Non-standard analysis in electrical engineering. Ideal DC inductive circuits with infinitesimal parameters of different orders

Abstract

The analysis of DC circuits with ideal inductive elements using standard methods of theoretical electrical engineering
is too difficult or even impossible, because when using them, it is often necessary to reveal type
00 uncertainties. In this regard, the article proposes to use not the usual mathematical analysis, but a nonstandard
one, in which the frequency of the direct current is taken not as zero, but as an infinitesimal number
 . In this case, the reactances of the inductive elements will be equal to L , and it becomes possible to apply
all standard methods of theoretical electrical engineering. The article considers examples of the analysis
of ideal DC inductive circuits, with particular attention paid to circuits whose calculation requires the use of
infinitesimal numbers for inhomogeneous parameters. In such cases, the order of these numbers is determined
based on individual considerations, and this is a non-standard task.