Calculus Of Variations First Editionwith Applications To Physics And Engineering

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Calculus of Variations

Robert Weinstock
Calculus of Variations Book PDF

Author : Robert Weinstock
Publisher : Courier Corporation
Page : 354 pages
File Size : 54,9 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486141060

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Calculus of Variations by Robert Weinstock Pdf

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.

Calculus of Variations - With Applications to Physics and Engineering

Robert Weinstock
Calculus of Variations With Applications to Physics and Engineering Book PDF

Author : Robert Weinstock
Publisher : READ BOOKS
Page : 344 pages
File Size : 50,7 Mb
Release : 2008-11
Category : Mathematics
ISBN : 1443728810

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Calculus of Variations - With Applications to Physics and Engineering by Robert Weinstock Pdf

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.

Calculus of Variations First Editionwith Applications to Physics and Engineering. - Scholar's Choice Edition

Robert Weinstock
Calculus of Variations First Editionwith Applications to Physics and Engineering Scholar s Choice Edition Book PDF

Author : Robert Weinstock
Publisher : Scholar's Choice
Page : 342 pages
File Size : 55,9 Mb
Release : 2015-02-14
Category : Electronic
ISBN : 1296021343

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Calculus of Variations First Editionwith Applications to Physics and Engineering. - Scholar's Choice Edition by Robert Weinstock Pdf

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Calculus of Variations

Charles R. MacCluer
Calculus of Variations Book PDF

Author : Charles R. MacCluer
Publisher : Courier Corporation
Page : 272 pages
File Size : 53,6 Mb
Release : 2013-05-20
Category : Mathematics
ISBN : 9780486278308

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Calculus of Variations by Charles R. MacCluer Pdf

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.

Variational Calculus with Engineering Applications

Constantin Udriste,Ionel Tevy
Variational Calculus with Engineering Applications Book PDF

Author : Constantin Udriste,Ionel Tevy
Publisher : John Wiley & Sons
Page : 228 pages
File Size : 43,6 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9781119944362

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Variational Calculus with Engineering Applications by Constantin Udriste,Ionel Tevy Pdf

A comprehensive overview of foundational variational methods for problems in engineering Variational calculus is a field in which small alterations in functions and functionals are used to find their relevant maxima and minima. It is a potent tool for addressing a range of dynamic problems with otherwise counter-intuitive solutions, particularly ones incorporating multiple confounding variables. Its value in engineering fields, where materials and geometric configurations can produce highly specific problems with unconventional or unintuitive solutions, is considerable. Variational Calculus with Engineering Applications provides a comprehensive survey of this toolkit and its engineering applications. Balancing theory and practice, it offers a thorough and accessible introduction to the field pioneered by Euler, Lagrange and Hamilton, offering tools that can be every bit as powerful as the better-known Newtonian mechanics. It is an indispensable resource for those looking for engineering-oriented overview of a subject whose capacity to provide engineering solutions is only increasing. Variational Calculus with Engineering Applications readers will also find: Discussion of subjects including variational principles, levitation, geometric dynamics, and more Examples and instructional problems in every Chapter, along with MAPLE codes for performing the simulations described in each Engineering applications based on simple, curvilinear, and multiple integral functionals Variational Calculus with Engineering Applications is ideal for advanced students, researchers, and instructors in engineering and materials science.

Calculus of Variations, Applications and Computations

C Bandle,Michel Chipot,J Saint Jean Paulin,Josef Bemelmans,I Shafrir
Calculus of Variations Applications and Computations Book PDF

Author : C Bandle,Michel Chipot,J Saint Jean Paulin,Josef Bemelmans,I Shafrir
Publisher : CRC Press
Page : 300 pages
File Size : 40,7 Mb
Release : 1995-04-26
Category : Mathematics
ISBN : 0582239621

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Calculus of Variations, Applications and Computations by C Bandle,Michel Chipot,J Saint Jean Paulin,Josef Bemelmans,I Shafrir Pdf

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.

Variational Methods with Applications in Science and Engineering

Kevin W. Cassel
Variational Methods with Applications in Science and Engineering Book PDF

Author : Kevin W. Cassel
Publisher : Unknown
Page : 432 pages
File Size : 54,7 Mb
Release : 2013
Category : Engineering
ISBN : 1316090671

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Variational Methods with Applications in Science and Engineering by Kevin W. Cassel Pdf

There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.

Advanced Mathematics for Engineers and Physicists

Sever Angel Popescu,Marilena Jianu
Advanced Mathematics for Engineers and Physicists Book PDF

Author : Sever Angel Popescu,Marilena Jianu
Publisher : Springer Nature
Page : 833 pages
File Size : 52,8 Mb
Release : 2023-01-25
Category : Mathematics
ISBN : 9783031215025

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Advanced Mathematics for Engineers and Physicists by Sever Angel Popescu,Marilena Jianu Pdf

This book is designed to be an introductory course to some basic chapters of Advanced Mathematics for Engineering and Physics students, researchers in different branches of Applied Mathematics and anyone wanting to improve their mathematical knowledge by a clear, live, self-contained and motivated text. Here, one can find different topics, such as differential (first order or higher order) equations, systems of differential equations, Fourier series, Fourier and Laplace transforms, partial differential equations, some basic facts and applications of the calculus of variations and, last but not least, an original and more intuitive introduction to probability theory. All these topics are carefully introduced, with complete proofs, motivations, examples, applications, problems and exercises, which are completely solved at the end of the book. We added a generous supplementary material (11.1) with a self-contained and complete introduction to normed, metric and Hilbert spaces. Since we used some topics from complex function theory, we also introduced in Chapter 11 a section (11.2) with the basic facts in this important field. What a reader needs for a complete understanding of this book? For a deep understanding of this book, it is required to take a course in undergraduate calculus and linear algebra. We mostly tried to use the engineering intuition instead of insisting on mathematical tricks. The main feature of the material presented here is its clarity, motivation and the genuine desire of the authors to make extremely transparent the "mysterious" mathematical tools that are used to describe and organize the great variety of impressions that come to the searching mind, from the infinite complexity of Nature. The book is recommended not only to engineering and physics students or researchers but also to junior students in mathematics because it shows the connection between pure mathematics and physical phenomena, which always supply motivations for mathematical discoveries.

Introduction to the Mathematics of Variation

Taha Sochi
Introduction to the Mathematics of Variation Book PDF

Author : Taha Sochi
Publisher : Taha Sochi
Page : 246 pages
File Size : 48,5 Mb
Release : 2022-08-16
Category : Mathematics
ISBN : 8210379456XXX

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Introduction to the Mathematics of Variation by Taha Sochi Pdf

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.

CALCULUS OF VARIATIONS WITH APPLICATIONS

A. S. GUPTA
CALCULUS OF VARIATIONS WITH APPLICATIONS Book PDF

Author : A. S. GUPTA
Publisher : PHI Learning Pvt. Ltd.
Page : 256 pages
File Size : 47,7 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 9788120311206

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CALCULUS OF VARIATIONS WITH APPLICATIONS by A. S. GUPTA Pdf

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.

An Introduction to Calculus of Variations

Aamer Haque
An Introduction to Calculus of Variations Book PDF

Author : Aamer Haque
Publisher : Unknown
Page : 225 pages
File Size : 49,8 Mb
Release : 2019-08-28
Category : Electronic
ISBN : 1689067411

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An Introduction to Calculus of Variations by Aamer Haque Pdf

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

Variational Calculus in Science and Engineering

Marvin J. Forray
Variational Calculus in Science and Engineering Book PDF

Author : Marvin J. Forray
Publisher : Unknown
Page : 248 pages
File Size : 49,7 Mb
Release : 1968
Category : Mathematics
ISBN : UOM:39015000972656

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Variational Calculus in Science and Engineering by Marvin J. Forray Pdf

Maxima and minima -- Introductory problems of the variational calculus -- Euler-Lagrange development with applications -- Hamilton's principle and Lagrange's equations -- Deformable bodies : theory of elasticity -- Energy principles, methods, and applications -- Rayleigh-Ritz method -- Methods of Galerkin, Kantorovich, and Euler -- Appendix : Summation convention and Cartesian tensors.

The Calculus of Variations

Bruce van Brunt
The Calculus of Variations Book PDF

Author : Bruce van Brunt
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 48,7 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387216973

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The Calculus of Variations by Bruce van Brunt Pdf

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.

Applied Calculus of Variations for Engineers

Louis Komzsik
Applied Calculus of Variations for Engineers Book PDF

Author : Louis Komzsik
Publisher : CRC Press
Page : 175 pages
File Size : 44,7 Mb
Release : 2008-10-27
Category : Mathematics
ISBN : 1420086626

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Applied Calculus of Variations for Engineers by Louis Komzsik Pdf

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 apart from the theoretical treatises of most texts. It is aimed at enhancing the engineer’s understanding of the topic as well as aiding in the application of the concepts in a variety of engineering disciplines. The first part of the book presents the fundamental variational problem and its solution via the Euler–Lagrange equation. It also discusses variational problems subject to constraints, the inverse problem of variational calculus, and the direct solution techniques of variational problems, such as the Ritz, Galerkin, and Kantorovich methods. With an emphasis on applications, the second part details the geodesic concept of differential geometry and its extensions to higher order spaces. It covers the variational origin of natural splines and the variational formulation of B-splines under various constraints. This section also focuses on analytic and computational mechanics, explaining classical mechanical problems and Lagrange’s equations of motion.

The Inverse Problem of the Calculus of Variations

Dmitry V. Zenkov
The Inverse Problem of the Calculus of Variations Book PDF

Author : Dmitry V. Zenkov
Publisher : Springer
Page : 296 pages
File Size : 51,9 Mb
Release : 2015-10-15
Category : Mathematics
ISBN : 9789462391093

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The Inverse Problem of the Calculus of Variations by Dmitry V. Zenkov Pdf

The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).