The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: How to Define Derivative of a Vector Field in this Case ( Curve in R^3)?
Replies: 3   Last Post: Jan 18, 2013 4:30 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Bacle H

Posts: 283
Registered: 4/8/12
How to Define Derivative of a Vector Field in this Case ( Curve in R^3)?
Posted: Jan 18, 2013 12:34 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Hi, All:

Let C:I-->R^3 be a smooth curve, and let Z(s) be a vector field along the curve,
parametrized by arc-length.

We define the derivative of a vector field Z along the curve to be the quotient:

Lim_ds->0 [Z(s+ds)-Z(s)]/ds

Now, I don't know how to make sense of the difference in the numerator:

The two vectors Z(s+ds) and Z(s) , are in different tangent spaces --

tangent space at s+ds and s respectively -- and , AFAIK, the difference

of vectors in different tangent spaces is not defined, except for cases

where there is a natural isomorphism between the tangent spaces, as in the

case where the tangent spaces are those in R^n itself. Any suggestions,


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.