The following identities are important in vector calculus:
== Operator notations ==
=== Gradient ===
Gradient of a tensor field, , of order n, is generally written as
and is a tensor field of order n + 1. In particular, if the tensor field has order 0 (i.e. a scalar), , the resulting gradient,
is a vector field.
=== Divergence ===
The divergence of a tensor field, , of non-zero order n, is generally written as
and is a contraction to a tensor field of order n − 1. Specifically, the divergence of a vector is a scalar. The divergence of a higher order tensor field may be found by d...
