Stationary Field: Why Professor and Books Differ

[ATY]

So, I got a question about stationary field.
In the lecture the professor said, that our field is stationary, so we have $\frac{du}{dt}=0$, but from what I read in books, it only means, that $\frac{\partial u}{\partial t} =0$. Who is right and why ?

 

[Orodruin]

The total derivative makes no sense unless you have a function of $t$ only. A stationary field is a field that does not depend on $t$ and therefore $\partial_t u = 0$.