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A description of the theory of dynamic programming as the study of multistage decision processes. An attempt is made to explain a multistage process that is a natural extension of semigroups of operations and to illustrate this process by means of the familiar difference and differential equations. To indicate the range and versatility of the functional-equation approach to multistage decision processes, the study considers some maximization problems taken from calculus; some trajectory problems of the type that occur in the study of rockets, satellites, and space travel; a typical feedback control problem of the type current in modern electronic engineering; and an interesting class of multistage games, "games of survival."

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