ASYMPTOTIC METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS: THE REDUCED WAVE EQUATION AND MAXWELL'S EQUATION

The short wavelength or high frequency asymptotic theory of the reduced wave equation and of Maxwell’s equations is presented. The theory is applied to representative problems involving reflection, transmission, and diffraction in both homogeneous and inhomogeneous media. It is a slightly revised version of a report1 written in 1964 by the authors. Despite its age, it still provides a convenient introduction to the formal asymptotic theory and to the geometrical theory of diffraction.

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