Exterior Derivative of a 1-Form

\[ \newcommand{\d}{\mathrm{d}} \newcommand{\e}{\mathrm{e}} \newcommand{\i}{\mathrm{i}} \]

The exterior derivative of a 1-form \(\omega\) in local coordinates is given by

\begin{equation*} d\omega= \sum_{i One observe, that \(d\omega=0\) when \(\omega\) is a closed covector field . This is a motivation of the exterior derivative.