Smooth transition map (easy?)

1. Sep 17, 2009

sk1001

Smooth transition map (easy!?)

1. The problem statement, all variables and given/known data
Check the transition map
http://img132.imageshack.us/img132/4341/18142532.png [Broken]
is smooth in the set for which their images intersect

3. The attempt at a solution
I have thought of two ways to show this.

(1) Show that Φ is a composition of two smooth functions and is therefore smooth.
(2) compute the composite function and then prove that is smooth

Which way do you suggest?
I have attempted method (1) to some extent, but wondering if method (2) is easier.

Last edited by a moderator: May 4, 2017
2. Sep 17, 2009

sk1001

Re: Smooth transition map (easy!?)