Chapter 16.5, Problem 12E

Let f be a scalar field and F a vector field. State whether each expression is meaningful. If not, explain why. If so, state whether it is a field or a vector field.

(a) curl f

(b) grad f

(c) div F

(d) curl(grad f)

(e) grad F

(f) grad(div F)

(g) div(grad f)

(h) grad(div f)

(i) curl(curl F)

(j) div(div F)

(k) $\left(gradf\right)\times \left(divF\right)$

(l) div(curl(grad f))