Training Manual . - M. MSU Faculty of Physics, 2010. 197 s. The manual is written on the basis of a special course of lectures, which the authors have been reading for a number of years at the physical faculty of Moscow State University .. The book discusses the application of mathematical modeling methods to the problems of propagation and diffraction of steady oscillations in continuous environments. The main attention is paid to the so-called resonance case, when the length of excited waves is of the same order as the characteristic dimensions of the inhomogeneities. This course is included in the curriculum of the Department of Mathematics of the Faculty of Physics of Moscow State University, but may be of interest to a wider range of students, graduate students and researchers specializing in the field of mathematical physics and its applications.