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Rigorous dirrerential definition and physics

  1. Oct 15, 2012 #1
    My question is rather simple but it puzzles me for a long time actually. If we have a look at differential as physicists usually do we came up with a simple definition of "infinitesimal variable change". And this idea then preserves elsewhere like in the definition of entropy:

    [itex]\mathrm{d} S = \frac{\mathrm{d} Q}{T}[/itex]

    or in calculus (e.g. for differential questions etc.). On the other hand mathematicians define the differential as a function:

    [itex]\mathrm{d} f (x_0) (h) = f'(x_0)h[/itex]

    for a given [itex]h[/itex] and so on. The question is how to find a bridge between those two formulations.

  2. jcsd
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