The divergence of the curl is equal to zero:
The curl of the gradient is equal to zero:
The volume integral of the divergence of a vector function is equal to the integral over the surface of the component normal to the surface.
Index
Vector calculus
The area integral of the curl of a vector function is equal to the line integral of the field around the boundary of the area.
Index
Vector calculus
In the following identities, u and v are scalar functions while A and B are vector functions. The overbar shows the extent of the operation of the del operator.