What does the notation Div with an arrow on top mean in PDE studies?

[island-boy]

I encountered this notation in my PDE studies, but I was confused by what it meant. What does the notation Div with an arrow on top (of the word) mean? I figured meant the divergence of something...but am curious about its exact meaning.

 

[nrqed]

I encountered this notation in my PDE studies, but I was confused by what it meant. What does the notation Div with an arrow on top (of the word) mean? I figured meant the divergence of something...but am curious about its exact meaning.

The divergence operator in Cartesian coordinates is
{\vec \nabla} = {\hat i} {\partial \over \partial x} + {\hat j} {\partial \over \partial y}+{\hat k} {\partial \over \partial z}

 

[island-boy]

so div \rightharpoonup = {\vec \nabla} right?
hmm, makes sense. Thanks!

 

[HallsofIvy]

Yes- since div f is a vector-valued function, many (but not all) texts use
{\vec \nabla}
to represent it. Other texts use just \nabla.