To compare the discrete with the continuous, to search for analogies between them, and ultimately to effect their unification, are patterns of mathematical development that did not begin with Zeno, and certainly did not end with Leibnitz and Newton, nor even with Riemann and Stieltjes. Such a pattern of investigation is especially appropriate to the theory of boundary problems, for which the discrete and the continuous pervade both physical origins and mathematical methods. It is the aim of this book to present in this light the theory of boundary problems in one dimension, that is to say, for "ordinary" differential equations and their analogs and extensions. It would be highly desirable to develop a corresponding theory for partial differential equations and their analogs; however, here the discrete theory seems ill-developed, and unification remote indeed.
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