Section 4.7 Poincare's lemma for two-forms
Objectives
You should be able to:
Show that a two-form that is closed on all of \(\mathbb{R}^3\) with coefficients that are \(C^1\) functions is always exact (Poincare's lemma).
Rephrase Poincare's lemma as the statement that \(C^1\) vector fields on \(\mathbb{R}^3\) that are divergence-free have a vector potential.