My calculus book states that a vector field is conservative if and only if the curl of the vector field is the zero vector. And, as far as I can tell a conservative vector field is the same as a path-independent vector field. The thing is, I came across this: http://www.math.umn.edu/~nykamp/m2374/readings/pathindex/ The site shows a vector field where the curl is equal to the zero vector, yet the vector field is not conservative. As far as I can tell, saying "F is conservative iff Curl(F) = 0" contradicts the claims of the site I posted. What conditions must be met for a vector field to be conservative?