
\def\dtdhxx{\frac{\partial t}{\partial h_{x_1}}}
\def\dtdxz {\frac{\partial t}{\partial x_3}}
\def\dtdhx {\frac{\partial t}{\partial h_{x_1}}}
\def\dtdhz {\frac{\partial t}{\partial h_{x_3}}}
\def\dtdhex{\frac{\partial t}{\partial h_{\xi_1}}}
\def\dtdhez{\frac{\partial t}{\partial h_{\xi_3}}}

\def\dtdxx{\frac{\partial t}{\partial x_1}}
\def\dtdxz{\frac{\partial t}{\partial x_3}}
\def\dtdex{\frac{\partial t}{\partial \xi_1}}
\def\dtdez{\frac{\partial t}{\partial \xi_3}}
\def\dzdh{\frac{\partial z}{\partial h}}

% e over x
\def\dexdxz{\frac{\partial \xi_1}{\partial x_3}}
\def\dexdxx{\frac{\partial \xi_1}{\partial x_1}}
\def\dezdxz{\frac{\partial \xi_3}{\partial x_3}}
\def\dezdxx{\frac{\partial \xi_3}{\partial x_1}}

% x over e
\def\dxxdex{\frac{\partial x_1}{\partial \xi_1}}
\def\dxzdex{\frac{\partial x_3}{\partial \xi_1}}
\def\dxxdez{\frac{\partial x_1}{\partial \xi_3}}
\def\dxzdez{\frac{\partial x_3}{\partial \xi_3}}

% hx over he
\def\dhxxdhex{\frac{\partial h_{x_1}}{\partial h_{\xi_1}}}
\def\dhxxdhez{\frac{\partial h_{x_1}}{\partial h_{\xi_3}}}
\def\dhxzdhex{\frac{\partial h_{x_3}}{\partial h_{\xi_1}}}
\def\dhxzdhez{\frac{\partial h_{x_3}}{\partial h_{\xi_3}}}

% he over hx
\def\dhexdhxx{\frac{\partial h_{\xi_1}}{\partial h_{x_1}}}
\def\dhexdhxz{\frac{\partial h_{\xi_1}}{\partial h_{x_3}}}
\def\dhezdhxx{\frac{\partial h_{\xi_3}}{\partial h_{x_1}}}
\def\dhezdhxz{\frac{\partial h_{\xi_3}}{\partial h_{x_3}}}

% hx over e
\def\dhxxdex{\frac{\partial h_{x_1}}{\partial {\xi_1}}}
\def\dhxxdez{\frac{\partial h_{x_1}}{\partial {\xi_3}}}
\def\dhxzdex{\frac{\partial h_{x_3}}{\partial {\xi_1}}}
\def\dhxzdez{\frac{\partial h_{x_3}}{\partial {\xi_3}}}

% he over x
\def\dhexdxx{\frac{\partial h_{\xi_1}}{\partial {x_1}}}
\def\dhexdxz{\frac{\partial h_{\xi_1}}{\partial {x_3}}}
\def\dhezdxx{\frac{\partial h_{\xi_3}}{\partial {x_1}}}
\def\dhezdxz{\frac{\partial h_{\xi_3}}{\partial {x_3}}}

% hx over x
\def\dhxxdxx{\frac{\partial h_{x_1}}{\partial {x_1}}}
\def\dhxxdxz{\frac{\partial h_{x_1}}{\partial {x_3}}}
\def\dhxzdxx{\frac{\partial h_{x_3}}{\partial {x_1}}}
\def\dhxzdxz{\frac{\partial h_{x_3}}{\partial {x_3}}}

% he over e
\def\dhexdex{\frac{\partial h_{\xi_1}}{\partial {\xi_1}}}
\def\dhexdez{\frac{\partial h_{\xi_1}}{\partial {\xi_3}}}
\def\dhezdex{\frac{\partial h_{\xi_3}}{\partial {\xi_1}}}
\def\dhezdez{\frac{\partial h_{\xi_3}}{\partial {\xi_3}}}

% x over he
\def\dxxdhex{\frac{\partial x_1}{\partial h_{\xi_1}}}
\def\dxxdhez{\frac{\partial x_1}{\partial h_{\xi_3}}}
\def\dxzdhex{\frac{\partial x_3}{\partial h_{\xi_1}}}
\def\dxzdhez{\frac{\partial x_3}{\partial h_{\xi_3}}}

% x over hx
\def\dxxdhxx{\frac{\partial x_1}{\partial h_{x_1}}}
\def\dxxdhxz{\frac{\partial x_1}{\partial h_{x_3}}}
\def\dxzdhxx{\frac{\partial x_3}{\partial h_{x_1}}}
\def\dxzdhxz{\frac{\partial x_3}{\partial h_{x_3}}}

% e over he
\def\dexdhex{\frac{\partial \xi_1}{\partial h_{\xi_1}}}
\def\dexdhez{\frac{\partial \xi_1}{\partial h_{\xi_3}}}
\def\dezdhex{\frac{\partial \xi_3}{\partial h_{\xi_1}}}
\def\dezdhez{\frac{\partial \xi_3}{\partial h_{\xi_3}}}

% rm font
\def\rtan{{\rm tan}}
\def\rcos{ {\rm cos} }
\def\rsin{ {\rm sin} }
\def\rsinh{ {\rm sinh} }
\def\rcosh{ {\rm cosh} }
\def\w{\omega}

\chapter{Generalized-coordinate ADCIGs} 
%\author{Jeff Shragge}

\lefthead{Shragge}
%\righthead{ADCIGs in generalized coordinates}
%\footer{SEP-134}


%\maketitle

%\author{Jeff Shragge}

\input{abstract}
\input{body}
%
%
%\bibliographystyle{seg}
%\bibliography{SEP,SEG,MISC,GEOTLE,allrefs}
 
%\input{appendix}
