Below is an approximate schedule of topics to be covered in the course. Topics may have been covered before or after the dates listed, but it is mostly accurate.
| Week of | Topics | Rudin sections |
|---|---|---|
| Aug 26 | Ordered sets, fields | 1.1-1.3 |
| Sep 2 | $\R$, the Archimedean Property, density of $\Q$, existence of roots | 1.4 |
| Sep 9 | Metric spaces, open and closed sets, compact sets | 2.2, 2.3 |
| Sep 16 | Compact sets, compact subsets of $\R^n$ | 2.3 |
| Sep 23 | Compact sets, sequences, convergence | 2.3, 3.1 |
| Sep 30 | Properties of limits; review; midterm 1 | 3.1 |
| Oct 7 | Subsequences; lack of electricity | 3.2 |
| Oct 14 | Cauchy sequences, completions, limits of functions | 3.3, *, 4.1 |
| Oct 21 | Limits of functions, continuous functions | 4.1-4.3 |
| Oct 28 | Uniform continuity, connected sets; lack of electricity | 4.3, 4.4 |
| Nov 4 | Limits and infinity, directional limits, derivatives; midterm 2 | 4.5, 4.7, 5.1 |
| Nov 11 | Derivatives, local extrema, mean value theorem | 5.1, 5.2 |
| Nov 18 | Riemann sums, integrals, the Fundamental Theorem of Calculus | 6.1-6.3 |
| Nov 25 | Sequences of functions; Thanksgiving | 7.1, 7.2 |
| Dec 2 | Uniform convergence, the Stone-Weierstrass Theorem | 7.3, 7.4, 7.7 |
| Dec 9 | RRR Week | |
| Dec 16 | Exam Week |
Last updated: September 13, 2021.