Understanding Divergence: Can You Find the Divergence of a Scalar Function?

[AXIS]

I'm doing an assignment where the lecturer has said scalar function g(x,y,z) = x^3 + y + z^2

and vector field F = (2xz,sin y,e^y)

and asked find


a) grad g


which is fairly easy, but then

b) div g

and my understanding was that you can only find the divergence of a vector field not a scalar function.

Am I right an there's been a typo and he meant div F, or can you actually find div g, Because there's no actually mention of F in any of the questions, which is odd.

 

[rachmaninoff]

You're entirely right. It's a typo.

 

[dextercioby]

The scalars don't have a divergence.The divergence is a differntial operator which,applied on a tensor of rank "n",reduces the rank by a unit,namely to "n-1".Since the scalar has already rank "0",you see that it makes no sense to apply the divergence.

Daniel.