Asymptotic Methods In Equations Of Mathematical Physics

DOWNLOAD

Download Asymptotic Methods In Equations Of Mathematical Physics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Asymptotic Methods In Equations Of Mathematical Physics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Asymptotic Methods In Equations Of Mathematical Physics

DOWNLOAD
Author : B Vainberg
language : en
Publisher: CRC Press
Release Date : 1989-02-25

Asymptotic Methods In Equations Of Mathematical Physics written by B Vainberg and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-02-25 with Science categories.

Typed English translation of a monograph first published (in Russian) in 1982. Provides graduate students and researchers with usefully detailed discussion of most of the asymptotic methods standard these days to the work of mathematical physicists. The author prefers not to dwell in the heights of abstraction; he has written a broadly intelligble book, which is informed at every point by his secure command of major physical applications. An expensive but valuable contribution to the literature of an important but too-little-written- about field. Twelve chapters, references. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Asymptotic Methods In Equations Of Mathematical Physics

DOWNLOAD
Author : B Vainberg
language : en
Publisher: CRC Press
Release Date : 2024-12-20

Asymptotic Methods In Equations Of Mathematical Physics written by B Vainberg and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-20 with Science categories.

This book provides a single source for both students and advanced researchers on asymptotic methods employed in the linear problems of mathematical physics. It opens with a section based on material from special courses given by the author, which gives detailed coverage of classical material on the equations of mathematical physics and their applications, and includes a simple explanation of the Maslov Canonical Operator method. The book goes on to present more advanced material from the author's own research. Topics range from radiation conditions and the principle of limiting absorption for general exterior problems, to complete asymptotic expansion of spectral function of equations over all of space. This book serves both as a manual and teaching aid for students of mathematics and physics and, in summarizing for the first time in a monograph problems previously investigated in journal articles, as a comprehensive reference for advanced researchers.

Introduction To Asymptotic Methods

DOWNLOAD
Author : David Y. Gao
language : en
Publisher: CRC Press
Release Date : 2006-05-03

Introduction To Asymptotic Methods written by David Y. Gao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-03 with Mathematics categories.

Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m

Advanced Mathematical Methods For Scientists And Engineers I

DOWNLOAD
Author : Carl M. Bender
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Advanced Mathematical Methods For Scientists And Engineers I written by Carl M. Bender 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 2013-03-09 with Mathematics categories.

The triumphant vindication of bold theories-are these not the pride and justification of our life's work? -Sherlock Holmes, The Valley of Fear Sir Arthur Conan Doyle The main purpose of our book is to present and explain mathematical methods for obtaining approximate analytical solutions to differential and difference equations that cannot be solved exactly. Our objective is to help young and also establiShed scientists and engineers to build the skills necessary to analyze equations that they encounter in their work. Our presentation is aimed at developing the insights and techniques that are most useful for attacking new problems. We do not emphasize special methods and tricks which work only for the classical transcendental functions; we do not dwell on equations whose exact solutions are known. The mathematical methods discussed in this book are known collectively as asymptotic and perturbative analysis. These are the most useful and powerful methods for finding approximate solutions to equations, but they are difficult to justify rigorously. Thus, we concentrate on the most fruitful aspect of applied analysis; namely, obtaining the answer. We stress care but not rigor. To explain our approach, we compare our goals with those of a freshman calculus course. A beginning calculus course is considered successful if the students have learned how to solve problems using calculus.

Partial Differential Equations V

DOWNLOAD
Author : M.V. Fedoryuk
language : en
Publisher: Springer
Release Date : 2012-10-11

Partial Differential Equations V written by M.V. Fedoryuk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-11 with Mathematics categories.

In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.

Asymptotic Theory Of Dynamic Boundary Value Problems In Irregular Domains

DOWNLOAD
Author : Dmitrii Korikov
language : en
Publisher: Springer Nature
Release Date : 2021-04-01

Asymptotic Theory Of Dynamic Boundary Value Problems In Irregular Domains written by Dmitrii Korikov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-01 with Mathematics categories.

This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.

Asymptotic Methods For Integrals

DOWNLOAD
Author : Nico M. Temme
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015

Asymptotic Methods For Integrals written by Nico M. Temme and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Differential equations categories.

This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.

Partial Differential Equations V

DOWNLOAD
Author : M.V. Fedoryuk
language : en
Publisher: Springer
Release Date : 2011-09-27

Partial Differential Equations V written by M.V. Fedoryuk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-27 with Mathematics categories.

In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.

Partial Differential Equations In Classical Mathematical Physics

DOWNLOAD
Author : Isaak Rubinstein
language : en
Publisher: Cambridge University Press
Release Date : 1998-04-28

Partial Differential Equations In Classical Mathematical Physics written by Isaak Rubinstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-28 with Mathematics categories.

The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.

Differential Equations Asymptotic Theory In Mathematical Physics

DOWNLOAD
Author : Zhen Hua
language : en
Publisher: World Scientific
Release Date : 2004

Differential Equations Asymptotic Theory In Mathematical Physics written by Zhen Hua and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings? (ISTP? / ISI Proceedings)? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences