Calculus Of Variations Applications And Computations
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Calculus Of Variations Applications And Computations
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Author : C Bandle
language : en
Publisher: CRC Press
Release Date : 1995-04-26
Calculus Of Variations Applications And Computations written by C Bandle and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-26 with Mathematics categories.
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.
Calculus Of Variations Applications And Computations
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Author : Catherine Bandle
language : en
Publisher:
Release Date : 1995
Calculus Of Variations Applications And Computations written by Catherine Bandle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Calculus of variations categories.
Introduction To The Calculus Of Variations And Control With Modern Applications
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Author : John A. Burns
language : en
Publisher: CRC Press
Release Date : 2013-08-28
Introduction To The Calculus Of Variations And Control With Modern Applications written by John A. Burns and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-28 with Mathematics categories.
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
Calculus Of Variations With Applications To Physics And Engineering
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Author : Robert Weinstock
language : en
Publisher: READ BOOKS
Release Date : 2008-11
Calculus Of Variations With Applications To Physics And Engineering written by Robert Weinstock and has been published by READ BOOKS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11 with Mathematics categories.
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.
Real Analysis And Applications
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Author : Frank Morgan
language : en
Publisher: American Mathematical Society
Release Date : 2021-10-25
Real Analysis And Applications written by Frank Morgan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-25 with Mathematics categories.
Real Analysis and Applications starts with a streamlined, but complete approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]." The text not only provides clear, logical proofs, but also shows the student how to come up with them. The excellent exercises come with select solutions in the back. Here is a text which makes it possible to do the full theory and significant applications in one semester. Frank Morgan is the author of six books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this applied version of his Real Analysis text, Morgan brings his famous direct style to the growing numbers of potential mathematics majors who want to see applications right along with the theory.
Applied Calculus Of Variations For Engineers
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Author : Louis Komzsik
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Applied Calculus Of Variations For Engineers written by Louis Komzsik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.
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.
Fundamental Theories And Their Applications Of The Calculus Of Variations
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Author : Dazhong Lao
language : en
Publisher: Springer Nature
Release Date : 2020-09-02
Fundamental Theories And Their Applications Of The Calculus Of Variations written by Dazhong Lao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-02 with Technology & Engineering categories.
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.
Calculus Of Variations
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Author : Charles R. MacCluer
language : en
Publisher: Courier Corporation
Release Date : 2013-05-20
Calculus Of Variations written by Charles R. MacCluer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-20 with Mathematics categories.
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 Methods With Applications In Science And Engineering
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Author : Kevin W. Cassel
language : en
Publisher: Cambridge University Press
Release Date : 2013-07-22
Variational Methods With Applications In Science And Engineering written by Kevin W. Cassel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-22 with Technology & Engineering categories.
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.
A Practical Guide To The Invariant Calculus
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Author : Elizabeth Louise Mansfield
language : en
Publisher: Cambridge University Press
Release Date : 2010-04-29
A Practical Guide To The Invariant Calculus written by Elizabeth Louise Mansfield and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-29 with Mathematics categories.
This book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail. The author demonstrates how new ideas lead to significant progress in two main applications: the solution of invariant ordinary differential equations and the structure of Euler-Lagrange equations and conservation laws of variational problems. The expository language used here is primarily that of undergraduate calculus rather than differential geometry, making the topic more accessible to a student audience. More sophisticated ideas from differential topology and Lie theory are explained from scratch using illustrative examples and exercises. This book is ideal for graduate students and researchers working in differential equations, symbolic computation, applications of Lie groups and, to a lesser extent, differential geometry.