The equations are a little easier to interpret with time-independent surfaces and volumes. Time-independent surfaces and volumes are "fixed" and do not change over a given time interval. For example, since the surface is time-independent, we can bring the differentiation under the integral sign in Faraday's law: d d t ∬ ∬ Σ Σ B ⋅ ⋅ d S = ∬ ∬ Σ Σ ∂ ∂ B ∂ ∂ t ⋅ ⋅ d S , Maxwell's equations can be formulated with possibly time-dependent surfaces and volumes by using the differential version and using Gauss and Stokes formula appropriately.