A few Terms:
A vector field is called conservative if it’s a gradient of some scalar function. In other words, if there exists a f u n c t i o n f s u c h t h a t F f = ∇ r .
r In this case, function f is called a potential function of F .
Not all vector fields are conservative. I guess it’s common in physics (gravitational fields).
We’ll find out later on in the chapter how to tell whether or not a vector field is conservative.
Physics students can enjoy reading examples 3, 4, & 5 pertaining to fluid flow, Newton’s Law of Gravitation and Electric Charge.