The approach for handling transient electrodynamics problems based on their description by an integral Volterra equation is presented. The expression for a resolvent of this three-dimensional space-time vector equation for the case of a time-varying dielectric restricted by a plane boundary is derived. Using this approach it is demonstrated that an oblique incidence of a plane monochromatic wave on a boundary of a dielectric whose permittivity changes abruptly in time leads to a formation of a continuous wave spectrum. In the case of a point source of electromagnetic radiation, the presence of a plane boundary leads to a replacement of a convergence point of secondary spherical waves to the mirror symmetrical point. The field in this point has a bounded value, as differentiated from the case of an unbounded medium. ¿ American Geophysical Union 1995