Coincidence of Poles and Zeros

The concept of poles and zeros of network functions is taught in many introductory circuit courses, but the methods of presentation vary widely. Among them, the introduction of the network function by way of the differential equation written in operational form offers some pedagogical advantages that justify its use in spite of its lack of mathematical rigor. This method also helps to realize that poles and zeros can actually coincide with each other. This is illustrated by an example in which the cancellation of factors in the numerator and denominator of the network function would lead to an error if arbitrary initial conditions are to be satisfied.