Unified approach to the impulse response and green function in the circuit and field theory part II : multi–dimensional case

In the circuit theory the concept of the impulse response of a linear system due to its excitation by the Dirac delta function δ(t) together with the convolution principle is widely used and accepted. The rigorous theory of symbolic functions, sometimes called distributions, where also the delta function belongs, is rather abstract and requires subtle mathematical tools [1-4]. Nevertheless, the most people intuitively well understand the delta function as a derivative of the (Heaviside) unit step function 1(t) without too much mathematical rigor. In the previous part [5] the concept of the impulse response of linear systems was approached in a unified manner and generalized to the time-space phenomena in one dimension (transmission lines). Here the phenomena in more dimensions (static and dynamic electromagnetic fields) are treated. It is shown that many formulas in the field theory, which are often postulated in an inductive way as results of the experiments, and therefore appear as “deux ex machina” effects, can be mathematically deduced from a few starting equations.