Subject: Recursive definitions and Derivatives, continued From: "William J. Rapaport" Date: Tue, 17 Nov 2009 20:49:49 -0500 (EST) In message 20091117-RecursiveDefinitions-Derivatives.txt, a student wrote: "I can't help noticing a similarity between the recursive definition of a discrete function, and the derivative of a continuous function. ... Is the recursive definition of a discrete function analogous to the derivative of a continuous function?" and I replied: "Yes; they are not only similar, but they are intimately related. ... For more on this topic take a look at some parts of the Rosen text. Unfortunately, as I write this, I don't have the text at hand. I'll give you page references tonight or tomorrow." Here are the promised page refs: Rosen, p. 460: read the paragraph following problem 61 (it has nothing to do with problem 61), and try (or at least read) problems 62-68. For more on difference equations (which are the discrete analog of differential equations) and on their relationship to recursion and recurrence relations (our next topic), see: http://en.wikipedia.org/wiki/Difference_equation#Relationship_to_difference_equations