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 Mathematics 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.

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.

An Introduction To The Mathematical Theory Of Dynamic Materials

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Author : Konstantin A. Lurie
language : en
Publisher: Springer
Release Date : 2017-10-17

An Introduction To The Mathematical Theory Of Dynamic Materials written by Konstantin A. Lurie and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-17 with Mathematics categories.

This fascinating book is a treatise on real space-age materials. It is a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials—that is, material substances whose properties are variable in space and time. Unlike conventional composites that are often found in nature, dynamic materials are mostly the products of modern technology developed to maintain the most effective control over dynamic processes.

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.

Nonlinear Waves An Introduction

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Author : Petar Radoev Popivanov
language : en
Publisher: World Scientific Publishing Company
Release Date : 2010-09-23

Nonlinear Waves An Introduction written by Petar Radoev Popivanov 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 2010-09-23 with Mathematics categories.

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, the authors propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks). The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding d-shocks are also considered. At the end of the book the authors study the interaction of two piecewise smooth waves in the case of two space variables and they verify the appearance of logarithmic singularities. As it concerns numerical methods in the case of periodic waves the authors apply Cellular Neural Network (CNN) approach.

An Introduction To The Mathematical Theory Of Geophysical Fluid Dynamics

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Author :
language : en
Publisher: Elsevier
Release Date : 1980-01-01

An Introduction To The Mathematical Theory Of Geophysical Fluid Dynamics written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-01 with Mathematics categories.

An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics

An Introduction To The Mathematical Theory Of Inverse Problems

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Author : Andreas Kirsch
language : en
Publisher: Springer Nature
Release Date : 2021-02-15

An Introduction To The Mathematical Theory Of Inverse Problems written by Andreas Kirsch and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-15 with Mathematics categories.

This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field’s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published.

New Foundations For Applied Electromagnetics The Spatial Structure Of Electromagnetic Fields

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Author : Said Mikki
language : en
Publisher: Artech House
Release Date : 2016-05-31

New Foundations For Applied Electromagnetics The Spatial Structure Of Electromagnetic Fields written by Said Mikki and has been published by Artech House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-31 with Technology & Engineering categories.

This comprehensive new resource focuses on applied electromagnetics and takes readers beyond the conventional theory with the use of contemporary mathematics to improve the practical use of electromagnetics in emerging areas of field communications, wireless power transfer, metamaterials, MIMO and direction-of-arrival systems. The book explores the existing and novel theories and principles of electromagnetics in order to help engineers analyze and design devices for today's applications in wireless power transfers, NFC, and metamaterials. This book is organized into clear and logical sections spanning from fundamental theory, to applications, promoting clear understanding through-out. This resource presents the theory of electromagnetic near fields including chapters on reactive energy, spatial and spectral theory, the scalar antenna, and the morphogenesis of electromagnetic radiation in the near field zone. The Antenna Current Green's Function Formalism is explored with an emphasis on the foundations, the organic interrelationships between the fundamental operational modes of general antenna systems, and the spectral approach to antenna-to-antenna interactions. The book offers perspective on nonlocal metamaterials, including the material response theory, the far-field theory, and the near-field theory.

Glimpses Of Soliton Theory

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Author : Alex Kasman
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Glimpses Of Soliton Theory written by Alex Kasman 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 2010 with Mathematics categories.

Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. --