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Memorandum on Notation

Vectors are denoted by letters in clarendon type, as E.

The three components of a vector E are denoted by E_x, E_y, E_z, and the magnitude of the vector is denoted by E, so that

$E^{2}=E_{x}^{2}+E_{y}^{2}+E_{z}^{2}$

The vector product of two vectors E and H, which is denoted by [E.H], is the vector whose components are (E_yH_z - E_zH_y, E_zH_x - E_xH_z, E_xH_y - E_yH_x). Its direction is at right angles to the direction of E and H, its magnitude is represented by twice the area of the triangle formed by them.

The scalar product of two vectors E and H is E_xH_x + E_yH_y + E_zH_z. It is denoted by (E.H).

The quantity ${\frac {\partial E_{x}}{\partial x}}+{\frac {\partial E_{y}}{\partial y}}+{\frac {\partial E_{z}}{\partial z}}$ is denoted by div E.

The vector whose components are

$\left({\frac {\partial E_{z}}{\partial y}}-{\frac {\partial E_{y}}{\partial z}},{\frac {\partial E_{x}}{\partial y}}-{\frac {\partial E_{z}}{\partial x}},{\frac {\partial E_{y}}{\partial x}}-{\frac {\partial E_{x}}{\partial z}}\right)$

is denoted by curl E.

If V denote a scalar quantity, the vector whose components are $\left(-{\frac {\partial V}{\partial x}},-{\frac {\partial V}{\partial y}},-{\frac {\partial V}{\partial z}}\right)$ is denoted by grad V.

The symbol ∇ is used to denote the vector operator whose components are ${\frac {\partial }{\partial x}}$, ${\frac {\partial }{\partial x}}$, ${\frac {\partial }{\partial x}}$.

Differentiation with respect to the time is frequently indicated by a dot placed over the symbol of the variable which is differentiated.