Here, it is proposed the short outline of the special master course on the directions related to radio engineering and telecommunications. The given topic concerns some more or less new analytical methods on the explicit solution and mathematical simulation of relevant problems in technical electrodynamics basing on the symmetrical differential Maxwell system.

Those aforesaid techniques deal with the operator analogy of algebraic Gauss method and inverse matrix operator construction. The latter generates solvability criterion of the symmetrical inhomogeneous Maxwell system in terms of equivalence to the general wave PDE (partial differential equation) with respect to all unknown electromagnetic field intensities. The proven theorem allows formulating relevant boundary problems that describe mathematically wave propagation in the various media. Such problems are solved explicitly using the classical integral transform method. Advantages of present procedures are their simplicity in direct applications including arbitrary finite dimensional systems of PDEs and consideration of non generalized functions.