%%% USER-DEFINED COMMANDS	
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
\newcommand{\scal}[1]{\left\langle {#1} \right\rangle}
\newcommand{\abs}[1]{\left\lvert {#1}\right\rvert}
\newcommand{\del}{\partial}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\e}{\mathrm{e}}
\newcommand{\ii}{\mathrm{i}}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\diff}[2][{}]{\frac{\dd^{#1}}{\dd#2^{#1}}}
\newcommand{\partdiff}[2][{}]{\frac{\del^{#1}}{\del#2^{#1}}}
\newcommand{\qed}{\ensuremath{\hfill\square}}
\newcommand{\mat}[1]{\ensuremath{\begin{pmatrix}#1\end{pmatrix}}}
\newcommand{\smat}[1]{\ensuremath{\left(\begin{smallmatrix}#1\end{smallmatrix}\right)}}
\renewcommand{\thesection}{\Roman{section}}
\renewcommand{\thesubsection}{\thesection.\it\alph{subsection}}