Recent content by bigbalpha

  1. B

    Graduate Making sense of the Differential of F at p, (where F: R^n -> R^m)

    Here is a snip of the fundamental relation: This is from the book "Intro to Smooth Manifolds" and in this section it is simplified down to F as a map between just the real spaces R^n -> R^m (as shown above). I understand the meaning of this relation, as the following: The rightside is the...
  2. B

    Why Does d/dx Not Equal d/dx' Even When x Equals x'?

    Thanks a lot for that explanation, that really helped!
  3. B

    Why Does d/dx Not Equal d/dx' Even When x Equals x'?

    Alright, always get index notation very confused, for example, earlier in the book, it says this. This is contradictory?
  4. B

    Why Does d/dx Not Equal d/dx' Even When x Equals x'?

    Summary: I'm stuck on this simple excersize, to show that in this coord transform, despite x = x', d/dx != d/dx' From "Intro to Smooth Manifolds" (this is a calculus excersize), The Problem I have is with showing d/dx != d/dx' When I write out the Jacobian matrix, I get exactly d/dx = d/dx'...