Greens Functions And Boundary Value Problems

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Green's Functions and Boundary Value Problems

Author : Ivar Stakgold
Publisher : John Wiley & Sons
ISBN 13 : 0470906529
Total Pages : 883 pages
Book Rating : 4.4/5 (79 download)

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Book Synopsis Green's Functions and Boundary Value Problems by : Ivar Stakgold

Download or read book Green's Functions and Boundary Value Problems written by Ivar Stakgold and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 883 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics for the Physical Sciences

Author : Leslie Copley
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110426242
Total Pages : 559 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Mathematics for the Physical Sciences by : Leslie Copley

Download or read book Mathematics for the Physical Sciences written by Leslie Copley and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-03-30 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Green's Functions and Linear Differential Equations

Author : Prem K. Kythe
Publisher : CRC Press
ISBN 13 : 1439840091
Total Pages : 382 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Green's Functions and Linear Differential Equations by : Prem K. Kythe

Download or read book Green's Functions and Linear Differential Equations written by Prem K. Kythe and published by CRC Press. This book was released on 2011-01-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Green's Functions with Applications

Author : Dean G. Duffy
Publisher : CRC Press
ISBN 13 : 1482251035
Total Pages : 685 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Green's Functions with Applications by : Dean G. Duffy

Download or read book Green's Functions with Applications written by Dean G. Duffy and published by CRC Press. This book was released on 2015-03-10 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 in the Theory of Ordinary Differential Equations

Author : Alberto Cabada
Publisher : Springer Science & Business Media
ISBN 13 : 1461495067
Total Pages : 168 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Green’s Functions in the Theory of Ordinary Differential Equations by : Alberto Cabada

Download or read book Green’s Functions in the Theory of Ordinary Differential Equations written by Alberto Cabada and published by Springer Science & Business Media. This book was released on 2013-11-29 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Yuri A. Melnikov
Publisher : Springer
ISBN 13 : 3319572431
Total Pages : 198 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Green's Functions by : Yuri A. Melnikov

Download or read book Green's Functions written by Yuri A. Melnikov and published by Springer. This book was released on 2017-05-08 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch. Green's functions is an instrument easily accessible to practitioners who are engaged in design and exploitation of machines and structures in modern engineering practice. To date, there are no books available on the market that are devoted to the Green's function formalism for equations covered in this volume. The reader, with an undergraduate background in applied mathematics, can become an active user of the Green's function approach. For the first time, Green's functions are discussed for a specific class of problems dealing with potential fields induced in thin-wall structures and therefore, the reader will have first-hand access to a novel issue. This Work is accessible to researchers in applied mathematics, mechanics, and relevant disciplines such as engineering, as well as to upper level undergraduates and graduate students.

Partial Differential Equations and Boundary-Value Problems with Applications

Author : Mark A. Pinsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821868896
Total Pages : 545 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Partial Differential Equations and Boundary-Value Problems with Applications by : Mark A. Pinsky

Download or read book Partial Differential Equations and Boundary-Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.

Boundary Value Problems of Mathematical Physics

Author : Ivar Stakgold
Publisher : SIAM
ISBN 13 : 0898714567
Total Pages : 1156 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Boundary Value Problems of Mathematical Physics by : Ivar Stakgold

Download or read book Boundary Value Problems of Mathematical Physics written by Ivar Stakgold and published by SIAM. This book was released on 2000-06-30 with total page 1156 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 30 years, this two-volume set has helped prepare graduate students to use partial differential equations and integral equations to handle significant problems arising in applied mathematics, engineering, and the physical sciences. Originally published in 1967, this graduate-level introduction is devoted to the mathematics needed for the modern approach to boundary value problems using Green's functions and using eigenvalue expansions. Now a part of SIAM's Classics series, these volumes contain a large number of concrete, interesting examples of boundary value problems for partial differential equations that cover a variety of applications that are still relevant today. For example, there is substantial treatment of the Helmholtz equation and scattering theory?subjects that play a central role in contemporary inverse problems in acoustics and electromagnetic theory.

Green's Functions with Applications

Author : Dean G. Duffy
Publisher : CRC Press
ISBN 13 : 1420034790
Total Pages : 461 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Green's Functions with Applications by : Dean G. Duffy

Download or read book Green's Functions with Applications written by Dean G. Duffy and published by CRC Press. This book was released on 2001-05-31 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Mixed Boundary Value Problems

Author : Dean G. Duffy
Publisher : CRC Press
ISBN 13 : 9781420010947
Total Pages : 488 pages
Book Rating : 4.0/5 (19 download)

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Book Synopsis Mixed Boundary Value Problems by : Dean G. Duffy

Download or read book Mixed Boundary Value Problems written by Dean G. Duffy and published by CRC Press. This book was released on 2008-03-26 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for Solving Mixed Boundary Value Problems An up-to-date treatment of the subject, Mixed Boundary Value Problems focuses on boundary value problems when the boundary condition changes along a particular boundary. The book often employs numerical methods to solve mixed boundary value problems and the associated integral equations. Straightforward Presentation of Mathematical Techniques The author first provides examples of mixed boundary value problems and the mathematical background of integral functions and special functions. He then presents classic mathematical physics problems to explain the origin of mixed boundary value problems and the mathematical techniques that were developed to handle them. The remaining chapters solve various mixed boundary value problems using separation of variables, transform methods, the Wiener–Hopf technique, Green’s function, and conformal mapping. Decipher Mixed Boundary Value Problems That Occur in Diverse Fields Including MATLAB® to help with problem solving, this book provides the mathematical skills needed for the solution of mixed boundary value problems.

Green's Functions

Author : Yuri A. Melnikov
Publisher : Walter de Gruyter
ISBN 13 : 3110253399
Total Pages : 447 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Green's Functions by : Yuri A. Melnikov

Download or read book Green's Functions written by Yuri A. Melnikov and published by Walter de Gruyter. This book was released on 2012-04-02 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. This 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.

Applications of Green's Functions in Science and Engineering

Author : Michael D. Greenberg
Publisher : Courier Dover Publications
ISBN 13 : 0486797961
Total Pages : 164 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis Applications of Green's Functions in Science and Engineering by : Michael D. Greenberg

Download or read book Applications of Green's Functions in Science and Engineering written by Michael D. Greenberg and published by Courier Dover Publications. This book was released on 2015-08-19 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Equivalence, Invariants and Symmetry

Author : Peter J. Olver
Publisher : Cambridge University Press
ISBN 13 : 9780521478113
Total Pages : 546 pages
Book Rating : 4.4/5 (781 download)

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Book Synopsis Equivalence, Invariants and Symmetry by : Peter J. Olver

Download or read book Equivalence, Invariants and Symmetry written by Peter J. Olver and published by Cambridge University Press. This book was released on 1995-06-30 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

Boundary Value Problems, Weyl Functions, and Differential Operators

Author : Jussi Behrndt
Publisher : Springer Nature
ISBN 13 : 3030367142
Total Pages : 772 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Boundary Value Problems, Weyl Functions, and Differential Operators by : Jussi Behrndt

Download or read book Boundary Value Problems, Weyl Functions, and Differential Operators written by Jussi Behrndt and published by Springer Nature. This book was released on 2020-01-03 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.

Green's Functions and Finite Elements

Author : Friedel Hartmann
Publisher : Springer Science & Business Media
ISBN 13 : 3642295231
Total Pages : 335 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Green's Functions and Finite Elements by : Friedel Hartmann

Download or read book Green's Functions and Finite Elements written by Friedel Hartmann and published by Springer Science & Business Media. This book was released on 2012-08-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book elucidates how Finite Element methods look like from the perspective of Green’s functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Green’s functions and how approximating of Green’s functions. It discusses in detail the discretization error and shows that are coherent with the strategy of “goal oriented refinement”. The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.

Green's Functions: Introductory Theory with Applications

Author : Gary Francis Roach
Publisher :
ISBN 13 :
Total Pages : 302 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Green's Functions: Introductory Theory with Applications by : Gary Francis Roach

Download or read book Green's Functions: Introductory Theory with Applications written by Gary Francis Roach and published by . This book was released on 1970 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems

Author : Graef John R
Publisher : World Scientific
ISBN 13 : 9813274042
Total Pages : 344 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems by : Graef John R

Download or read book Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems written by Graef John R and published by World Scientific. This book was released on 2018-09-18 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.A discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.The important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.While this Volume II complements , it can be used as a stand-alone work.