Non-standard analysis in electrical engineering. Transient analysis in second-order electrical circuits with violation of switching laws

For the first time, the authors proposed the use of the mathematical apparatus of non-standard analysis to solve certain non-trivial problems of theoretical electrical engineering. It was established that the axiomatics of non-standard analysis allows to simplify the analysis of transient processes in high-order electric circuits when the switching laws are violated. It is shown that the application of non-standard analysis methods in theoretical electrical engineering provides an opportunity to use the traditional classical method of transient processes analysis of circuits with violation of switching laws. Only by using methods of non-standard analysis, it is possible to strictly prove the fulfillment of the law of energy conservation in such schemes. Also, examples of solving such tasks are given. It is recommended to expand the scope of application of non-standard methods of analysis in problems of various branches of science and technology, which use differential calculus and boundary transitions, and the solution of which is limited or impossible by standard approaches