1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Discrete-Space Derivative

  1. Mar 25, 2010 #1
    I was looking up how to find the derivative of a factorial and found this thread:
    https://www.physicsforums.com/showthread.php?t=1328

    What is a discrete-space derivative? I tried looking it up, but had no luck. If someone could explain it in a way someone in calc 2 could understand that would be great, or at least point me in the direction of more information.
     
  2. jcsd
  3. Mar 25, 2010 #2
    A discrete space is a space where all subsets are open. I have never heard of a discrete space derivative, however.

    Have you heard of the gamma function? http://en.wikipedia.org/wiki/Gamma_function
    Take a look at how it relates to the factorial function. It does take a lot of work to understand if you're only at the first year level in math.
     
  4. Mar 25, 2010 #3
    I was looking at the Gamma Function. I understood it a little bit, but in general it was way over my head.
     
  5. Mar 25, 2010 #4

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    The general idea is that the more familiar continuous space derivative,

    [tex]\frac{df}{dx}=\lim_{\Delta x\to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}[/tex]

    Can be generalized in cases where the smallest possible difference between two different values of a discrete variable [itex]x[/itex] is a constant (in other words, all elements of the set are equally spaced) [itex]\delta x[/itex] according to the equation

    [tex]\frac{df}{dx}=\frac{f(x+\delta x)-f(x)}{\delta x}[/tex]

    (For a continuous space, [itex]\delta x[/itex] is infinitesimally small)

    If [itex]x[/itex] is only allowed to be a natural number, then the smallest diffence between two different values of x is 1, and so

    [tex]\frac{df}{dx}=f(x+1)-f(x)[/tex]

    Whether or not this is really the type of derivative you are interested in depends on the context of your problem.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook