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Author: Ivar Stakgold
Publisher: John Wiley & Sons
ISBN: 0470906529
Category : Mathematics
Languages : en
Pages : 883
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Book Description
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: Ivar Stakgold
Publisher: John Wiley & Sons
ISBN: 0470906529
Category : Mathematics
Languages : en
Pages : 883
Get Book Here
Book Description
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: Ivar Stakgold
Publisher: John Wiley & Sons
ISBN: 0470609702
Category : Mathematics
Languages : en
Pages : 883
Get Book Here
Book Description
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: CRC Press
ISBN: 1439840091
Category : Mathematics
Languages : en
Pages : 376
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Book Description
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
Publisher: Springer
ISBN: 3319572431
Category : Mathematics
Languages : en
Pages : 211
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Book Description
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.
Author: Dean G. Duffy
Publisher: CRC Press
ISBN: 1482251035
Category : Mathematics
Languages : en
Pages : 673
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Book Description
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.
Author: Leslie Copley
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110426242
Category : Mathematics
Languages : en
Pages : 498
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Book Description
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.
Author: Alberto Cabada
Publisher: Springer Science & Business Media
ISBN: 1461495067
Category : Mathematics
Languages : en
Pages : 180
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Book Description
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: Tyn Myint-U
Publisher: Springer Science & Business Media
ISBN: 0817645608
Category : Mathematics
Languages : en
Pages : 790
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Book Description
This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry; solutions are provided.
Author: Mark A. Pinsky
Publisher: American Mathematical Soc.
ISBN: 0821868896
Category : Mathematics
Languages : en
Pages : 545
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Book Description
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.
Author: Qing-Hua Qin
Publisher: Elsevier
ISBN: 0080478069
Category : Technology & Engineering
Languages : en
Pages : 267
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Book Description
Green's Function and Boundary Elements of Multifield Materials contains a comprehensive treatment of multifield materials under coupled thermal, magnetic, electric, and mechanical loads. Its easy-to-understand text clarifies some of the most advanced techniques for deriving Green's function and the related boundary element formulation of magnetoelectroelastic materials: Radon transform, potential function approach, Fourier transform. Our hope in preparing this book is to attract interested readers and researchers to a new field that continues to provide fascinating and technologically important challenges. You will benefit from the authors' thorough coverage of general principles for each topic, followed by detailed mathematical derivation and worked examples as well as tables and figures where appropriate. - In-depth explanations of the concept of Green's function - Coupled thermo-magneto-electro-elastic analysis - Detailed mathematical derivation for Green's functions
