Variational Methods for Eigenvalue Problems
Variational Methods for Eigenvalue Problems

Author: S. H. Gould

Publisher: University of Toronto Press

Published: 1966-12-15

Total Pages: 321

ISBN-13: 1487597711

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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.

Eigenvalues of Inhomogeneous Structures
Eigenvalues of Inhomogeneous Structures

Author: Isaac Elishakoff

Publisher: CRC Press

Published: 2004-10-28

Total Pages: 746

ISBN-13: 142003801X

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The engineering community generally accepts that there exists only a small set of closed-form solutions for simple cases of bars, beams, columns, and plates. Despite the advances in powerful computing and advanced numerical techniques, closed-form solutions remain important for engineering; these include uses for preliminary design, for evaluation

Extremum Problems for Eigenvalues of Elliptic Operators
Extremum Problems for Eigenvalues of Elliptic Operators

Author: Antoine Henrot

Publisher: Springer Science & Business Media

Published: 2006-08-29

Total Pages: 205

ISBN-13: 3764377062

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This book focuses on extremal problems. For instance, it seeks a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. Also considered is the case of functions of eigenvalues. The text probes similar questions for other elliptic operators, such as Schrodinger, and explores optimal composites and optimal insulation problems in terms of eigenvalues.

Methods of Mathematical Physics
Methods of Mathematical Physics

Author: Richard Courant

Publisher: John Wiley & Sons

Published: 2008-09-26

Total Pages: 575

ISBN-13: 3527617221

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Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953.

The Numerical Solution of Ordinary and Partial Differential Equations
The Numerical Solution of Ordinary and Partial Differential Equations

Author: Granville Sewell

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 284

ISBN-13: 1483259145

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The Numerical Solution of Ordinary and Partial Differential Equations is an introduction to the numerical solution of ordinary and partial differential equations. Finite difference methods for solving partial differential equations are mostly classical low order formulas, easy to program but not ideal for problems with poorly behaved solutions or (especially) for problems in irregular multidimensional regions. FORTRAN77 programs are used to implement many of the methods studied. Comprised of six chapters, this book begins with a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when differential equations are solved. The next four chapters deal with the more commonly used finite difference methods for solving a variety of problems, including both ordinary differential equations and partial differential equations, and both initial value and boundary value problems. The final chapter is an overview of the basic ideas behind the finite element method and covers the Galerkin method for boundary value problems. Examples using piecewise linear trial functions, cubic hermite trial functions, and triangular elements are presented. This monograph is appropriate for senior-level undergraduate or first-year graduate students of mathematics.

Mathematical Analysis of Physical Problems
Mathematical Analysis of Physical Problems

Author: Philip Russell Wallace

Publisher: Courier Corporation

Published: 1984-01-01

Total Pages: 644

ISBN-13: 0486646769

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This mathematical reference for theoretical physics employs common techniques and concepts to link classical and modern physics. It provides the necessary mathematics to solve most of the problems. Topics include the vibrating string, linear vector spaces, the potential equation, problems of diffusion and attenuation, probability and stochastic processes, and much more. 1972 edition.

Operator Theory and Boundary Eigenvalue Problems
Operator Theory and Boundary Eigenvalue Problems

Author: I. Gohberg

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 327

ISBN-13: 3034891067

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The Workshop on Operator Theory and Boundary Eigenvalue Problems was held at the Technical University, Vienna, Austria, July 27 to 30, 1993. It was the seventh workshop in the series of IWOTA (International Workshops on Operator Theory and Applications). The main topics at the workshop were interpolation problems and analytic matrix functions, operator theory in spaces with indefinite scalar products, boundary value problems for differential and functional-differential equations and systems theory and control. The workshop covered different aspects, starting with abstract operator theory up to contrete applications. The papers in these proceedings provide an accurate cross section of the lectures presented at the workshop. This book will be of interest to a wide group of pure and applied mathematicians.

Mathematics for the Physical Sciences
Mathematics for the Physical Sciences

Author: Leslie Copley

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2015-03-30

Total Pages: 498

ISBN-13: 3110426242

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The book begins with a thorough introduction to complex analysis, which is then used to understand the properties of ordinary differential equations and their solutions. The latter are obtained in both series and integral representations. Integral transforms are introduced, providing an opportunity to complement complex analysis with techniques that flow from an algebraic approach. This moves naturally into a discussion of eigenvalue and boundary vale problems. A thorough discussion of multi-dimensional boundary value problems then introduces the reader to the fundamental partial differential equations and “special functions” of mathematical physics. Moving to non-homogeneous boundary value problems the reader is presented with an analysis of Green’s functions from both analytical and algebraic points of view. This leads to a concluding chapter on integral equations.