Variational Calculus With Engineering Applications

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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 : 54,8 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.

Applied Calculus of Variations for Engineers

Louis Komzsik
Applied Calculus of Variations for Engineers Book PDF

Author : Louis Komzsik
Publisher : CRC Press
Page : 234 pages
File Size : 55,5 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781482253603

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Applied Calculus of Variations for Engineers by Louis Komzsik Pdf

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

Louis Komzsik
Applied Calculus of Variations for Engineers Book PDF

Author : Louis Komzsik
Publisher : CRC Press
Page : 175 pages
File Size : 40,5 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.

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 : Cambridge University Press
Page : 433 pages
File Size : 46,5 Mb
Release : 2013-07-22
Category : Mathematics
ISBN : 9781107022584

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

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

Calculus of Variations

Robert Weinstock
Calculus of Variations Book PDF

Author : Robert Weinstock
Publisher : Courier Corporation
Page : 354 pages
File Size : 55,8 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.

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 : 41,6 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.

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 : 51,8 Mb
Release : 2022-10-20
Category : Mathematics
ISBN : 9781119944386

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

VARIATIONAL CALCULUS WITH ENGINEERING APPLICATIONS 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.

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 : 48,6 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.

Advanced Engineering Analysis

L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev
Advanced Engineering Analysis Book PDF

Author : L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev
Publisher : World Scientific
Page : 500 pages
File Size : 49,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814390477

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Advanced Engineering Analysis by L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev Pdf

Advanced Engineering Analysis: The Calculus of Variations and Functional Analysis with Applications in Mechanics Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, and control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study. Book jacket.

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 : 45,7 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.

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 : 50,6 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.

Calculus of Variations

Charles R. MacCluer
Calculus of Variations Book PDF

Author : Charles R. MacCluer
Publisher : Courier Corporation
Page : 272 pages
File Size : 50,9 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.

Fundamental Theories and Their Applications of the Calculus of Variations

Dazhong Lao,Shanshan Zhao
Fundamental Theories and Their Applications of the Calculus of Variations Book PDF

Author : Dazhong Lao,Shanshan Zhao
Publisher : Springer Nature
Page : 1006 pages
File Size : 46,8 Mb
Release : 2020-09-02
Category : Technology & Engineering
ISBN : 9789811560705

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Fundamental Theories and Their Applications of the Calculus of Variations by Dazhong Lao,Shanshan Zhao Pdf

This book focuses on the calculus of variations, including fundamental theories and applications. This textbook is intended for graduate and higher-level college and university students, introducing them to the basic concepts and calculation methods used in the calculus of variations. It covers the preliminaries, variational problems with fixed boundaries, sufficient conditions of extrema of functionals, problems with undetermined boundaries, variational problems of conditional extrema, variational problems in parametric forms, variational principles, direct methods for variational problems, variational principles in mechanics and their applications, and variational problems of functionals with vector, tensor and Hamiltonian operators. Many of the contributions are based on the authors’ research, addressing topics such as the extension of the connotation of the Hilbert adjoint operator, definitions of the other three kinds of adjoint operators, the extremum function theorem of the complete functional, unified Euler equations in variational methods, variational theories of functionals with vectors, modulus of vectors, arbitrary order tensors, Hamiltonian operators and Hamiltonian operator strings, reconciling the Euler equations and the natural boundary conditions, and the application range of variational methods. The book is also a valuable reference resource for teachers as well as science and technology professionals.

Applied Calculus of Variations for Engineers, Second Edition

Louis Komzsik
Applied Calculus of Variations for Engineers Second Edition Book PDF

Author : Louis Komzsik
Publisher : Unknown
Page : 234 pages
File Size : 48,9 Mb
Release : 2014-01-01
Category : Calculus of variations
ISBN : 1306866111

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Applied Calculus of Variations for Engineers, Second Edition by Louis Komzsik Pdf

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."

Variational Principles of Continuum Mechanics with Engineering Applications

V. Komkov
Variational Principles of Continuum Mechanics with Engineering Applications Book PDF

Author : V. Komkov
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400945647

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Variational Principles of Continuum Mechanics with Engineering Applications by V. Komkov Pdf

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.