way to express a general vector field

by 0rthodontist
Tags: express, field, vector
0rthodontist is offline
Apr18-06, 08:33 PM
Sci Advisor
P: 1,253
Is there a simple way to express a general vector field in terms of the gradient of another (perhaps higher dimensional) function?
Phys.Org News Partner Mathematics news on Phys.org
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
Pseudo-mathematics and financial charlatanism
HallsofIvy is offline
Apr19-06, 07:29 AM
Sci Advisor
PF Gold
P: 38,881
Only if it is "exact" (in fact, the definition of "exact" is that it is the derivative of some other function). Even in 2 dimensions, there exist vector fields f(x,y)i+ g(x,y)j that are not graf F for any f.
0rthodontist is offline
Apr19-06, 07:31 AM
Sci Advisor
P: 1,253
I know; I am wondering if there is a way to write vector fields that are not gradients of functions in their own dimension as some simple transformation of a gradient of some function of a higher dimension.

Register to reply

Related Discussions
Gradient Precalculus Mathematics Homework 8
testing gradient against a value Introductory Physics Homework 1
Gradient of 1/r Advanced Physics Homework 8
Temperature Gradient Introductory Physics Homework 3
gradient help Calculus 4