Skip to main content\( \newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\mnr}{mnr}
\DeclareMathOperator{\cof}{cof}
\DeclareMathOperator{\adj}{adj}
\newcommand{\real}[1]{\operatorname{Re}(#1)}
\newcommand{\imag}[1]{\operatorname{Im}(#1)}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Applied Mathematics
Peter Staab
Department of Mathematics
Fitchburg State University
January 8, 2026
