Lecture 27: Vector fields in 3D, surface integrals, and flux

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Taught by OCW
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Lesson Summary:

In this lesson, we learn about vector fields in 3 dimensions and how to find surface integrals and 3-dimensional flux. We see that a vector field in space is just like in the plane, where at every point we have a vector and the components of this vector depend on the coordinates x, y, and z. We look at examples of vector fields that come up in physics, such as gravitational attraction, electric fields, and velocity fields. We also learn about flux, which is measured through a surface, and how to set up and evaluate a double integral to calculate the flux through a surface, with examples such as finding the flux through a sphere of radius a centered at the origin.

Lesson Description:

Learn what vector fields look and act like in 3 dimensions, how to find surface integrals, and 3-dimensional flux.

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 do vector fields look and act like in three dimensions?
  • How do you find flux and surface integrals in 3D?
  • What is the formula for flux in three dimensions?
  • What is the surface integral of Fn dS?
  • How do you find the flux of F = <x, y, z> through a sphere of radius a centered at the origin?
  • What is the geometric interpretation of 3D flux and surface integrals?
  • Staff Review

    • Currently 4.0/5 Stars.
    Vector fields, flux, and surface integrals are all discussed in three dimensions in the lecture. The 2-dimensional counterparts of these ideas are reviewed and then moved to 3 dimensions. Some good, concrete examples are shown and the geometric interpretation is explained.