Introduction to Vector Calculus

Many vector fields - such as the gravitational field - have a remarkable property called being a conservative vector field which means that line integrals over that field are path independent. That is, if you want to compute a line integral (physically interpreted as work) the ONLY thing that matters is the endpoints, not what happens along the field. Cool! We are going to have a very powerful theorem called the Fundamental Theorem of Line Integrals that will apply to conservative vector fields.