% punctuation
\newcommand{\com}{\, ,}
\newcommand{\per}{\, .}
\newcommand{\andd}{\qquad \text{and} \qquad }

% equations
\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}

%% A nice definition
\newcommand{\defn}{\ensuremath{\stackrel{\mathrm{def}}{=}}}

%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\sqr}{\mbox{sqr}}
\newcommand{\saw}{\mbox{saw}}
\newcommand{\ramp}{\mbox{ramp}}
\newcommand{\cusp}{\mbox{cusp}}
\newcommand{\ind}{\mbox{ind}}
\newcommand{\sgn}{\mbox{sgn}}
\newcommand{\erfc}{\mbox{erfc}}
\newcommand{\erf}{\mbox{erf}}%%%%%%%%% %%%%

%\newcommand{\ord}{\mbox{ord}}
\newcommand{\ord}{\mathit{O}}
\newcommand{\Ai}{\mbox{Ai}}
\newcommand{\Bi}{\mbox{Bi}}
\newcommand{\half}{\tfrac{1}{2}}

\newcommand{\mathematica}{\textsc{mathematica}}
\newcommand{\matlab}{\textsc{matlab}}
%
%\def\bx{{\vec x}}
%\def\bX{{\vec X}}
%\def\bq{{\vec q}}
%\def\bu{{\vec u}}
%\def\by{{\vec y}}
%\def\br{{\vec r}}
%\def\bi{{\vec i}}
%%\def\nabs{\vec{\nabla}}  %% boldface nabla
\newcommand{\nabs}{{\boldsymbol{\nabla}}}

% roman
\newcommand{\ii}{\mathrm{i}}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\ee}{\mathrm{e}}
\newcommand{\DD}{\mathrm{D}}
\newcommand{\EE}{\mathrm{E}}

\newcommand{\tr}{\text{tr}}
\renewcommand{\det}{\text{det}}

%%% Cals here %%%%%
\newcommand{\D}{{\mathcal D}}
\newcommand{\E}{{\mathcal E}}
\newcommand{\B}{{\mathcal B}}
\newcommand{\F}{{\mathcal F}}
\newcommand{\HH}{{\mathcal H}}
\newcommand{\LL}{\mathcal{L}}
\def\Q{{\cal Q}}
\def\Z{{\cal Z}}
\def\C{{\cal C}}
\def\R{{\cal R}}


%\def\E{{\cal E}}


\newcommand{\sL}{\mathsf{L}}
\def\GG{{\mathbb G}}
%%%%%%%%%%%%%%%%%%%%%

\def\la{\langle}
\def\ra{\rangle}
%%%%%%%%% SHOCK DEFS  %%%%
\def\laa{[\!\![}
\def\raa{]\!\!]}
\def\xip{\xi_+}
\def\xim{\xi_-}

%% stop typing all of epsilon
\newcommand{\ep}{\ensuremath {\epsilon}}
\newcommand{\de}{\ensuremath {\delta}}

\newcommand{\sig}{\ensuremath {\sigma}}
\newcommand{\om}{\ensuremath {\omega}}


%% bold
\newcommand{\bA}{\ensuremath {\boldsymbol {A}}}
\newcommand{\bU}{\ensuremath {\boldsymbol {U}}}
\newcommand{\bJ}{\ensuremath {\boldsymbol {J}}}
\newcommand{\bX}{\ensuremath {\boldsymbol {X}}}
\newcommand{\bQ}{\ensuremath {\boldsymbol {Q}}}
\newcommand{\bn}{\ensuremath {{\boldsymbol {n}}}}
\newcommand{\bv}{\ensuremath {{\boldsymbol {v}}}}
\newcommand{\bu}{\ensuremath {{\boldsymbol {u}}}}
\newcommand{\ba}{\ensuremath {{\boldsymbol {a}}}}
\newcommand{\bx}{\ensuremath {{\boldsymbol {x}}}}
\newcommand{\bp}{\ensuremath {{\boldsymbol {p}}}}
\newcommand{\bq}{\ensuremath {{\boldsymbol {q}}}}
\newcommand{\be}{\ensuremath {{\boldsymbol {e}}}}
\newcommand{\br}{\ensuremath {{\boldsymbol {r}}}}
\newcommand{\bt}{\ensuremath {{\boldsymbol {t}}}}
\newcommand{\by}{\ensuremath {{\boldsymbol {y}}}}
\newcommand{\bz}{\ensuremath {{\boldsymbol {z}}}}


\newcommand{\bff}{\ensuremath {{\boldsymbol {f}}}}
\newcommand{\bbff}{\ensuremath {{\boldsymbol {\bar f}}}}
%
%\renewcommand{\bff}{\ensuremath {{\boldsymbol {f}}}}


\newcommand{\p}{\partial}
\newcommand{\vg}{v_{\mathrm{g}}}
\newcommand{\cp}{c_{\mathrm{p}}}
\newcommand{\ks}{k_{\star}}




\newcommand{\pde}{\textsc{pde}}
\newcommand{\ode}{\textsc{ode}}
\newcommand{\cc}{\textsc{cc}}
\newcommand{\cbc}{\textsc{cbc}}
\newcommand{\dc}{\textsc{dc}}
\newcommand{\dbc}{\textsc{dbc}}
\newcommand{\byu}{\textsc{byu}}
\newcommand{\rhs}{\textsc{rhs}}
\newcommand{\lhs}{\textsc{lhs}}
\newcommand{\fit}{\textsc{fit}}
\newcommand{\aka}{\textsc{aka}}
\newcommand{\pdf}{\textsc{pdf}}

\newcommand{\WKB}{\text{WKB}}


%vector analysis
\newcommand{\cross}{\times}
\newcommand{\grad}{\boldsymbol{\nabla}}
\newcommand{\bnabla}{\boldsymbol{\nabla}}

\newcommand{\gradH}{\bnablaH}
\newcommand{\curl}{\boldsymbol{\nabla} \!\times\!}
\newcommand{\bcdot}{ \boldsymbol{\cdot} }
\renewcommand{\div}{\boldsymbol{\nabla} \!\bcdot\!}
%\newcommand{\lap}{\triangle}
\newcommand{\lap}{\nabla^2}


\newcommand{\ddxi}{\left(\bxt\!\bcdot \!\grad\right)\!}
\newcommand{\ddu}{\left(\bu\!\bcdot \!\grad\right)\!}


\newcommand{\eye}{\boldsymbol{\hat x}}
\newcommand{\jay}{\boldsymbol{\hat y}}
\newcommand{\kay}{\boldsymbol{\hat z}}


\newcommand{\bxh}{\boldsymbol{\hat x}}
\newcommand{\byh}{\boldsymbol{\hat y}}
\newcommand{\bzh}{\boldsymbol{\hat z}}


\newcommand{\rp}{\right)}
\newcommand{\lp}{\left(}
\newcommand{\ov}{\overline}
\newcommand{\eqand}{\hspace{0.5cm} \text{and} \hspace{0.5cm}}


