Abstract: It is proved that the sequence of integral symbol and derivation symbol could be exchanged when the rate of change over time of the flux that vector field through moving Gaussian surface is calculated. The formula on the rate of change over time of the area element vector on the sports surface is derived. Several algorithms about the rate of change over time of the flux that vector field through moving Gaussian surface are given.

Key words: vector field, moving Gaussian surface, area element vector, flux, time varing rate