Mathematical Theory of Wave Motion
Author | : G. R. Baldock |
Publisher | : |
Total Pages | : 272 |
Release | : 1981 |
Genre | : Science |
ISBN | : |
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Author | : G. R. Baldock |
Publisher | : |
Total Pages | : 272 |
Release | : 1981 |
Genre | : Science |
ISBN | : |
Author | : G. R. Baldock |
Publisher | : Halsted Press |
Total Pages | : 261 |
Release | : 1983-07-01 |
Genre | : |
ISBN | : 9780470274644 |
Author | : James Johnston Stoker |
Publisher | : Courier Dover Publications |
Total Pages | : 593 |
Release | : 2019-04-17 |
Genre | : Science |
ISBN | : 0486839923 |
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.
Author | : Roger Knobel |
Publisher | : American Mathematical Soc. |
Total Pages | : 212 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821820397 |
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.
Author | : J. J. Stoker |
Publisher | : John Wiley & Sons |
Total Pages | : 598 |
Release | : 2011-08-15 |
Genre | : Mathematics |
ISBN | : 1118031350 |
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.
Author | : J. Billingham |
Publisher | : Cambridge University Press |
Total Pages | : 476 |
Release | : 2001-01-22 |
Genre | : Mathematics |
ISBN | : 1316583910 |
Waves are a ubiquitous and important feature of the physical world, and throughout history it has been a major challenge to understand them. They can propagate on the surfaces of solids and of fluids; chemical waves control the beating of your heart; traffic jams move in waves down lanes crowded with vehicles. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, thus making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as an acquaintance with fluid mechanics, elasticity and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers.
Author | : Robin Stanley Johnson |
Publisher | : Cambridge University Press |
Total Pages | : 468 |
Release | : 1997-10-28 |
Genre | : Mathematics |
ISBN | : 9780521598323 |
This text considers classical and modern problems in linear and non-linear water-wave theory.
Author | : Thomas Craig |
Publisher | : |
Total Pages | : 190 |
Release | : 1879 |
Genre | : Hydrodynamics |
ISBN | : |
Author | : James Johnston Stoker |
Publisher | : Courier Dover Publications |
Total Pages | : 593 |
Release | : 2019-04-17 |
Genre | : Science |
ISBN | : 0486832996 |
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.
Author | : AlexandreJ. Chorin |
Publisher | : Springer Science & Business Media |
Total Pages | : 345 |
Release | : 2013-03-08 |
Genre | : Science |
ISBN | : 1461395836 |
The 60th birthday of Peter Lax was celebrated at Berkeley by a conference entitled Wave Motion: theory, application and computation held at the mathematical Sciences Research Institute, June 9-12, 1986. Peter Lax has made profound and essential contributions to the topics described by the title of the conference, and has also contributed in important ways to many other mathematical subjects, and as a result this conference volume dedicated to him includes research work on a variety of topics, not all clearly related to its title.