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Differential notation help

  • Thread starter Castilla
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  • #1
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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.
 

Answers and Replies

  • #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].
 
  • #3
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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).
 

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