Module 1 : A Crash Course in Vectors
Lecture 4 : Gradient of a Scalar Function
  Combining the above with contributions from the two remaining pairs of faces, the total flux is
 
\begin{displaymath}\left(\frac{\partial F_x}{\partial x}+ \frac{\partial F_y} {\partial y}+ \frac{\partial F_z}{\partial z}\right)dV\end{displaymath}
  Thus
 
\begin{displaymath}\int_S\vec F\cdot\vec{dS}= \int \left(\frac{\partial F_x}{\pa... ...tial F_y}{\partial y}+ \frac{\partial F_z}{\partial z}\right)dV\end{displaymath}
  Comparing with the statement of the divergence theorem, we have
 
\begin{displaymath}{\rm div}\vec F = \left(\frac{\partial F_x}{\partial x}+ \fr... ...artial F_y}{\partial y}+ \frac{\partial F_z}{\partial z}\right)\end{displaymath}
   
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