Vector Fields
A vector functions of three variables is defined as
(1)
Curl of a Vector Field
The curl of a vector field is a vector field itself, defined as
(2)
Watch the following YouTube video for 2D curl intuition.
Divergence of a Vector Field
The divergence of a vector field is a scalar defined as
(3)
Watch the following YouTube videos for divergence intuition.
Reference
Dennis G. Zill. Advanced Engineering Mathematics, edition. Jones Bartlett Learning. 2016.