$$ \renewcommand{\vec}[1]{\mathbf{#1}} \newcommand{\nhat}{\mathbf{\hat{n}}} \newcommand{\x}{\mathbf{\hat{x}}} \newcommand{\y}{\mathbf{\hat{y}}} \newcommand{\z}{\mathbf{\hat{z}}} \newcommand{\uhat}{\mathbf{\hat{u}}} \newcommand{\rhat}{\mathbf{\hat{r}}} \newcommand{\Rhat}{\mathbf{\hat{R}}} \newcommand{\phihat}{\boldsymbol{\hat{\phi}}} \newcommand{\thetahat}{\boldsymbol{\hat{\theta}}} \newcommand{\rhohat}{\boldsymbol{\hat{\rho}}} \newcommand{\rvec}{\mathbf{r}} \renewcommand{\d}{\mathrm{d}} \newcommand{\pz}{\frac{\partial}{\partial z}} $$