This was a "plan for the quarter";
in retrospect, it's more useful as "outline of possible topics"

me:
5th week
W: growth
   l'hopital + algorithm
F: series intro

6th
M/W: evelin/aliaa: convergence tests etc.
F: taylor series/polynomials

taylor:
- definition
- sum/index notation
- non-analytic functions:
  + $e^{-1/x^2}$
  + bump functions $e^{1/(x^2-1)}$, extended by $0$
- analytic functions
- error term (Lagrange)
  (do not bother memorizing it: just note that it's something that
  depends on the next derivative (divided by a factorial!).
  thus if the derivatives don't blow up (faster than a factorial),
  the series converges)
...maybe do taylor series of tan?

7th
M: more taylor series
W: how do taylor series converge?
 - oscillation/discontinuous
 - uniform limit of continuous is continuous
 - yada, so you can differentiate/integrate termwise
F: binomial?

8th -- fun 1
construction of reals
(start by reviewing construction of $\bN, \bZ, \bQ, \bC$)
F: lil' note about "distributions": completing functions
  with respect to a certain topology
  i.e., weak convergence as $(C^\infty)^*$
  hence get $\delta$ and $\delta'$!

9th -- fun 2
differential equations:
- review of techniques (lotta problems)
- frobenius' method
(complex integration and poles: $\log$ of a complex number
 and why $\log\abs{x}$ works as an antiderivative of $1/x$)

10th
M/W: big review of what we've done
F: "All questions answered"
