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 For a vector with components $$X, Y, Z$$ we sometimes also write $$(X, Y, Z)$$.

e. If $$\phi$$ is a scalar magnitude, then we understand by $$\dot{\phi}$$ the derivative with respect to time t. The letter $$\dot{\mathfrak{A}}$$ denotes a vector with components: $$\dot{\mathfrak{A}}_{x}, \dot{\mathfrak{A}}_{y}, \dot{\mathfrak{A}}_{z}$$, or $$\tfrac{\partial\mathfrak{A}_{x}}{\partial t}$$ etc.

f. The expression

we call the "integral of vector $$\mathfrak{A}$$ over the surface $$\sigma$$", and the magnitude

the "line integral of line s".

g. If a vector $$\mathfrak{A}$$ 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 $$\mathfrak{A}$$ and denote it by

For any space limited by a surface $$\sigma$$, 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 $$\mathfrak{B}$$, which (independent from the choses coordinate system) is defined by the distribution of $$\mathfrak{A}$$. We call this vector the rotation of $$\mathfrak{A}$$ and denote it by