$$ \newcommand{\dt}{\,\mathrm{d}t} \newcommand{\dx}{\,\mathrm{d}x} \newcommand{\dy}{\,\mathrm{d}y} \newcommand{\dh}{\,\mathrm{d}h} \newcommand{\pt}{\partial t} \newcommand{\px}{\partial x} \newcommand{\py}{\partial y} \newcommand{\QEDA}{\hfill\ensuremath{\blacksquare}} \newcommand{\QEDB}{\hfill\ensuremath{\square}} \newcommand{\R}{\mathbb{R}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\bmat}[1]{\begin{bmatrix}#1\end{bmatrix}} \renewcommand{\vec}[1]{\mathbf{#1}} $$