On friday I did Arzela-Ascoli ¡­

On friday I did Arzela-Ascoli and finished 3.5. To day I will do chapter 3.7 called "Polynomials are dense in C([a,b], R)". The main result is the Weierstrass approximation theorem. I will follow a path a little different from Tom. The mathematical content is the same in the two approaches, but I will not use a statistical language.

I will probably not be through with Weierstrass to day; I would guess we need one hour also on friday. And then we start on chapter 4!

For the moment I plan to do chapter 4 in its entirety (if time permits). I would guess some of things there are more or less well known, so I ll try to put emphasis on the new things and do the well known "with a rabbit's foot".

This means:

3.6, "Differential equations revisited" is not part of the curriculum.

3.8 "Baire's category theorem" is not part of the curriculum.

G