Famous PDEs, Maxwell's equations
Important systems of linear partial differential equations are the famous Maxwell equations
\frac{\partial \mathbf{E}}{\partial t} = \mathrm{curl}\mathbf{B},
and
-\mathrm{curl} \mathbf{E} = \mathbf{B}
and
\mathrm{div} \mathbf{E} = \mathrm{div}\mathbf{B} = 0.