Editing Del (section)

===Divergence===
The [[divergence]] of a [[vector field]]
<math> \mathbf v(x, y, z) = v_x \hat\mathbf x  + v_y \hat\mathbf y + v_z \hat\mathbf z </math> is a [[scalar field]] that can be represented as:
:<math>\operatorname{div}\mathbf v = {\partial v_x \over \partial x} + {\partial v_y \over \partial y} + {\partial v_z \over \partial z} = \nabla \cdot \mathbf v </math>

The divergence is roughly a measure of a vector field's increase in the direction it points; but more accurately, it is a measure of that field's tendency to converge toward or diverge from a point.

The power of the del notation is shown by the following product rule:
:<math> \nabla \cdot (f \mathbf v) = (\nabla f) \cdot \mathbf v + f (\nabla \cdot \mathbf v) </math>

The formula for the [[vector product]] is slightly less intuitive, because this product is not commutative:
:<math> \nabla \cdot (\mathbf u \times \mathbf v) = (\nabla \times \mathbf u) \cdot \mathbf v - \mathbf u \cdot (\nabla \times \mathbf v)</math>