$$
\newcommand{\partd}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\partdd}[2]{\frac{\partial^{2} #1}{\partial {#2}^{2}}}
\newcommand{\ddt}{\frac{d}{dt}}
\newcommand{\Int}{\int\limits}
\newcommand{\D}{\displaystyle}
\newcommand{\ie}{\textit{i.e. }}
\newcommand{\dA}{\; \mbox{dA}}
\newcommand{\dz}{\; \mbox{dz}}
\newcommand{\tr}{\mathrm{tr}}
\renewcommand{\eqref}[1]{Eq.~(\ref{#1})}
\newcommand{\reqs}[2]{\req{#1} and \reqand{#2}}
\newcommand{\rthreeeqs}[3]{Eqs.~(\ref{#1}), (\ref{#2}), and (\ref{#3})}
$$