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Some Playing with Derivatives
This is a summary of what I’ve been playing with in case people find it interesting. In general, there are three ways to find the derivative of a function: Do the symbolic manipulation of formulae that we all learned in school when we were 16 years old. This assumes that one has the function as an algebraic expression of some kind in terms of known quantities. Do it numerically, by computing (f(x
Beautiful Haskell implementation of math's "power set": import Control.Monad powerset :: [a] -> [[a]] powerset = filterM (const [True, False]) And powerset [1,2,3] produces [[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3],[]]. Oh man is that hard for me to grok, mostly because I haven't internalized the list monad. (It helped me to write out the definition of filterM, which has type Monad m => (a -> m Bool)
Sample from the book (table of contents plus first chapter): compressed postscript Addendum to Chapter 9 of the Book: Direct Computation of Polynomial Representations for Sequences: PolAddendum.pdf PolAddendum.hs Errata A list of errata is here. Software Getting Started: GS.hs Talking about Mathematical Objects: TAMO.hs The Use of Logic: Proof: TUOLP.hs Sets, Types and Lists: STAL.hs Database used
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