next up previous
Next: The Divergence of a Up: The Del Operator Previous: The Gradient-Your First Operator

What else can we do with Del?

Since $\nabla$ is almost a vector, we can think of all the ways that we can act on vectors and see how del should respond.


  Vectors Del
1 Multiply by a scalar, a: $\vec{A}a$ Operate on scalar f: $\nabla
f$ (the gradient)
2 Dot product with $\vec{B}$: $\vec{A} \cdot \vec{B}$ Dot product with $\vec{F}(x,y,z)$: $\nabla \cdot \vec{F}$
3 Cross product with $\vec{B}$: $\vec{A} \times \vec{B}$ Cross product on $\vec{F}(x,y,z)$: $\nabla \times \vec{F}$

The gradient is described in the chapter on derivatives. Below, we discuss the other operations of del.



Vector Calculus
8/19/1998