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Author: Yuri A. Melnikov
Publisher: Springer Science & Business Media
ISBN: 0817682805
Category : Mathematics
Languages : en
Pages : 171
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Book Description
Green's Functions and Infinite Products provides a thorough introduction to the classical subjects of the construction of Green's functions for the two-dimensional Laplace equation and the infinite product representation of elementary functions. Every chapter begins with a review guide, outlining the basic concepts covered. A set of carefully designed challenging exercises is available at the end of each chapter to provide the reader with the opportunity to explore the concepts in more detail. Hints, comments, and answers to most of those exercises can be found at the end of the text. In addition, several illustrative examples are offered at the end of most sections. This text is intended for an elective graduate course or seminar within the scope of either pure or applied mathematics.
Author: Yuri A. Melnikov
Publisher: Springer Science & Business Media
ISBN: 0817682805
Category : Mathematics
Languages : en
Pages : 171
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Book Description
Green's Functions and Infinite Products provides a thorough introduction to the classical subjects of the construction of Green's functions for the two-dimensional Laplace equation and the infinite product representation of elementary functions. Every chapter begins with a review guide, outlining the basic concepts covered. A set of carefully designed challenging exercises is available at the end of each chapter to provide the reader with the opportunity to explore the concepts in more detail. Hints, comments, and answers to most of those exercises can be found at the end of the text. In addition, several illustrative examples are offered at the end of most sections. This text is intended for an elective graduate course or seminar within the scope of either pure or applied mathematics.
Author: Friedel Hartmann
Publisher: Springer Science & Business Media
ISBN: 3642295231
Category : Science
Languages : en
Pages : 335
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Book Description
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.
Author: Dean G. Duffy
Publisher: CRC Press
ISBN: 1482251035
Category : Mathematics
Languages : en
Pages : 685
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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: Michael D. Greenberg
Publisher: Courier Dover Publications
ISBN: 0486797961
Category : Mathematics
Languages : en
Pages : 164
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Book Description
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: Kevin Cole
Publisher: Taylor & Francis
ISBN: 143989521X
Category : Science
Languages : en
Pages : 666
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Book Description
Since its publication more than 15 years ago, Heat Conduction Using Green's Functions has become the consummate heat conduction treatise from the perspective of Green's functions-and the newly revised Second Edition is poised to take its place. Based on the authors' own research and classroom experience with the material, this book organizes the so
Author: Ivar Stakgold
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 664
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Book Description
This revised and updated Second Edition of Green's Functions and Boundary Value Problems maintains a careful balance between sound mathematics and meaningful applications. Central to the text is a down-to-earth approach that shows the reader how to use differential and integral equations when tackling significant problems in the physical sciences, engineering, and applied mathematics. Ivar Stakgold incorporates developments that have altered the field of applied mathematics in recent decades-particularly in areas of modeling, Fourier analysis, fixed-point theorems, inverse problems, asymptotics, and nonlinear methods. This modernized text, however, retains the many features that made its predecessor one of the most successful graduate-level texts of its kind, including: A unique blend of topics A balanced discussion of theory and applications 44 illustrations and numerous practical examples that supplement the text Chapter introductions and clear explanations of basic concepts Plentiful exercises, many of which are new to this edition Green's Functions and Boundary Value Problems is an ideal text for a modern course in applied mathematics designed for students in the physical sciences, engineering, and mathematics. It is also an excellent reference for practicing professionals in these areas.
Author: Yuri A. Melnikov
Publisher: Walter de Gruyter
ISBN: 3110253399
Category : Mathematics
Languages : en
Pages : 447
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Book Description
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.
Author: Prem K. Kythe
Publisher: CRC Press
ISBN: 1439840091
Category : Mathematics
Languages : en
Pages : 382
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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: Alberto Cabada
Publisher: Springer Science & Business Media
ISBN: 1461495067
Category : Mathematics
Languages : en
Pages : 168
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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: Gary Francis Roach
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 302
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Book Description
