Vectors are written in boldface upright type, e.g., $\mathbf{r}, \mathbf{F}$; the same letters printed in lightface italic type $(r, F)$ denote the modulus of a vector.
Unit vectors
$\mathbf{i}, \mathbf{j}, \mathbf{k}$ are the unit vectors of the Cartesian coordinates $x, y, z$ (sometimes the unit vectors are denoted as $\mathbf{e}_{x}, \mathbf{e}_{y}, \mathbf{e}_{z}$ ),
$\mathbf{e}_{\rho}, \mathbf{e}_{\varphi}, \mathbf{e}_{z}$ are the unit vectors of the cylindrical coordinates $\rho, \varphi, z$, $\mathbf{n}, \boldsymbol{\tau}$ are the unit vectors of a normal and a tangent.
Mean values are taken in angle brackets \langle\rangle , e.g., $\langle\mathbf{v}\rangle,\langle P\rangle$.
Symbols $\Delta, d$, and $\delta$ in front of quantities denote:
$\Delta$, the finite increment of a quantity, e.g. $\Delta \mathrm{r}=\mathrm{r}_{2}-\mathrm{r}_{1} ; \Delta U=$ $=U_{2}-U_{1}$,
$d$, the differential (infinitesimal increment), e.g. $d \mathbf{r}, d U$,
$\delta$, the elementary value of a quantity, e.g. $\delta A$, the elementary work.
Time derivative of an arbitrary function $f$ is denoted by $d f / d t$, or by a dot over a letter, $\dot{f}$.

Vector operator $
abla$ (\”nabla\”). It is used to denote the following operations:
$\boldsymbol{
abla}_{\varphi}$, the gradient of $\varphi(\operatorname{grad} \varphi)$.
$\boldsymbol{
abla} \cdot \mathbf{E}$, the divergence of $\mathbf{E}(\operatorname{div} \mathbf{E})$,
$\boldsymbol{
abla} \times \mathbf{E}$, the curl of $\mathbf{E}$ (curl $\mathbf{E}$ ).
Integrals of any multiplicity are denoted by a single sign $\int$ and differ only by the integration element: $d V$, a volume element, $d \mathbf{S}$, a surface element, and $d \mathbf{r}$, a line element. The sign $\oint$ denotes an integral over a closed surface, or around a closed loop.