deletions | additions       diff --git a/begin_equation_3_begin_align__.tex b/begin_equation_3_begin_align__.tex  deleted file mode 100644  index f933622..0000000  --- a/begin_equation_3_begin_align__.tex  +++ /dev/null 
...
\begin{equation}  (3)\;  \begin{align*}  % d/dy  \frac{\partial}{\partial y}: \;  % v*u_y  v \frac{\partial u}{\partial y}   \to  \frac{\partial}{\partial y} \left( v \frac{\partial u}{\partial y}\right)   = \frac{\partial v}{\partial y} \cdot \frac{\partial u}{\partial y} + v \frac{\partial^2 u}{\partial y^2}   &= \frac{\partial}{\partial y} \left[ \frac{\partial \zeta}{\partial x} \cdot \frac{\partial}{\partial y} \left( -\frac{\partial \zeta}{\partial y} \right) \right] = \\  %newline   &=-\frac{\partial^2 \zeta}{\partial x \partial y } \cdot \frac{\partial^2 \zeta}{\partial y^2 }   + -\frac{\partial \zeta}{\partial x } \cdot \frac{\partial^3 \zeta}{\partial y^3 }\\  %newline  % d/dx  \frac{\partial}{\partial x}: \;  % v*v_y  v \frac{\partial v}{\partial y}   \to  \frac{\partial}{\partial x} \left( v \frac{\partial v}{\partial y}\right)   = \frac{\partial v}{\partial x} \cdot \frac{\partial v}{\partial y} + v \frac{\partial^2 v}{\partial x \partial y}   &= \frac{\partial}{\partial x}\left[ \frac{\partial \zeta}{\partial x} \cdot \frac{\partial}{\partial y} \left( \frac{\partial \zeta}{\partial x} \right) \right] = \\  %newline   &= \frac{\partial^2 \zeta}{\partial x^2 } \cdot \frac{\partial^2 \zeta}{\partial x \partial y }   - \frac{\partial \zeta}{\partial x } \cdot \frac{\partial^3 \zeta}{\partial x^2 \partial y }\\  \end{align*}  \end{equation}