In Lecture 20, we learn about path independence and conservative fields. The fundamental theorem of calculus for line integrals tells us that if we integrate a vector field that's a gradient along a curve, we'll get the value of the potential function at the endpoints. This means that we can avoid computing line integrals by finding a function whose gradient is the given vector field. We also see an example where we use the potential function to easily find the work done by a vector field along a curve, without having to compute line integrals.
Learn about path independence and conservative fields, what they mean and how to find them.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 21, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.