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Waves And Distributions
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This book begins with a description of continuum mechanics and a derivation of the linear equations for sound waves in fluids and elastic waves in solids. There is a brief chapter on the wave equations of electrodynamics. This is followed by a description of plane wave solutions and a discussion on concepts like reflection, refraction, polarization and the role of boundary conditions. The second part of the book deals with the development and application of distributions and Fourier transforms. Towards the end, dispersion, the method of stationary phase, Kramers-Kronig relations and various examples including surface waves on liquids are discussed. This text emphasizes the use of distributions to analyze the solutions of the wave equation. The treatment of continuum mechanics is complete and self-contained, as well as the discussion of distributions and Fourier transforms. In addition, many classical methods of theoretical physics are thoroughly discussed, eg the use of Green functions and multiple expansions.
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