"outer" differentiation?


by Creator
Tags: differentiation, outer
Creator
Creator is offline
#1
Feb19-04, 10:08 AM
P: 534
Since I didn't get a response on the "Diff. Eqns." thread, I put it here.

Can someone give me a clear explaination of what is meant by "outer" differentiation.

As for example, when we differentiate the vector potential, dA/dx, in order to arrive at the magnetic field, B, why would this be called an 'outer' differentiation??


[?]
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
turin
turin is offline
#2
Feb19-04, 10:03 PM
HW Helper
turin's Avatar
P: 2,327
Originally posted by Creator
... when we differentiate the vector potential, dA/dx, in order to arrive at the magnetic field, B, why would this be called an 'outer' differentiation??
Probably because d/dx is not exactly what you do. You take the cross product of the gradient operator with the vector potential to get the magnetic field. The cross product is sometimes called/related to the outer product, but that's tensor jargon with which I am unfamiliar.
Creator
Creator is offline
#3
Feb20-04, 10:07 AM
P: 534
Thanks for the response, Turin;

and thanks for the correction. Oc course, you are accurate in saying it is the cross product of the gradient.
I guess then if someone says "dA/dt is the outer differentiation" I should interpret that to mean they are simply referring to it as being a cross product.??

[:)]

turin
turin is offline
#4
Feb20-04, 11:07 AM
HW Helper
turin's Avatar
P: 2,327

"outer" differentiation?


Originally posted by Creator
... if someone says "dA/dt is the outer differentiation" I should interpret that to mean they are simply referring to it as being a cross product.??
I would ask them what they mean. I wouldn't know how to make sense of that.


Register to reply

Related Discussions
Difference between "Identical", "Equal", "Equivalent" Calculus & Beyond Homework 9
"Outer World" and "Inner World" General Discussion 9
"outer" differentiation ? Differential Equations 0
"Simple" differentiation question Calculus 3