Heaviside's operational calculus applied to electrical circuit problems

摘要

Heaviside's operational calculus approach is compared with the one-sided Laplace transform method augmented with distribution theory analysis as applied to electrical circuit problems. It is seen that there is a high degree of commonality to these methods, but also several significant problem-solving and pedagogical advantages to Heaviside's method. In particular, the Heaviside operational calculus is better physically motivated, conceptually parallel to the well-established complex sinusoidal circuit analysis (the jw method), and less mathematically intricate, and may with ease also handle initial value problems. Moreover, the mathematical theory of the impulse or delta (t) function, defined as the convolution identity and developed using Heaviside's operational approach, compares very favorably with the quite extensive mathematical machinery of the theory of distributions.