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\begin{equation}
  \Dgrad A
 = \left( \frac{1}{h_1} \DP{A}{x_1}, \frac{1}{h_2} \DP{A}{x_2}, 
          \frac{1}{h_3} \DP{A}{x_3} \right),
\end{equation}
\begin{equation}
  \Ddiv \Dvect{F} 
  = \frac{1}{h_1 h_2 h_3} 
    \left[ \DP{}{x_1} ( h_2 h_3 F_1)
           +  \DP{}{x_2} ( h_1 h_3 F_2)
           +  \DP{}{x_3} ( h_1 h_2 F_3)
    \right],
\end{equation}
\begin{equation}
    \nabla^2 A 
  = \frac{1}{h_1 h_2 h_3} 
    \left[   \DP{}{x_1} \left( \frac{h_2 h_3}{h_1} \DP{A}{x_1} \right)
           + \DP{}{x_2} \left( \frac{h_1 h_3}{h_2} \DP{A}{x_2} \right)
           + \DP{}{x_3} \left( \frac{h_1 h_2}{h_3} \DP{A}{x_3} \right)
    \right],
\end{equation}
\begin{equation}
  \Drot \Dvect{F}
  = \left(  \frac{1}{h_2 h_3}
            \left[ \DP{(h_3 F_3)}{x_2}  - \DP{(h_2 F_2)}{x_3}  \right],
            \frac{1}{h_3 h_1}
            \left[ \DP{(h_1 F_1)}{x_3}  - \DP{(h_3 F_3)}{x_1}  \right],
            \frac{1}{h_1 h_2}
            \left[ \DP{(h_2 F_2)}{x_1}  - \DP{(h_1 F_1)}{x_2}  \right]
   \right),
\end{equation}
\begin{equation}
  \DD{A}{t} 
  = \DP{A}{t} + \frac{v_1}{h_1} \DP{A}{x_1}
    + \frac{v_2}{h_2} \DP{A}{x_2}  + \frac{v_3}{h_3} \DP{A}{x_3},
\end{equation}
\begin{equation}
  \DD{\Dvect{v}}{t}
  =  \sum^3_{j=1} \left[ \left( \DP{v_j}{t} + \Dvect \nabla v_j \right)
      + \sum^3_{i=1, i=j}
        \left( \frac{v_j}{h_j} \frac{v_i}{h_i} \DP{h_j}{x_i}
              - \frac{v_i}{h_i} \frac{v_i}{h_j} \DP{h_i}{x_j} \right)
     \right] \Dvect{e}_j.
\end{equation}

\vspace{5mm}

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\begin{equation}
  \Dgrad A
 = \left( \frac{1}{r \cos \varphi} \DP{A}{\lambda}, 
          \frac{1}{r} \DP{A}{\varphi}, 
          \DP{A}{r} \right),
\end{equation}
\begin{equation}
  \Ddiv \Dvect{F} 
  = \frac{1}{r^2 \cos \varphi} 
    \left[ r \DP{F_1}{\lambda}
           + r \DP{}{\varphi} ( \cos \varphi F_2)
           +  \cos \varphi  \DP{}{r} ( r^2 F_3)
    \right],
\end{equation}
\begin{equation}
    \nabla^2 A 
  = \frac{1}{r^2 \cos \varphi} 
    \left[   \DP{}{\lambda} \left( \frac{1}{\cos \varphi} \DP{A}{\lambda}\right)
           + \DP{}{\varphi} \left( \cos \varphi \DP{A}{\varphi} \right)
           + \DP{}{r} \left( r^2 \cos \varphi  \DP{A}{r} \right)
    \right],
\end{equation}
\begin{equation}
  \Drot \Dvect{F}
  = \left(  \frac{1}{r}
            \left[ \DP{F_3}{\varphi} - \DP{}{r} (r F_2) \right], 
           \frac{1}{r \cos \varphi}
            \left[ \DP{}{r} (r \cos \varphi F_1) - \DP{F_3}{\lambda} \right],
           \frac{1}{r \cos \varphi}
            \left[ \DP{F_2}{\lambda} - \DP{}{\varphi} (\cos \varphi F_1) \right]
   \right),
\end{equation}
\begin{equation}
  \DD{A}{t} 
  = \DP{A}{t} + \frac{u}{r \cos \varphi} \DP{A}{\lambda}
    + \frac{v}{r} \DP{A}{\varphi}  + w \DP{A}{r},
\end{equation}
%\begin{equation}
%  \DD{\Dvect{v}}{t}
%  =  \sum^3_{j=1} \left[ \left( \DP{v_j}{t} + \Dvect \nabla v_j \right)
%      + \sum^3_{i=1, i=j}
%        \left( \frac{v_j}{h_j} \frac{v_i}{h_i} \DP{h_j}{x_i}
%              - \frac{v_i}{h_i} \frac{v_i}{h_j} \DP{h_i}{x_j} \right)
%     \right] \Dvect{e}_j,
%\end{equation}
