Lecture 21: Gradient fields and potential functions

Sick of ads?​ Sign up for MathVids Premium
Taught by OCW
  • Currently 4.0/5 Stars.
4992 views | 1 rating
Lesson Summary:

In this lesson, you will learn about gradient fields and potential functions, how they are related, and why they are useful. The lesson covers how to test if a vector field is a gradient field, and how to find the potential function if it is. The lecture also discusses the criterion to decide whether a vector field is a gradient field or not and how to find the potential function if it is. Two methods of finding the potential function are presented: by computing line integrals and by guessing.

Lesson Description:

Learn about gradient fields and potential functions, how they are related, and why they are 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.

Additional Resources:
Questions answered by this video:
  • What is a gradient field?
  • What are potential functions?
  • What are the properties of a gradient field?
  • How do you find a potential function?
  • What is the definition of the curl of a field F?
  • What does curl measure in a velocity field?
  • How do you find the torque exerted on an object in a field using curl?
  • Staff Review

    • Currently 4.0/5 Stars.
    This video takes off from where the last left off, talking more about the properties of gradient fields, and certain things that we know are true if we have a gradient field. These turn out to be very convenient. Curl and potential functions are also explained in gradient fields.