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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.