In this lesson on line integrals in space, students learn about computing line integrals and work in 3D, testing whether a vector field is a gradient field, and the concepts of curl, exactness, and potentials. The criterion for determining whether a vector field is a gradient field involves checking three conditions, which is different from the criterion for the two-variable case. The lesson includes examples and shows how to find the potential when there is one.
A lesson about line integrals, curl, exactness, and potentials in 3-dimensional space.
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.