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Differential notation help

  1. Sep 27, 2005 #1

    Castilla

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    A question: is it possible (maybe handling differentials, I don't know) to have in the same formula these two expressions: [tex] \frac{dp}{dq}[/tex] and
    [tex] \frac{dq}{dp}[/tex]?

    I think it is illogical. It would imply that at same time p is a function of q and q is a function of p. That seems nonsense to me. Am I allright?

    Thanks for any answer.
     
    Castilla, Sep 27, 2005
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  3. Sep 27, 2005 #2

    Hurkyl

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    Isn't differential notation great? :rolleyes:

    There are several routes to happiness, but they all will give the same answer in the end (which is the reason such notation continues to be popular -- brevity is surprisingly important in mathematical notation).


    One route to happiness is to have p be a function of q, and if the conditions of the inverse function theorem are satisfied, we can (locally) define a function [itex]\hat{q}[/itex] with the property that [itex]\hat{q}(p(q)) = q[/itex], and then we can say that [itex]dq/dp[/itex] really "means" [itex]d\hat{q}/dp[/itex].
     
    Hurkyl, Sep 27, 2005
  4. Sep 27, 2005 #3

    Castilla

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    I have not here the paper where I found the formula that contained both
    derivatives, but tomorrow I will get it and I will post it here with all its context. Then I will ask you, Hurkyl, if said formula is aceptable on grounds of the explanation that you kindly have posted. (Excuse my english).
     
    Castilla, Sep 27, 2005
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