A Most of the Calculus topics from Rudin (Chapters 5-10), fortified with 55 vitamins, minerals, and secret herbs & spices; and a selection of topics in Fourier analysis from Körner.
A I expect so; at any rate it should be no easier than Math 55a for most students.
A It's in the dictionary -- once : twice : thrice :: 1 : 2 : 3. As far as I know the sequence ``once, twice, thrice'' has no fourth term in English (though it does have a zeroth term of sorts in ``never'').
A Use \ll (and likewise \gg for >>). See This PDF document for an extensive list of such commands.
A Yes.
A
See Dunford & Schwartz, Linear Operators I, p.274 ff.;
for one overview, see
this Web page.
(The name Cech should have a v-shaped diacritical mark
above the capital C; this can be done in LaTeX with ``\v{C}'',
but does not seem to have a standard HTML command.
The pronunciation is like the first syllable of ``Chekhov''.)
A Start here.