Differentials, gradients, and partial derivatives

Given u = f(x, y, z), we may speak of the differential du of this quantity as well as the gradientf of the function. Within du, we can find the partial derivatives of u with respect to x, y, and z (holding the other two fixed); within ∇f, we can find the partial derivatives of f with respect its first, second, or third arguments. Here are a bunch of relationships between these.
Go back to the course homepage.
Valid HTML 4.01 Transitional

This web page was written between 2014 and 2016 by Toby Bartels, last edited on 2016 April 19. Toby reserves no legal rights to it.

The permanent URI of this web page is http://tobybartels.name/MATH-2080/2016SP/gradient/.