\begin{equation} \Delta t = \Delta t_0 \, \gamma = \frac{\Delta t_0}{\sqrt{1 - u^2 / c^2}} \end{equation} \begin{equation} \gamma = \frac{1}{\sqrt{1 - u^2 / c^2}} \end{equation}
\begin{equation} l = l_0 \, \sqrt{1 - u^2 / c^2} = \frac{l_0}{\gamma} \end{equation}
\begin{equation} x' = \frac{x - ut}{\sqrt{1 - u^2 / c^2}} = \gamma (x - ut) \end{equation} \begin{equation} \qquad \qquad y = y' \end{equation} \begin{equation} \qquad \qquad \qquad \qquad z = z' \end{equation} \begin{equation} t' = \frac{t - ux/c^2}{\sqrt{1 - u^2/c^2}} = \gamma \, (t - ux/c^2) \end{equation} \begin{equation} v_x = \frac{v_x + u}{1 + u \, v_x' /c^2} \end{equation} \begin{equation} v_x' = \frac{v_x - u}{1 - u \, v_x' /c^2} \end{equation}
\begin{equation} f = f_0 \, \sqrt{\frac{c + u}{c - u}} \end{equation}
\begin{equation} \vec{p} = \gamma \, m \, \vec{v} = \frac{m \, \vec{v}}{\sqrt{1 - u^2/c^2}} \end{equation} \begin{equation} K = (\gamma - 1)mc^2 = \frac{m c^2}{\sqrt{1 - u^2/c^2}} \end{equation} \begin{equation} E = \gamma \, mc^2 = \frac{m c^2}{\sqrt{1 - u^2/c^2}} = K + mc^2 \end{equation} \begin{equation} E^2 = (mc^2)^2 + (pc)^2 \end{equation}