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Math Help - Clairaut's Theorem Clarification

  1. #1
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    Clairaut's Theorem Clarification

    Hi

    I'm trying to learn this specific proof on the Equality of Mixed Partials and I pretty much understand the proof, but I need one clarification.

    The proof is posted here:
    http://homepage.smc.edu/nestler_andr...11clairaut.pdf

    I am confused on what \Delta(h) means. At first I thought it was the change in h, but the parenthesis lead me to believe that it stands for a function of h. It would make sense to me if this was actually just a function of h, but I am not one-hundred percent sure.

    Could someone tell me what \Delta(h) represents?

    Thank you.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Anthonny View Post
    Hi

    I'm trying to learn this specific proof on the Equality of Mixed Partials and I pretty much understand the proof, but I need one clarification.

    The proof is posted here:
    http://homepage.smc.edu/nestler_andr...11clairaut.pdf

    I am confused on what \Delta(h) means. At first I thought it was the change in h, but the parenthesis lead me to believe that it stands for a function of h. It would make sense to me if this was actually just a function of h, but I am not one-hundred percent sure.

    Could someone tell me what \Delta(h) represents?

    Thank you.
    In the second line of the proof, we're told that \Delta(h)=(f(a+h,b+h)-f(a+h,b))-(f(a,b+h)-f(a,b))...
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  3. #3
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    \Delta(h) is not the change in h. \Delta(h) is a function of h. So, yes, you are right.
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