Integration in the complex plane

IN the first article of this series Professor J. B. Russell¹ gave a survey of Heaviside's direct operational calculus. This direct calculus has proved to be very successful. It may be applied to a large class of problems concerning differential equations of transients. Nevertheless there has been much criticism about the validity of the operational method. The theory of complex integration, the topic of the present article, is the main tool which permits us to put Heaviside's calculus on a solid basis. Aside from this justification, however, complex integration is an indispensable tool for any advanced mathematical treatment of transient problems, transmission problems, or related problems in electrical theory.