Differentiate the first-order chain rule again, including derivatives of the coordinate coefficients. The second derivatives under a two-variable coordinate change are
(1)
and
(2)
The last two terms account for derivatives of the coordinate functions; they vanish for an affine map. Smoothness justifies equality of the two mixed partial derivatives.

Ancestors (13)

  1. b
  2. 11
  3. Paper 2
  4. 2006
  5. Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
  6. Mathematics course of the year 1 of the natural sciences course of the University of Cambridge
  7. Year 1 of the natural sciences course of the University of Cambridge
  8. Year of the natural sciences course of the University of Cambridge
  9. Natural sciences course of the University of Cambridge
  10. Course of the University of Cambridge
  11. University of Cambridge
  12. List of universities
  13. Home

View article source

Discussion (0) New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version