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Wavefronts And Rays As Characteristics And Asymptotics
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Book Synopsis Wavefronts and Rays as Characteristics and Asymptotics by : Andrej Bóna
Download or read book Wavefronts and Rays as Characteristics and Asymptotics written by Andrej Bóna and published by World Scientific Publishing Company. This book was released on 2014-12-30 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook — incorporated with many illuminating examples and exercises — is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation — by a pure mathematician's standards — is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and phenomena such as caustics.
Book Synopsis Wavefronts And Rays As Characteristics And Asymptotics (Third Edition) by : Andrej Bona
Download or read book Wavefronts And Rays As Characteristics And Asymptotics (Third Edition) written by Andrej Bona and published by World Scientific. This book was released on 2020-09-24 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Characteristics and asymptotics of partial differential equations play an important role in mathematical physics since they lead to insightful solutions of complex problems that might not be solvable otherwise. They constitute, however, a difficult subject, and the purpose of this book, with its additions and refinements that led to its third edition, is to present this subject in an accessible manner, without decreasing the rigor. As any method, characteristics and asymptotics have their limitations. This important issue is addressed in the last chapter, where we discuss caustics, which must be understood in applications of the method, and which constitute a fertile ground for further mathematical research.The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for senior undergraduate and graduate courses, as well as for independent studies. Six appendices are provided, which form a self-contained course on applied mathematics and can be used as a textbook on its own.
Book Synopsis Wavefronts and Rays by : Andrej Bóna
Download or read book Wavefronts and Rays written by Andrej Bóna and published by . This book was released on 2014 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Wavefronts and Rays as Characteristics and Asymptotics by : Andrej Bóna
Download or read book Wavefronts and Rays as Characteristics and Asymptotics written by Andrej Bóna and published by World Scientific Publishing Company. This book was released on 2011-05-09 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook — incorporated with many illuminating examples and exercises — is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation — by a pure mathematician's standards — is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and the phenomena such as caustics.
Book Synopsis Wavefronts and Rays as Characteristics and Asymptotics (Third Edition) by : Andrej Bona
Download or read book Wavefronts and Rays as Characteristics and Asymptotics (Third Edition) written by Andrej Bona and published by World Scientific Publishing Company. This book was released on 2020-09-14 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Characteristics and asymptotics of partial differential equations play an important role in mathematical physics since they lead to insightful solutions of complex problems that might not be solvable otherwise. They constitute, however, a difficult subject, and the purpose of this book, with its additions and refinements that led to its third edition, is to present this subject in an accessible manner, without decreasing the rigor. As any method, characteristics and asymptotics have their limitations. This important issue is addressed in the last chapter, where we discuss caustics, which must be understood in applications of the method, and which constitute a fertile ground for further mathematical research. The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for senior undergraduate and graduate courses, as well as for independent studies. Six appendices are provided, which form a self-contained course on applied mathematics and can be used as a textbook on its own.
Author :Michael A Slawinski Publisher :World Scientific Publishing Company ISBN 13 :9814644218 Total Pages :656 pages Book Rating :4.8/5 (146 download)
Book Synopsis Waves and Rays in Elastic Continua by : Michael A Slawinski
Download or read book Waves and Rays in Elastic Continua written by Michael A Slawinski and published by World Scientific Publishing Company. This book was released on 2014-12-15 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book — which is the third, significantly revised edition of the textbook originally published by Elsevier Science — emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves. The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices. In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we invoke the concept of a ray. In Variational Formulation of Rays, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols. Request Inspection Copy
Book Synopsis Asymptotic and Hybrid Methods in Electromagnetics by : I. Andronov
Download or read book Asymptotic and Hybrid Methods in Electromagnetics written by I. Andronov and published by IET. This book was released on 2005-07-18 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods provide considerable physical insight and understanding of diffraction mechanisms and are very useful in the design of electromagnetic devices such as radar targets and antennas. However, difficulties can arise when trying to solve problems using multipole and asymoptotic methods together, such as in radar crosssection objects. This new book offers a solution to this problem by combining these approaches into hybrid methods, therefore creating high demand for both understanding and learning how to apply asymptotic and hybrid methods to solve diffraction problems.
Book Synopsis Radiation and Scattering of Waves by : Leopold B. Felsen
Download or read book Radiation and Scattering of Waves written by Leopold B. Felsen and published by John Wiley & Sons. This book was released on 1994-01-15 with total page 934 pages. Available in PDF, EPUB and Kindle. Book excerpt: As relevant today as it was when it was first published 20 years ago, this book is a classic in the field. Nowhere else can you find more complete coverage of radiation and scattering of waves. The chapter: Asympotic Evaluation of Integrals is considered the definitive source for asympotic techniques. This book is essential reading for engineers, physicists and others involved in the fields of electromagnetics and acoustics. It is also an indispensable reference for advanced engineering courses.
Book Synopsis Rays, Waves, and Scattering by : John A. Adam
Download or read book Rays, Waves, and Scattering written by John A. Adam and published by Princeton University Press. This book was released on 2017-05-30 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes. Provides a panoramic look at wave motion in many different contexts Features problems and exercises throughout Includes numerous appendixes, some on topics not often covered An ideal reference book for practitioners Can also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineering Accessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable
Book Synopsis Asymptotic Perturbation Theory Of Waves by : Ostrovsky Lev
Download or read book Asymptotic Perturbation Theory Of Waves written by Ostrovsky Lev and published by World Scientific. This book was released on 2014-09-23 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theoretical ideas are illustrated by many physical examples throughout the book.
Book Synopsis Singularities of Caustics and Wave Fronts by : Vladimir Arnold
Download or read book Singularities of Caustics and Wave Fronts written by Vladimir Arnold and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi, ... ) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Book Synopsis Ray Methods for Nonlinear Waves in Fluids and Plasmas by : Marcelo Anile
Download or read book Ray Methods for Nonlinear Waves in Fluids and Plasmas written by Marcelo Anile and published by CRC Press. This book was released on 1993-05-04 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.
Book Synopsis Singular Perturbations and Asymptotics by : Richard E. Meyer
Download or read book Singular Perturbations and Asymptotics written by Richard E. Meyer and published by Academic Press. This book was released on 2014-05-10 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Research Center Symposia and Advanced Seminar Series: Singular Perturbations and Asymptotics covers the lectures presented at an Advanced Seminar on Singular Perturbation and Asymptotics, held in Madison, Wisconsin on May 28-30, 1980 under the auspices of the Mathematics Research Center of the University of Wisconsin—Madison. The book focuses on the processes, methodologies, reactions, and principles involved in singular perturbations and asymptotics, including boundary value problems, equations, perturbations, water waves, and gas dynamics. The selection first elaborates on basic concepts in the analysis of singular perturbations, limit process expansions and approximate equations, and results on singularly perturbed boundary value problems. Discussions focus on quasi-linear and nonlinear problems, semilinear systems, water waves, expansion in gas dynamics, asymptotic matching principles, and classical perturbation analysis. The text then takes a look at multiple solutions of singularly perturbed systems in the conditionally stable case and singular perturbations, stochastic differential equations, and applications. The book ponders on connection problems in the parameterless case; general connection-formula problem for linear differential equations of the second order; and turning-point problems for ordinary differential equations of hydrodynamic type. Topics include the comparison equation method, boundary layer flows, compound matrix method, asymptotic solution of the connection-formula problem, and higher order equations. The selection is a valuable source of information for researchers interested in singular perturbations and asymptotics.
Book Synopsis An Introduction to Geometrical Physics by : Ruben Aldrovandi
Download or read book An Introduction to Geometrical Physics written by Ruben Aldrovandi and published by World Scientific. This book was released on 1995 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and other subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation.The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level of understanding, a more advanced treatment of the mathematical topics. It is aimed as an elementary text, more so than most others on the market, and is intended for first year graduate students.
Book Synopsis Asymptotic Methods in Electromagnetics by : Daniel Bouche
Download or read book Asymptotic Methods in Electromagnetics written by Daniel Bouche and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerically rigorous techniques for the computation of electromagnetic fields diffracted by an object become computationally intensive, if not impractical to handle, at high frequencies and one must resort to asymptotic methods to solve the scattering problem at short wavelengths. The asymptotic methods provide closed form expansions for the diffracted fields and are also useful for eliciting physical interpretations of the various diffraction phenomena. One of the principal objectives of this book is to discuss the different asymptotic methods in a unified manner. Although the book contains explicit formulas for computing the field diffracted by conducting or dielectric-coated objects, it also provides the mathematical foundations of the different methods and explains how they are interrelated.
Download or read book Elastic Waves written by Vassily Babich and published by CRC Press. This book was released on 2018-04-09 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elastic Waves: High Frequency Theory is concerned with mathematical aspects of the theory of high-frequency elastic waves, which is based on the ray method. The foundations of elastodynamics are presented along with the basic theory of plane and spherical waves. The ray method is then described in considerable detail for bulk waves in isotropic and anisotropic media, and also for the Rayleigh waves on the surface of inhomogeneous anisotropic elastic solids. Much attention is paid to analysis of higher-order terms and to generation of waves in inhomogeneous media. The aim of the book is to present a clear, systematic description of the ray method, and at the same time to emphasize its mathematical beauty. Luckily, this beauty is usually not accompanied by complexity and mathematical ornateness.
Book Synopsis Partial Differential Equations of Applied Mathematics by : Erich Zauderer
Download or read book Partial Differential Equations of Applied Mathematics written by Erich Zauderer and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition features the latest tools for modeling, characterizing, and solving partial differential equations The Third Edition of this classic text offers a comprehensive guide to modeling, characterizing, and solving partial differential equations (PDEs). The author provides all the theory and tools necessary to solve problems via exact, approximate, and numerical methods. The Third Edition retains all the hallmarks of its previous editions, including an emphasis on practical applications, clear writing style and logical organization, and extensive use of real-world examples. Among the new and revised material, the book features: * A new section at the end of each original chapter, exhibiting the use of specially constructed Maple procedures that solve PDEs via many of the methods presented in the chapters. The results can be evaluated numerically or displayed graphically. * Two new chapters that present finite difference and finite element methods for the solution of PDEs. Newly constructed Maple procedures are provided and used to carry out each of these methods. All the numerical results can be displayed graphically. * A related FTP site that includes all the Maple code used in the text. * New exercises in each chapter, and answers to many of the exercises are provided via the FTP site. A supplementary Instructor's Solutions Manual is available. The book begins with a demonstration of how the three basic types of equations-parabolic, hyperbolic, and elliptic-can be derived from random walk models. It then covers an exceptionally broad range of topics, including questions of stability, analysis of singularities, transform methods, Green's functions, and perturbation and asymptotic treatments. Approximation methods for simplifying complicated problems and solutions are described, and linear and nonlinear problems not easily solved by standard methods are examined in depth. Examples from the fields of engineering and physical sciences are used liberally throughout the text to help illustrate how theory and techniques are applied to actual problems. With its extensive use of examples and exercises, this text is recommended for advanced undergraduates and graduate students in engineering, science, and applied mathematics, as well as professionals in any of these fields. It is possible to use the text, as in the past, without use of the new Maple material.
