I have looked at the documentation for tensor and vector calculus but still struggling with the Grad and Div functions. For example, I want to show that:
Grad (Div V) = Vj,ji ii
I tried
\!\(
\*SubscriptBox[\(\[Del]\), \({x, y, z}\)]\((
\*SubscriptBox[\(\[Del]\), \({x, y, z}\)] . v /@ {x, y, z})\)\)
This gives me a vector alright, but not all the terms I expected, i.e.
What am I missing?
You have to provide arguments for the vector v and it also has to be in the form of a list of 3 components: as in:
Grad[Div[{v1[x1, x2, x3], v2[x1, x2, x3], v3[x1, x2, x3]}, {x1, x2, x3}], {x1, x2, x3}]
which gives
$ \left{\text{v1}^{(2,0,0)}(\text{x1},\text{x2},\text{x3})+\text{v2}^{(1,1,0)}(\text{x1},\text{x2},\text{x3})+\text{v3}^{(1,0,1)}(\text{x1},\text{x2},
\text{x3}),\text{v1}^{(1,1,0)}(\text{x1},\text{x2},\text{x3})+\text{v2}^{(0,2,0)}(\text{x1},\text{x2},\text{x3})+\text{v3}^{(0,1,1)}(\text{x1},\text{x2},\text{x3}),\text{v1}^{(1,0,1)}(\text{x1},\text{x2},\text{x3})+\text{v2}^{(0,1,1)}(\text{x1},\text{x2},\text{x3})+\text{v3}^{(0,0,2)}(\text{
x1},\text{x2},\text{x3})\right} $
Ah, v /@ {x, y, z} describes a scalar function, not a vector.
Thanks David!