Lecture 21: Gradient fields and potential functions
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.
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.
- Transcript of Lesson - Written transcript from this lesson.
- Problem Set - A problem set with some problems from this lecture.
- Lecture Notes - Lecture Notes from this lesson.
- 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?
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Staff Review
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.
