Waves are a ubiquitous and important feature of the physical world, and, throughout history, it has been a major challenge to understand them. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, 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 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.
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Waves on a Stretched String
Այլ խմբագրություններ - View all
acoustic approximation asymptotic bound state eigenvalues boundary condition capillary waves characteristics chemical components consider constant define density determine differential equation diffraction diffusion dispersion relation displacement eigenvalues elastic electric field electromagnetic waves energy example finite fluid flux Fourier transform free surface frequency function given gives governing equations gravity waves group velocity hence homoclinic orbit incident wave initial conditions initial value problem integral interface KdV equation kinematic wave leading order linear linearised magnetic field nonlinear Note obtain one-dimensional phase piston plane wave reflected wave reflectionless potential region satisfies shallow water shock wave shown in figure small amplitude ſº solitary wave solitons solve stationary string subsection substitute transmitted wave travelling wave solution tube variables vector water waves wave crests wave equation wave propagation wave speed waveguide wavelength wavenumber whilst write x-direction zero