Module 1 : A Crash Course in Vectors
Lecture 4 : Gradient of a Scalar Function
 
\begin{displaymath}\left[F_y(y+dy)-F_y(y)\right]dxdz \end{displaymath}
Expanding $F_y(y+dy)$ in a Taylor series and retaining only the fiirst order term
 
\begin{displaymath}F_(y+dy)= F_y+\frac{\partial F_y}{\partial y}dy\end{displaymath}
  so that the flux from these two faces is
 
\begin{displaymath}\frac{\partial F_y}{\partial y}dxdydz=\frac{\partial F_y}{\partial y}dV\end{displaymath}
  where $dV=dxdydz$ is the volume of the cuboid.
   
1
9