Closed Forms and Exact Forms

In the applications of vector analysis to physics, it is often important to know whether a given vector field F in ℝ³ is the gradient of a scalar field f. If it is, F is said to be conservative, and the function f (or sometimes its negative) is called a potential function for F. Translated into the language of forms, this question is just the question whether a given 1-form ω in ℝ³ is the differential of a 0-form, that is, whether ω is exact.