   Chapter 16.5, Problem 12E

Chapter
Section
Textbook Problem

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 scalar 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) (grad f) × (div F)(l) div(curl(grad f))

(a)

To determine

To state and explain: Whether the expression curl f is meaningful or not.

Explanation

In general to perform the curl operation, the field should be a vector (F)

(b)

To determine

To state and explain: Whether the expression grad f is meaningful or not.

(c)

To determine

To state and explain: Whether the expression div F is meaningful or not.

(d)

To determine

To state and explain: Whether the expression curl(gradf) is meaningful or not.

(e)

To determine

To state and explain: Whether the expression grad F is meaningful or not.

(f)

To determine

To state and explain: Whether the expression grad(divF) is meaningful or not.

(g)

To determine

To state and explain: Whether the expression div(gradf) is meaningful or not.

(h)

To determine

To state and explain: Whether the expression grad(divf) is meaningful or not.

(i)

To determine

To state and explain: Whether the expression curl(curlF) is meaningful or not.

(j)

To determine

To state and explain: Whether the expression div(divF) is meaningful or not.

(k)

To determine

To state and explain: Whether the expression (gradf)×(divF) is meaningful or not.

(l)

To determine

To state and explain: Whether the expression div(curl(gradf)) is meaningful or not.

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