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Difference Operator

  1. Dec 2, 2012 #1
    We all know the greek letter delta is the mathematical symbol that represents "change in."

    I though about a new form of delta: Δn. Where n2 = the # of terms when you expand the delta operator.

    For example: the usual Δx = x2 - x1
    But now: Δ2x = (X4-X3) - (X2-X1). We can see that for Δ2 there are 22 (4) terms.

    Why the heck haven't I head of this notation. Does it just not exist? It does not seem to be used that much in mathematics.

    Taking a Δn is like taking the nth derivative of a function is it not?

    Wow. I discovered something by myself and I didn't even know it existed.
    Look here: http://en.wikipedia.org/wiki/Difference_operator
    Scroll down untill you get to the title called "nth difference"
     
    Last edited: Dec 2, 2012
  2. jcsd
  3. Dec 2, 2012 #2

    micromass

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    In my understanding, it is mainly engineers (or at least: applied people) who work with finite difference methods. So if you don't care for applications, then it makes sense that you never heard of it.

    Please correct me if I'm wrong.
     
  4. Dec 2, 2012 #3

    Stephen Tashi

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    The basic topic to look up is "The Calculus Of Finite Differences". A interesting book on the subject was written by George Boole himself.
     
  5. Dec 2, 2012 #4

    pwsnafu

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