Abstract
The direct and averaging methods are applied to analyze the propagation of 1D and electromagnetic waves through three different media separated by plane-parallel interfaces. It is shown that application of the direct method for calculation of the amplitudes of propagating waves is ideologically simpler but the averaging method yields simpler final expressions. Universal boundary conditions are obtained for the averaging method. These conditions are suitable for the solution of problems on the normal and oblique incidence of vertically and horizontally polarized electromagnetic waves. It is demonstrated that vector electrodynamic problems and the corresponding scalar 1D problems have the same mathematical contents and that a solution to an electrodynamic problem can be obtained from a solution to a 1D problem with the help of certain changes of coefficients and variables.
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