Green S Functions With Applications

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Green S Functions With Applications

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Author : Dean G. Duffy
language : en
Publisher: CRC Press
Release Date : 2015-03-10

Green S Functions With Applications written by Dean G. Duffy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-10 with Mathematics categories.

Since publication of the first edition over a decade ago, Green’s Functions with Applications has provided applied scientists and engineers with a systematic approach to the various methods available for deriving a Green’s function. This fully revised Second Edition retains the same purpose, but has been meticulously updated to reflect the current state of the art. The book opens with necessary background information: a new chapter on the historical development of the Green’s function, coverage of the Fourier and Laplace transforms, a discussion of the classical special functions of Bessel functions and Legendre polynomials, and a review of the Dirac delta function. The text then presents Green’s functions for each class of differential equation (ordinary differential, wave, heat, and Helmholtz equations) according to the number of spatial dimensions and the geometry of the domain. Detailing step-by-step methods for finding and computing Green’s functions, each chapter contains a special section devoted to topics where Green’s functions particularly are useful. For example, in the case of the wave equation, Green’s functions are beneficial in describing diffraction and waves. To aid readers in developing practical skills for finding Green’s functions, worked examples, problem sets, and illustrations from acoustics, applied mechanics, antennas, and the stability of fluids and plasmas are featured throughout the text. A new chapter on numerical methods closes the book. Included solutions and hundreds of references to the literature on the construction and use of Green's functions make Green’s Functions with Applications, Second Edition a valuable sourcebook for practitioners as well as graduate students in the sciences and engineering.

Green S Functions With Applications

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Author : Dean G. Duffy
language : en
Publisher: CRC Press
Release Date : 2001-05-31

Green S Functions With Applications written by Dean G. Duffy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-31 with Mathematics categories.

Since its introduction in 1828, using Green's functions has become a fundamental mathematical technique for solving boundary value problems. Most treatments, however, focus on its theory and classical applications in physics rather than the practical means of finding Green's functions for applications in engineering and the sciences. Green's

Green S Functions In Quantum Physics

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Author : Eleftherios N. Economou
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Green S Functions In Quantum Physics written by Eleftherios N. Economou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.

In this edition the second and main part of the book has been considerably expanded as to cover important applications of the formalism. In Chap.5 a section was added outlining the extensive role of the tight binding (or equivalently the linear combination of atomic-like orbitals) approach to many branches of solid-state physics. Some additional informa tion (including a table of numerical values) regarding square and cubic lattice Green's functions were incorporated. In Chap.6 the difficult subjects of superconductivity and the Kondo effect are examined by employing an appealingly simple connection to the question of the existence of a bound state in a very shallow potential well. The existence of such a bound state depends entirely on the form of the un perturbed density of states near the end of the spectrum: if the density of states blows up there is always at least one bound state. If the density of states approaches zero continuously, a critical depth (and/or width) of the well must be reached in order to have a bound state. The borderline case of a finite discontinuity (which is very important to superconductivity and the Kondo effect) always produces a bound state with an exponentially small binding energy.

Elements Of Green S Functions And Propagation

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Author : Gabriel Barton
language : en
Publisher: Oxford University Press
Release Date : 1989

Elements Of Green S Functions And Propagation written by Gabriel Barton and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

This text takes the student with a background in the standard undergraduate courses in physics and mathematics towards the skills and insights needed for graduate work in theoretical physics. The author uses Green's functions to explore the physics of potentials, diffusion and waves. These are important phenomena of classical physics in their own right, but this study of the partial differential equations describing them also prepares the student for more advanced applications in many-body physics and field theory. Calculations are carried through in enough detail for self-study, and case histories illustrate the interplay between physical insight and mathematical formalism. The aim is to develop the habit of dialogue with the equations and the craftsmanship this fosters in tackling problems.

Green S Functions In The Theory Of Ordinary Differential Equations

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Author : Alberto Cabada
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-29

Green S Functions In The Theory Of Ordinary Differential Equations written by Alberto Cabada and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-29 with Mathematics categories.

This book provides a complete and exhaustive study of the Green’s functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value problems. Classic methods of lower and upper solutions are explored, with a particular focus on monotone iterative techniques that flow from them. In addition, Cabada proves the existence of positive solutions by constructing operators defined in cones. The book will be of interest to graduate students and researchers interested in the theoretical underpinnings of boundary value problem solutions.

Green S Functions And Linear Differential Equations

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Author : Prem K. Kythe
language : en
Publisher: CRC Press
Release Date : 2011-01-21

Green S Functions And Linear Differential Equations written by Prem K. Kythe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-21 with Mathematics categories.

Green's Functions and Linear Differential Equations: Theory, Applications, and Computation presents a variety of methods to solve linear ordinary differential equations (ODEs) and partial differential equations (PDEs). The text provides a sufficient theoretical basis to understand Green's function method, which is used to solve initial and boundary

Applications Of Green S Functions In Science And Engineering

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Author : Michael D. Greenberg
language : en
Publisher: Courier Dover Publications
Release Date : 2015-08-19

Applications Of Green S Functions In Science And Engineering written by Michael D. Greenberg and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with Mathematics categories.

In addition to coverage of Green's function, this concise introductory treatment examines boundary value problems, generalized functions, eigenfunction expansions, partial differential equations, and acoustics. Suitable for undergraduate and graduate students. 1971 edition.

Green S Functions And Condensed Matter

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Author : G. Rickayzen
language : en
Publisher: Courier Corporation
Release Date : 2013-06-03

Green S Functions And Condensed Matter written by G. Rickayzen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-03 with Science categories.

Presentation of the basic theoretical formulation of Green's functions, followed by specific applications: transport coefficients of a metal, Coulomb gas, Fermi liquids, electrons and phonons, superconductivity, superfluidity, and magnetism. 1984 edition.

Green S Functions

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Author : Gary Francis Roach
language : en
Publisher:
Release Date : 1970

Green S Functions written by Gary Francis Roach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.

Green S Functions And Boundary Value Problems

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Author : Ivar Stakgold
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-01

Green S Functions And Boundary Value Problems written by Ivar Stakgold and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Mathematics categories.

Praise for the Second Edition "This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics "No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.