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

The analysis of DC circuits with ideal inductive elements using standard methods of theoretical electrical engineeringis too difficult or even impossible, because when using them, it is often necessary to reveal type00 uncertainties. In this regard, the article proposes to use not the usual mathematical analysis, but a nonstandardone, 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 applyall standard methods of theoretical electrical engineering. The article considers examples of the analysisof ideal DC inductive circuits, with particular attention paid to circuits whose calculation requires the use ofinfinitesimal numbers for inhomogeneous parameters. In such cases, the order of these numbers is determinedbased on individual considerations, and this is a non-standard task.