Variational Methods for Eigenvalue Problems PDF Download
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Author: Sydney Henry Gould
Publisher: Courier Corporation
ISBN: 9780486687124
Category : Science
Languages : en
Pages : 210
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Book Description
Purely mathematical treatment offers simple exposition of general theory of variational methods with special reference to the vibrating plate. No math beyond basic calculus. Includes exercises. 1957 edition.
Author: Sydney Henry Gould
Publisher: Courier Corporation
ISBN: 9780486687124
Category : Science
Languages : en
Pages : 210
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Book Description
Purely mathematical treatment offers simple exposition of general theory of variational methods with special reference to the vibrating plate. No math beyond basic calculus. Includes exercises. 1957 edition.
Author: S. H. Gould
Publisher: University of Toronto Press
ISBN: 1487597711
Category : Education
Languages : en
Pages : 321
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Book Description
The first edition of this book gave a systematic exposition of the Weinstein method of calculating lower bounds of eigenvalues by means of intermediate problems. From the reviews of this edition and from subsequent shorter expositions it has become clear that the method is of considerable interest to the mathematical world; this interest has increased greatly in recent years by the success of some mathematicians in simplifying and extending the numerical applications, particularly in quantum mechanics. Until now new developments have been available only in articles scattered throughout the literature: this second edition presents them systematically in the framework of the material contained in the first edition, which is retained in somewhat modified form.
Author: S. H. Gould
Publisher: Courier Corporation
ISBN: 0486165809
Category : Science
Languages : en
Pages : 210
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Book Description
Purely mathematical treatment offers simple exposition of general theory of variational methods with special reference to the vibrating plate. No math beyond basic calculus. Includes exercises. 1957 edition.
Author: Dumitru Motreanu
Publisher: Springer Science & Business Media
ISBN: 9781402013850
Category : Mathematics
Languages : en
Pages : 400
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Book Description
This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.
Author: Roland Glowinski
Publisher: SIAM
ISBN: 1611973783
Category : Mathematics
Languages : en
Pages : 473
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Book Description
Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems?addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics. This book differs from others on the topic by presenting examples of the power and versatility of operator-splitting methods; providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly nonsmooth) problems from science and engineering; and showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems. The book provides useful insights suitable for advanced graduate students, faculty, and researchers in applied and computational mathematics as well as research engineers, mathematical physicists, and systems engineers.
Author: H. F. Weinberger
Publisher: SIAM
ISBN: 089871012X
Category : Mathematics
Languages : en
Pages : 163
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Book Description
Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships. A mapping principle is presented to connect many of the methods. The eigenvalue problems studied are linear, and linearization is shown to give important information about nonlinear problems. Linear vector spaces and their properties are used to uniformly describe the eigenvalue problems presented that involve matrices, ordinary or partial differential operators, and integro-differential operators.
Author: S. Nemat-Nasser
Publisher: Elsevier
ISBN: 1483145832
Category : Technology & Engineering
Languages : en
Pages : 429
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Book Description
Variational Methods in the Mechanics of Solids contains the proceedings of the International Union of Theoretical and Applied Mechanics Symposium on Variational Methods in the Mechanics of Solids, held at Northwestern University in Evanston, Illinois, on September 11-13, 1978. The papers focus on advances in the application of variational methods to a variety of mathematically and technically significant problems in solid mechanics. The discussions are organized around three themes: thermomechanical behavior of composites, elastic and inelastic boundary value problems, and elastic and inelastic dynamic problems. This book is comprised of 58 chapters and opens by addressing some questions of asymptotic expansions connected with composite and with perforated materials. The following chapters explore mathematical and computational methods in plasticity; variational irreversible thermodynamics of open physical-chemical continua; macroscopic behavior of elastic material with periodically spaced rigid inclusions; and application of the Lanczos method to structural vibration. Finite deformation of elastic beams and complementary theorems of solid mechanics are also considered, along with numerical contact elastostatics; periodic solutions in plasticity and viscoplasticity; and the convergence of the mixed finite element method in linear elasticity. This monograph will appeal to practitioners of mathematicians as well as theoretical and applied mechanics.
Author: Bruce A. Finlayson
Publisher: SIAM
ISBN: 1611973236
Category : Mathematics
Languages : en
Pages : 429
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Book Description
This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element method for more complex problems, and provides detailed information on error bounds. Problem sets make this book ideal for self-study or as a course text.
Author: Donald R. Smith
Publisher: Courier Corporation
ISBN: 9780486404554
Category : Mathematics
Languages : en
Pages : 406
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Book Description
Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.
Author: Philippe Blanchard
Publisher: Springer Science & Business Media
ISBN: 1461200490
Category : Mathematics
Languages : en
Pages : 469
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Book Description
Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.
