Application-oriented relativistic electrodynamics

The following is a summerized version of the complete text to appear in PEER- Progress In Electromagnetic Research (Editorin-chief J.A. Kong) intended to accompany the talk in the present conference. Relativistic electrodynamics is nowadays recognized as pertinent to many practical applications. We need to define a suitable syllabus and explore the best methods for educating future generations of engineers and applied physicists. The attempt presented here is of course biassed by personal preferences. It is argued that relativistic electrodynamics should be presented axiomatically, without trying to "explain the physical meaning" of special relativity, and that four-vectors and their mathematical properties should be emphasized, and that the field tensors, a formalism of limited practical use, should be avoided. Use of four-fold Fourier transforms greatly simplifies the relevant manipulations, and is also important for discussion of dispersive media. This approach yields many concepts as mathematical results, e.g., the relativistic Doppler effect, which therefore do not require a long phenomenological discussion with many "explanations". One of the main results shown here is the fact that the generalized Fermat principle states that the ray will propagate in such a manner that the proper time will be minimized (or extremized, in general). It also strips the mystique of this principle, showing that it is in fact equivalent to a modest mathematical condition on the smoothness of the phase function. The presentation is constructed in a way that allows the student to gradually overcome difficulties in assimilating new concepts and applying them. In that too it is different from many conventional presentations.