For a vector with components we sometimes also write .
e. If is a scalar magnitude, then we understand by the derivative with respect to time t. The letter denotes a vector with components: , or etc.
f. The expression
we call the "integral of vector over the surface ", and the magnitude
the "line integral of line s".
g. If a vector in any point of space is given, then
has everywhere a certain value, independent of the choice of coordinate system. We call this magnitude "divergence" of vector and denote it by
.
For any space limited by a surface , the relation is given
when, as already mentioned, the perpendicular n will be drawn into the outside.
h. The magnitudes
can be interpreted as the components of vector , which (independent from the choses coordinate system) is defined by the distribution of . We call this vector the rotation of and denote it by