How to Understand conservative vector fields

A conservative vector field is defined as being the gradient of a function, or as a scaler potential. Conservative vector fields are not dependent on the path; they are path independent. Conversely, the path independence of the vector field is measured by how conservative it is. These fields are also characterized as being ir-rotational, which means they have vanishing curls. Actually, ir-rotational vector fields are conservative as long as a certain condition on the geometry of the domain is true: there must be a simple connection.