# Lecture 31: Stokes' theorem

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Lesson Summary:

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.

Lesson Description:

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.