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This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas.Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes.Provides a panoramic look at wave motion in many different contextsFeatures problems and exercises throughoutIncludes numerous appendixes, some on topics not often coveredAn ideal reference book for practitionersCan also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineeringAccessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable

Mathematical physics. --- Physical mathematics --- Physics --- Mathematics --- Airy approximation. --- Airy functions. --- Airy integral. --- Airy theory. --- Airy wavefront. --- Alexander's dark band. --- Bessel functions. --- Earth. --- Fermat's principle. --- Fresnel integrals. --- Hamilton's principle. --- Hamilton-Jacobi equation. --- Hamilton-Jacobi theory. --- Hamiltonian. --- Hooke's law. --- Kepler's laws of planetary motion. --- Lagrangian. --- Liouville transformation. --- Love waves. --- Navier equations. --- Ptolemy's theorem. --- Rayleigh scattering. --- Schrödinger equation. --- Sir George Biddle Airy. --- Snell's laws. --- Taylor–Goldstein equation. --- WKB(J) approximation. --- Wiechert-Herglotz inverse problem. --- acoustic wave propagation. --- action. --- angle of minimum deviation. --- applied mathematics. --- atmospheric waves. --- billow clouds. --- boundary-value problem. --- buoyancy waves. --- caustics. --- classical mechanics. --- classical wave equation. --- colors. --- complex plane. --- constant phase lines. --- contours. --- corona. --- currents. --- cusp catastrophes. --- deep water waves. --- differential equations. --- diffraction catastrophes. --- diffraction. --- dispersion relations. --- dispersion. --- divergence problem. --- earthquakes. --- eikonal equation. --- elastic solid. --- elastic waves. --- elementary mathematics. --- equations of motion. --- fluid equations. --- fold catastrophes. --- free surface. --- geometric wavefronts. --- geometrical optics. --- glory. --- inhomogeneous medium. --- integrals. --- intensity law. --- internal gravity waves. --- inverse scattering problem. --- islands. --- leading waves. --- lee waves. --- light waves. --- long waves. --- mathematics. --- meteorological optics. --- mountain waves. --- ocean acoustic waveguides. --- ocean acoustics. --- ocean waves. --- one-dimensional waves. --- optics. --- path. --- plane wave incident. --- plane waves. --- polarization. --- potential well. --- rainbow. --- ray equations. --- ray optics. --- ray theory. --- rays. --- reflection. --- refraction. --- ridge. --- scattering. --- seafloor. --- seismic rays. --- seismic tomography. --- seismic waves. --- semicircle theorem. --- shallow water waves. --- ship waves. --- short waves. --- strain. --- stratified fluid. --- stress. --- surface gravity waves. --- surface waves. --- transient waves. --- tsunami propagation. --- tsunamis. --- wave energy. --- wave refraction. --- wave trapping. --- wavefront. --- wavepackets. --- waves. --- wind shear.