formulations and theory of linear integral equations. Annotated problems and exercises accompany each chapter.
Download or read book Variational Methods with Applications in Science and Engineering written by Kevin W. Cassel and published by Cambridge University Press. This book was released on 2013-07-22 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.
Download or read book The Calculus of Variations written by N.I. Akhiezer and published by CRC Press. This book was released on 1988-01-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text on the calculus of variations for first-year graduate students. From a study of the simplest problem it goes on to cover Lagrangian derivatives, Jacobi’s condition, and field theory. Devotes considerable attention to direct methods and the Sturm-Liouville problem in a finite interval. Contains numerous interesting and challenging exercises plus five appendices on important results, generalizations, and applications of the material,
Download or read book Advanced Calculus Revised Edition written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
