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% calc.tex
% Anders G S Svensson
% $Date: 1994/08/18 00:55:29 $
% $Revision: 1.0 $
\chardef\CalccodE=\catcode`\@
\catcode`\@=11
% Get superscript height right. Plain has
%
% \def\sin{\mathop{\rm sin}\nolimits}
%
% etc, but \sin^2 x and \cos^2 x should have the superscript at the same
% height.
%
\def\sin{\mathop{\smash{\rm sin}}\nolimits}
\def\cos{\mathop{\smash{\rm cos}}\nolimits}
\def\tan{\mathop{\smash{\rm tan}}\nolimits}
\def\csc{\mathop{\smash{\rm csc}}\nolimits}
\def\sec{\mathop{\smash{\rm sec}}\nolimits}
\def\cot{\mathop{\smash{\rm cot}}\nolimits}
\def\invsin{\sin^{-1}} \def\arcsin{\mathop{\smash{\rm arcsin}}\nolimits}
\def\invcos{\cos^{-1}} \def\arccos{\mathop{\smash{\rm arccos}}\nolimits}
\def\invtan{\tan^{-1}} \def\arctan{\mathop{\smash{\rm arctan}}\nolimits}
\def\invcsc{\csc^{-1}} \def\arccsc{\mathop{\smash{\rm arccsc}}\nolimits}
\def\invsec{\sec^{-1}} \def\arcsec{\mathop{\smash{\rm arcsec}}\nolimits}
\def\invcot{\cot^{-1}} \def\arccot{\mathop{\smash{\rm arccot}}\nolimits}
% First partials
%
\def\p#1\wrt#2{{\def\@@tmp{#1}\partial \ifx\@@tmp\empty \else #1\fi
\over \partial #2}}
\let\fp\p % "partial wrt"
%
% Second partials
% \sp is for superscripts!
%
\def\spar#1\wrt#2#3{{\def\@@tmp{#1}\partial^2 \ifx\@@tmp\empty \else \!#1 \fi
\over \partial #2 \partial #3}}
\let\smp\spar % Second mixed partial
\def\spp#1\wrt#2{{\def\@@tmp{#1}\partial^2 \ifx\@@tmp\empty \else \!#1 \fi
\over \partial #2^2}} % "2nd pure partial..."
%
% Ordinary first derivatives
%
\def\d#1\wrt#2{{\def\@@tmp{#1}d \ifx\@@tmp\empty \else #1 \fi
\over d #2}}
\let\fd\d
%
% Ordinary second derivatives
%
\def\sd#1\wrt#2#3{{\def\@@tmp{#1}d^2 \ifx\@@tmp\empty \else \!#1 \fi
\over d #2 d #3}}
\let\smd\sd
\def\spd#1\wrt#2{{\def\@@tmp{#1}d^2 \ifx\@@tmp\empty \else \!#1 \fi
\over d #2^2}}
\let\grad\nabla
\let\implies\Longrightarrow
% Unit vectors
%
\def\unit#1{\hat{#1}}
\def\ui{\unit \imath}
\def\uj{\unit \jmath}
\def\uk{\unit k}
\def\ue{\unit e} % \ue_1,...,\ue_n
\catcode`\@=\CalccodE
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