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An Introduction To The Mathematical Theory Of Waves
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Book Synopsis An Introduction to the Mathematical Theory of Waves by : Roger Knobel
Download or read book An Introduction to the Mathematical Theory of Waves written by Roger Knobel and published by American Mathematical Soc.. This book was released on 2000 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Modern Introduction to the Mathematical Theory of Water Waves by : Robin Stanley Johnson
Download or read book A Modern Introduction to the Mathematical Theory of Water Waves written by Robin Stanley Johnson and published by Cambridge University Press. This book was released on 1997-10-28 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text considers classical and modern problems in linear and non-linear water-wave theory.
Book Synopsis The Mathematical Theory of Permanent Progressive Water-waves by : Hisashi Okamoto
Download or read book The Mathematical Theory of Permanent Progressive Water-waves written by Hisashi Okamoto and published by World Scientific. This book was released on 2001 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Foundations of the Mathematical Theory of Electromagnetic Waves by : Carl Müller
Download or read book Foundations of the Mathematical Theory of Electromagnetic Waves written by Carl Müller and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Water Waves: The Mathematical Theory with Applications by : James Johnston Stoker
Download or read book Water Waves: The Mathematical Theory with Applications written by James Johnston Stoker and published by Courier Dover Publications. This book was released on 2019-04-17 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to the Mathematical Theory of Vibrations of Elastic Plates by : Raymond David Mindlin
Download or read book An Introduction to the Mathematical Theory of Vibrations of Elastic Plates written by Raymond David Mindlin and published by World Scientific. This book was released on 2006 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Sample Chapter(s). Chapter 1: Elements of the Linear Theory of Elasticity (416 KB). Contents: Elements of the Linear Theory of Elasticity; Solutions of the Three-Dimensional Equations; Infinite Power Series of Two-Dimensional Equations; Zero-Order Approximation; First-Order Approximation; Intermediate Approximations. Readership: Researchers in mechanics, civil and mechanical engineering and applied mathematics.
Book Synopsis An Introduction to the Mathematical Theory of Dynamic Materials by : Konstantin A. Lurie
Download or read book An Introduction to the Mathematical Theory of Dynamic Materials written by Konstantin A. Lurie and published by Springer Science & Business Media. This book was released on 2007-05-15 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to the Mathematical Physics of Nonlinear Waves by : Minoru Fujimoto
Download or read book Introduction to the Mathematical Physics of Nonlinear Waves written by Minoru Fujimoto and published by Morgan & Claypool Publishers. This book was released on 2014-03-01 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environment
Book Synopsis The Water Waves Problem by : David Lannes
Download or read book The Water Waves Problem written by David Lannes and published by American Mathematical Soc.. This book was released on 2013-05-08 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.
Book Synopsis Oscillations and Waves by : Richard Fitzpatrick
Download or read book Oscillations and Waves written by Richard Fitzpatrick and published by CRC Press. This book was released on 2018-07-17 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing physics over mathematics, this popular, classroom-tested text helps advanced undergraduates acquire a sound physical understanding of wave phenomena. This second edition of Oscillations and Waves: An Introduction contains new widgets, animations in Python, and exercises, as well as updated chapter content throughout; continuing to ease the difficult transition for students between lower-division courses that mostly encompass algebraic equations and upper-division courses that rely on differential equations. Assuming familiarity with the laws of physics and college-level mathematics, the author covers aspects of optics that crucially depend on the wave-like nature of light, such as wave optics. Examples explore discrete mechanical, optical, and quantum mechanical systems; continuous gases, fluids, and elastic solids; electronic circuits; and electromagnetic waves. The text also introduces the conventional complex representation of oscillations and waves during the discussion of quantum mechanical waves. Features: Fully updated throughout and featuring new widgets, animations, and end of chapter exercises to enhance understanding Offers complete coverage of advanced topics in waves, such as electromagnetic wave propagation through the ionosphere Includes examples from mechanical systems, elastic solids, electronic circuits, optical systems, and other areas
Download or read book Water Waves written by J. J. Stoker and published by John Wiley & Sons. This book was released on 2011-08-15 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Water Waves: The Mathematical Theory with Applications by : James Johnston Stoker
Download or read book Water Waves: The Mathematical Theory with Applications written by James Johnston Stoker and published by Courier Dover Publications. This book was released on 2019-04-17 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Theory of Quantum Fields by : Huzihiro Araki
Download or read book Mathematical Theory of Quantum Fields written by Huzihiro Araki and published by Oxford University Press. This book was released on 1999-10-22 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to the mathematical foundations of quantum field theory, using operator algebraic methods and emphasizing the link between the mathematical formulations and related physical concepts. It starts with a general probabilistic description of physics, which encompasses both classical and quantum physics. The basic key physical notions are clarified at this point. It then introduces operator algebraic methods for quantum theory, and goes on to discuss the theory of special relativity, scattering theory, and sector theory in this context.
Book Synopsis Mathematical Theory of Wave Motion by : G. R. Baldock
Download or read book Mathematical Theory of Wave Motion written by G. R. Baldock and published by . This book was released on 1981 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Mathematical Theory of Wave Motion by : G. R. Baldock
Download or read book The Mathematical Theory of Wave Motion written by G. R. Baldock and published by Halsted Press. This book was released on 1983-07-01 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Theory of Scattering Resonances by : Semyon Dyatlov
Download or read book Mathematical Theory of Scattering Resonances written by Semyon Dyatlov and published by American Mathematical Soc.. This book was released on 2019-09-10 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Book Synopsis Introduction to the Physics of Waves by : Tim Freegarde
Download or read book Introduction to the Physics of Waves written by Tim Freegarde and published by Cambridge University Press. This book was released on 2013 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Balancing concise mathematical analysis with real-world examples and practical applications, to provide a clear and approachable introduction to wave phenomena.
