In Lecture 28, we learn about the Divergence Theorem and how to use it to compute the flux of a vector field for a given surface. The formula for NDS is explained in detail and we see how it applies to various surfaces, including the graph of a function. An example problem is presented in which we find the flux of a vector field through a portion of a paraboloid above the unit disk, using the Divergence Theorem and polar coordinates. This theorem is a powerful tool for computing flux integrals and is a crucial concept in vector calculus.
Learn what the Divergence Theorem is, what it means, and how to use it.
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.