# Rigorous dirrerential definition and physics

1. Oct 15, 2012

### rkaminski

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:

$\mathrm{d} S = \frac{\mathrm{d} Q}{T}$

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

$\mathrm{d} f (x_0) (h) = f'(x_0)h$

for a given $h$ and so on. The question is how to find a bridge between those two formulations.