Lecture 28: Divergence theorem

Sick of ads?‚Äč Sign up for MathVids Premium
Taught by OCW
  • Currently 4.0/5 Stars.
6507 views | 1 rating
Lesson Summary:

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.

Lesson Description:

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.

Additional Resources:
Questions answered by this video:
  • What is the Divergence Theorem in three dimensions?
  • How do you find the normal vector in three dimensions?
  • Why does n hat dS = +- <-fx, -fy, 1> dx dy?
  • How do you find the flux F = zk through a portion of paraboloid z = x^2 + y^2 above the unit disk?
  • What is the Gauss-Green Theorem?
  • Staff Review

    • Currently 4.0/5 Stars.
    More about flux and surface integrals are covered in this lecture. Example problems are computed and explained in the video. The Divergence Theorem (or the Gauss-Green Theorem) is finally introduced and explained quickly in the final six minutes of this lecture. An example is shown and the geometric idea is explained.