0708-1300/Homework Assignment 1
Revision as of 09:12, 20 September 2007 by Drorbn
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Read sections 1-5 of chapter II of Bredon's book three times:
- First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
- Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.
- And then a third time, again at a quicker pace, to remind yourself of the bigger picture all those little details are there to paint.
- Solve and submit the following two problems:
- Show explicitly that the restricted implicit function theorem, with and , is equivalent to general implicit function theorem, in which and are arbitrary and is an arbitrary invertible matrix.
- Show that the definition reduces the implicit function theorem to the inverse function theorem. A key fact to verify is that differential of at the relevant point is invertible.
- Solve the following problems from Bredon's book, but submit only the solutions of the starred problems:
|*1, 2, 3, *4, 5||71|
This assignment is due in class on Thursday October 4, 2007.