An Introduction To The Mathematical Theory Of Waves
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An Introduction To The Mathematical Theory Of Waves
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Author : Roger Knobel
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
An Introduction To The Mathematical Theory Of Waves written by Roger Knobel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Wave-motion, Theory of categories.
This book is based on an undergraduate course taught at the IAS/Park City Mathematics Institute (Utah) on linear and nonlinear waves. The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques. The second part of the book discusses traveling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small vibrations of a taut string, and solutions are constructed via d'Alembert's formula and Fourier series.The last part of the book discusses waves arising from conservation laws. After deriving and discussing the scalar conservation law, its solution is described using the method of characteristics, leading to the formation of shock and rarefaction waves. Applications of these concepts are then given for models of traffic flow. The intent of this book is to create a text suitable for independent study by undergraduate students in mathematics, engineering, and science. The content of the book is meant to be self-contained, requiring no special reference material. Access to computer software such as MathematicaR, MATLABR, or MapleR is recommended, but not necessary. Scripts for MATLAB applications will be available via the Web. Exercises are given within the text to allow further practice with selected topics.
A Modern Introduction To The Mathematical Theory Of Water Waves
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Author : Robin Stanley Johnson
language : en
Publisher: Cambridge University Press
Release Date : 1997-10-28
A Modern Introduction To The Mathematical Theory Of Water Waves written by Robin Stanley Johnson 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 1997-10-28 with Mathematics categories.
This text considers classical and modern problems in linear and non-linear water-wave theory.
The Mathematical Theory Of Permanent Progressive Water Waves
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Author : Hisashi Okamoto
language : en
Publisher: World Scientific Publishing Company
Release Date : 2001-09-28
The Mathematical Theory Of Permanent Progressive Water Waves written by Hisashi Okamoto 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 2001-09-28 with Mathematics categories.
This book is a self-contained introduction to the theory of periodic, progressive, permanent waves on the surface of incompressible inviscid fluid. The problem of permanent water-waves has attracted a large number of physicists and mathematicians since Stokes' pioneering papers appeared in 1847 and 1880. Among many aspects of the problem, the authors focus on periodic progressive waves, which mean waves traveling at a constant speed with no change of shape. As a consequence, everything about standing waves are excluded and solitary waves are studied only partly. However, even for this restricted problem, quite a number of papers and books, in physics and mathematics, have appeared and more will continue to appear, showing the richness of the subject. In fact, there remain many open questions to be answered. The present book consists of two parts: numerical experiments and normal form analysis of the bifurcation equations. Prerequisite for reading it is an elementary knowledge of the Euler equations for incompressible inviscid fluid and of bifurcation theory. Readers are also expected to know functional analysis at an elementary level. Numerical experiments are reported so that any reader can re-examine the results with minimal labor: the methods used in this book are well-known and are described as clearly as possible. Thus, the reader with an elementary knowledge of numerical computation will have little difficulty in the re-examination.
Rogue Waves
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Author : Boling Guo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-06-26
Rogue Waves written by Boling Guo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-26 with Mathematics categories.
This book gives an overview of the theoretical research on rogue waves and discusses solutions to rogue wave formation via the Darboux and bilinear transformations, algebro-geometric reduction, and inverse scattering and similarity transformations. Studies on nonlinear optics are included, making the book a comprehensive reference for researchers in applied mathematics, optical physics, geophysics, and ocean engineering. Contents The Research Process for Rogue Waves Construction of Rogue Wave Solution by the Generalized Darboux Transformation Construction of Rogue Wave Solution by Hirota Bilinear Method, Algebro-geometric Approach and Inverse Scattering Method The Rogue Wave Solution and Parameters Managing in Nonautonomous Physical Model
Water Waves
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Author : J. J. Stoker
language : en
Publisher: John Wiley & Sons
Release Date : 1992-04-16
Water Waves written by J. J. Stoker and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-04-16 with Mathematics categories.
Offers an integrated account of the mathematical hypothesis of wave motion in liquids with a free surface, subjected to gravitational and other forces. Uses both potential and linear wave equation theories, together with applications such as the Laplace and Fourier transform methods, conformal mapping and complex variable techniques in general or integral equations, methods employing a Green's function. Coverage includes fundamental hydrodynamics, waves on sloping beaches, problems involving waves in shallow water, the motion of ships and much more.
Water Waves The Mathematical Theory With Applications
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Author : James Johnston Stoker
language : en
Publisher: Courier Dover Publications
Release Date : 2019-04-17
Water Waves The Mathematical Theory With Applications written by James Johnston Stoker and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-17 with Science categories.
First published in 1957, this is a classic monograph in the area of applied mathematics. It offers a connected account of the mathematical theory of wave motion in a liquid with a free surface and subjected to gravitational and other forces, together with applications to a wide variety of concrete physical problems. A never-surpassed text, it remains of permanent value to a wide range of scientists and engineers concerned with problems in fluid mechanics. The four-part treatment begins with a presentation of the derivation of the basic hydrodynamic theory for non-viscous incompressible fluids and a description of the two principal approximate theories that form the basis for the rest of the book. The second section centers on the approximate theory that results from small-amplitude wave motions. A consideration of problems involving waves in shallow water follows, and the text concludes with a selection of problems solved in terms of the exact theory. Despite the diversity of its topics, this text offers a unified, readable, and largely self-contained treatment.
Mathematical Theory Of Wave Motion
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Author : G. R. Baldock
language : en
Publisher:
Release Date : 1981
Mathematical Theory Of Wave Motion written by G. R. Baldock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Wave-motion, Theory of categories.
The Mathematical Theory Of Wave Motion
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Author : G. R. Baldock
language : en
Publisher: Halsted Press
Release Date : 1983-07-01
The Mathematical Theory Of Wave Motion written by G. R. Baldock and has been published by Halsted Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-07-01 with categories.
An Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates
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Author : Raymond David Mindlin
language : en
Publisher: World Scientific
Release Date : 2006
An Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates written by Raymond David Mindlin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Technology & Engineering categories.
This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices.
Waves In Continuous Media
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Author : S. L. Gavrilyuk
language : en
Publisher: Springer
Release Date : 2017-01-27
Waves In Continuous Media written by S. L. Gavrilyuk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-27 with Mathematics categories.
Starting with the basic notions and facts of the mathematical theory of waves illustrated by numerous examples, exercises, and methods of solving typical problems Chapters 1 & 2 show e.g. how to recognize the hyperbolicity property, find characteristics, Riemann invariants and conservation laws for quasilinear systems of equations, construct and analyze solutions with weak or strong discontinuities, and how to investigate equations with dispersion and to construct travelling wave solutions for models reducible to nonlinear evolution equations. Chapter 3 deals with surface and internal waves in an incompressible fluid. The efficiency of mathematical methods is demonstrated on a hierarchy of approximate submodels generated from the Euler equations of homogeneous and non-homogeneous fluids. The self-contained presentations of the material is complemented by 200+ problems of different level of difficulty, numerous illustrations, and bibliographical recommendations.