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The numerical-analysis techniques appropriate for the rapid ap- proximate analysis of network response can be unified in terms of the z transform, or generalized Laplace transform. Application of the methods of analysis requires knowledge of only the z -domain integra- tion operators for the multiple integration of impulse trains. The time functions can be approximated by rectangular pulses, straight lines, or parabolas of any order. The numerical methods are illustrated with several examples. The transient response of a network can be evaluated without factoring a polynomial or adding damped sinusoids; the closed-loop transient response of a feedback system can be determined directly from the open-loop characteristics; a system with a transportation lag can be analyzed; the relations between frequency-domain and time-domain characteristics can be simplified; and a variety of other analysis prob- lems are rapidly and easily considered. The same numerical methods can be utilized to determine the transfer function of a network for a prescribed transient response.