Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Connection between summation and integration

  1. Apr 18, 2014 #1
    If exist a connection between the infinitesimal derivative and the discrete derivative $$d = \log(\Delta + 1)$$ $$\Delta = \exp(d) - 1$$ exist too a coneection between summation ##\Sigma## and integration ##\int## ?
     
  2. jcsd
  3. Apr 18, 2014 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Yep, both are special cases of measure-theoretic integration. Summation is with respect to the counting measure, regular integration is with respect to the Lebesgue measure.
     
  4. Apr 18, 2014 #3

    Stephen Tashi

    User Avatar
    Science Advisor

  5. Apr 18, 2014 #4
    Extremely complicated! I already know this article, but yet so I oponed this thread with the hope that could exist a simple formula and somebody that knew it could post it here...
     
  6. Apr 18, 2014 #5

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    It's not complicated, it's just

    [tex]\int_n^m f(t) dt \sim \sum_{k=n}^m f(k) - \frac{f(m) + f(n)}{2}[/tex]

    If you want a better approximation, then it becomes more complicated.
     
  7. Apr 18, 2014 #6

    Mark44

    Staff: Mentor

    There's an old saying (due to Einstein, I believe), "Make things as simple as possible, but no simpler."
     
  8. Apr 18, 2014 #7
    "The simplicity is the most high degree of perfection."
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Connection between summation and integration
Loading...