Recent content by krcmd1

Thank you!

1. The problem statement, all variables and given Before I try to work through the book, it would be great to have a list of typos, if there are any. Homework EquationsThe Attempt at a Solution

I can understand why a)if this particular theorem is true for \lambda^{-1}\circf it is true for f, but b) is it true as your posting suggests that any theorem true for \lambda^{-1}\circf is true for f? and c) how does his proof depend upon (a)? I mean, how does the subsequent...

On p. 36 of "Calculus on Manifolds" Spivak writes: "If the theorem is true for (\lambda^{-1})\circf , it is clearly true for f." This far I understand. However, he next says: "Therefore we may assume at the outset that \lambda is the identity." I don't understand how this follows...

Thank you I will try another browser for now. I'm afraid some thinkpad software might not work with IE8.

Yes, it is IE 6; but it worked a few months ago when I last visited this forum.

Please advise. thank you.

"Suppose that f: R^{n} -> R^{m} is continuously differentiable in an open set containing a, and det f'(a) \neq 0. Then there is an open set V containing a and an open set W containing f(a) such that f: V -> W has a continuous inverse f^{-1}: W -> V which is differentiable and for all y \in W...

Is there a way to scan a page and post it?

In his proof of the IFT, on p. 36 of "Calculus on Manifolds," Spivak states: "If the theorem is true for \lambda^{-1} \circf, it is clearly true for f. Therefore we may assume at the outset that \lambda is the identity. I don't understand why we may assume that. thanks for your help...

I apologize for the ambiguity in my original posting. Is it then that there was a typo? thanks Ken Cohen

Working my way through Spivak "Calculus on Manifolds." On p. 34, problem 2-33, the problem asks "show that the continuity of D1f^{i} at a can be eliminated from the hypothesis of Theorem 2-8. Is this a typo? Is he saying that there is no need for continuity of ONE partial derivative, or...

Thank you!

I have been trying to teach myself math, and for quite a while have been struggling through "Calculus on Manifolds" by Spivak. Theorem 2-8, on p.31, uses the Mean Value theorem to establish the existence of the Derivative assuming the existence of the partial derivatives. Doesn't that also...

Thank you! So I can't in fact multiply exponents like (x**2)**(1/2) = x without knowing in advance that x=>0. It has been many years since I took algebra. OK, then, it seems like my initial application of the inner product to showing that |x| is not differentiable is OK, until I misused...