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Homework Help: Exact Differentials

  1. Sep 1, 2010 #1
    I am reading a math review in my thermodynamics text and I a little confused by this. Here is the excerpt:


    I am confused by the part where it says
    If they selected x = (y, z) then isn't that saying that x is dependent on y? So how can we just turn around and say y = y(x, z) ? That is, if we selected x as dependent in the first function, why can we turn around and call it independent in the second.

    Sorry, this might be a stupid question. I just don't see why we bother calling variables independent and dependent in a situation like this?
  2. jcsd
  3. Sep 1, 2010 #2


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    As a simple example if you had the equation x+y+z=0 you could write any variable as a function of the other two quite simply.

    The dependent/independent lines are obviously blurred here; you just use them for the purposes of being able to describe what counts as a function and what's being considered as a variable when differentiating
  4. Sep 1, 2010 #3
    Office Shredder strikes again! Thanks boss. This explanation makes great sense. I figured I was over-analyzing the words here.

    Thanks again!
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