In Lecture 31, you will learn about Stokes' Theorem and its applications. The curl of a vector field in space measures the rotation of a velocity field, and a vector field is conservative if its curl is zero. Stokes' Theorem states that the work done by a vector field along a closed curve can be replaced by a double integral of the curl of the vector field over a suitably chosen surface bounded by the curve. However, the orientations of the curve and surface need to be compatible, and there are conventions to determine their orientations. The right-hand rule can be used to determine the orientations, and the examples provided will help you understand the concept better.
Learn about Stokes' Theorem and why it is useful.
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.