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.