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.
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.