Module 15 :  Vector fields, Gradient, Divergence and Curl
Lecture 44 :  Gradient Divergence and Curl [Section 44.1]
 

Hence, the net change in all directions is given by

where and so on. On the other hand, the rate of change of density is and hence the loss of mass in time across parallelepiped is

Since there are no sinks or sources, we have, as approaches

i.e.,

i.e.,

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