Ordinary vs. partial derivatives

[DiracPool]

I'm thinking in particular about Lenny Susskind's lectures, but I've seen other lecturers do it too. They'll be writing equation after equation using the partial derivative symbol:

$\frac{\partial f}{\partial a}$

And then at some point they'll realize that some problem they're currently doing is only in one variable and they'll get very embarassed, erase the partial d symbol, and replace it with an ordinary d symbol, like so:

$\frac{df}{dt}$

My question is, Why does it matter? Why not just always use the partial symbol? You'd get the same result, wouldn't you? I mean, you wouldn't get a wrong answer if you used the partial symbol instead of the ordinary one. The only relevance in their distinction is to indicate whether or not the problem is a single or multi-variable one, right?

 

[jedishrfu]

I think in using the partial symbol you are acknowledging that there are several independent variables to the function you're differentiating whereas in using the d/dx notation you are saying its dependent on x only and no other.

Computationally they are the same but your insight into what's going is more important and this helps the reader understand the problem better knowing that there are other free variables in the mix.