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Thread: Derivation

  1. #1
    Forum Admin topsquark's Avatar
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    Derivation

    I tried to Google this but I don't know how to weed out things like the derivation of the quadratic formula and such.

    Succinctly put we define a derivation as a map $\displaystyle \delta$ on real functions f and g with the property $\displaystyle \delta (f g) = g \delta (f) + f \delta (g)$

    The problem is that I really only know one example: the derivative map. (I have seen one operating on "flows" but I'm getting a little lost on the topic.)

    Does anyone know of any other derivations that have a more or less geometric interpretation?

    Thanks!

    -Dan
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    Re: Derivation

    Quote Originally Posted by topsquark View Post
    I tried to Google this but I don't know how to weed out things like the derivation of the quadratic formula and such.

    Succinctly put we define a derivation as a map $\displaystyle \delta$ on real functions f and g with the property $\displaystyle \delta (f g) = g \delta (f) + f \delta (g)$

    The problem is that I really only know one example: the derivative map. (I have seen one operating on "flows" but I'm getting a little lost on the topic.)

    Does anyone know of any other derivations that have a more or less geometric interpretation?

    Thanks!

    -Dan
    did you find this?
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  3. #3
    Forum Admin topsquark's Avatar
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    Re: Derivation

    Quote Originally Posted by romsek View Post
    did you find this?
    Thanks for the search help. I never thought of looking under Differential Geometry. Time to do some surfing.

    By the way I actually have come across the Pincherle derivative. I never knew it had an actual name for it.

    Thanks for the info. Except in reference to the Lie Algebra and tensor concepts it looks like I won't be running into too many types of derivations in my work. (But I've been wrong before.)

    -Dan
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