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Author : Gary Francis Roach
Publisher : Unknown
Page : 302 pages
File Size : 41,7 Mb
Release : 1970
Category : Mathematics
ISBN : UCSD:31822014275655
Author : Dean G. Duffy
Publisher : CRC Press
Page : 461 pages
File Size : 46,8 Mb
Release : 2001-05-31
Category : Mathematics
ISBN : 9781420034790
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
Author : Michael D. Greenberg
Publisher : Courier Dover Publications
Page : 164 pages
File Size : 55,8 Mb
Release : 2015-08-19
Category : Mathematics
ISBN : 9780486797960
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.
Author : Prem K. Kythe
Publisher : CRC Press
Page : 382 pages
File Size : 43,7 Mb
Release : 2011-01-21
Category : Mathematics
ISBN : 9781439840092
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
Author : Yuri A. Melnikov,Max Y. Melnikov
Publisher : Walter de Gruyter
Page : 448 pages
File Size : 48,7 Mb
Release : 2012-04-02
Category : Mathematics
ISBN : 9783110253399
Green's functions represent one of the classical and widely used issues in the area of differential equations. This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. The book is attractive for practical needs: It contains many easily computable or computer friendly representations of Green's functions, includes all the standard Green's functions and many novel ones, and provides innovative and new approaches that might lead to Green's functions. The book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations.
Author : Alberto Cabada
Publisher : Springer Science & Business Media
Page : 180 pages
File Size : 51,7 Mb
Release : 2013-11-29
Category : Mathematics
ISBN : 9781461495062
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.
Author : Ivar Stakgold,Michael J. Holst
Publisher : John Wiley & Sons
Page : 883 pages
File Size : 54,6 Mb
Release : 2011-03-01
Category : Mathematics
ISBN : 9780470906521
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.
Author : Prem K. Kythe
Publisher : Unknown
Page : 128 pages
File Size : 47,5 Mb
Release : 2011
Category : Electronic book
ISBN : OCLC:1066581433
Author : H. M. Fried
Publisher : Cambridge University Press
Page : 183 pages
File Size : 50,8 Mb
Release : 2002-10-10
Category : Science
ISBN : 9781139433051
This book presents a functional approach to the construction, use and approximation of Green's functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics.
Author : Alberto Cabada
Publisher : Unknown
Page : 184 pages
File Size : 40,7 Mb
Release : 2013-12-31
Category : Electronic
ISBN : 1461495075
Author : G. F. Roach
Publisher : Cambridge University Press
Page : 344 pages
File Size : 51,6 Mb
Release : 1982-05-27
Category : Mathematics
ISBN : 0521238900
Green's functions are an important tool used in solving boundary value problems associated with ordinary and partial differential equations. This self-contained and systematic introduction to Green's functions has been written with applications in mind. The material is presented in an unsophisticated and rather more practical manner than usual. Consequently advanced undergraduates and beginning postgraduate students in mathematics and the applied sciences will find this account particularly attractive. Many exercises and examples have been supplied throughout to reinforce comprehension and to increase familiarity with the technique.
Author : Gabriel Barton
Publisher : Oxford University Press
Page : 484 pages
File Size : 46,9 Mb
Release : 1989
Category : Mathematics
ISBN : 0198519982
This text takes the student with a background in undergraduate 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 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 the problem. The book is based on the author's extensive teaching experience.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 43,7 Mb
Release : 1985
Category : Differential equations
ISBN : OCLC:861474979
Author : G. Rickayzen
Publisher : Courier Corporation
Page : 368 pages
File Size : 49,7 Mb
Release : 2013-06-03
Category : Science
ISBN : 9780486315867
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.
Author : Anatoliĭ Grigorʹevich Butkovskiĭ
Publisher : Unknown
Page : 248 pages
File Size : 51,5 Mb
Release : 1982
Category : Differential equations
ISBN : UCSD:31822010199453
