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In order to introduce sophomore engineering students to the scientific applications of personal computers, we have used a simple computer algorithm for analyzing linear systems. This algorithm, mathematically equivalent to Euler's method, is derived from the analog computer block diagram with which most students are either already familiar or the principles of which they can grasp very quickly. We have found the method to be of significant pedagogical value in developing a feel for the use and limitations of numerical metbods, and indeed, for the intrinsic opeation of computers as such. It also demonstrates dramatically the educational impact of small, pesonal computers (with a price comparable to that of a textbook) when their simulation capabilities are used in combination with even the lowest resolution graphics.