| Week | Monday | Wednesday | Assignments, suggested reading |
|---|---|---|---|
| 1/24 | Administrivia Discussion: what is analysis and why do I care? Integers, rationals, and reals Class Notes courtesy Stephanie. |
The real numbers as a complete ordered field. Class Notes |
Abbot: sections 1.1-1.3, 8.6. Alcock: ch.1-4, ch.10 HW 1 Due Wed, 2/2 solutions |
| 1/31 | Completeness and its consequences: sup, inf, Nested Intervals theorem, the Archimedian Property. Class Notes |
Rationals and irrationals as decimals (in base 10 and otherwise); The limit of an increasing sequence Class Notes |
Abbot: section 1.3 Wu: Chapter 3 HW 2 Due Wed, 2/9 solutions |
| 2/7 | Limits Class Notes |
More on limits Class Notes |
Abbot: section 1.4-1.6,2.2,2.3 HW 3 Due Wed, 2/16 solutions |
| 2/14 | There will be a short quiz on this day. (Here is the solution). Limits of sequences and infinite sums. Class Notes |
The Harmonic series (see also many different proofs of the divergence of the harmonic series). Cauchy condesation test, subsequences. Class Notes |
Abbot: section 2.3-2.5 HW 4 Due Wed, 2/23 solutions |
| 2/21 | The Bolzano-Weierstrass Theorem Cauchy sequences Class Notes |
Rearrangements of series Absolute convergence, products Class Notes |
Abbot: section 2.1,2.6-2.9 HW 5 Due Wed, 3/2 solutions |
| 2/28 | Cardinality Class Notes |
The Cantor set (see also the Koch snowflake and box dimension). Class Notes |
Abbot: section 1.5,1.6, 3.1 A crash course on infinite sets HW 6 Due Wed, 3/23 solutions |
| 3/7 | review for midterm To help you prepare, here is a midterm from Spring 17 that you can use to study; here are the solutions. Class Notes courtesy Stephanie. |
We had a midterm on 3/9. In case you want to relive the magic, here is a copy of the midterm. Also, you might (or might not) want to look at the solutions. |
Just enjoy spring break, although don't forget that there is a homework assignment due on 3/23. |
| 3/14 | Spring Break (probably not like this) |
Spring Break | |
| 3/21 | Open and closed sets, compactness. Class Notes |
More on compactness, open covers, the Heine-Borel Theorem Class Notes |
Abbot: section 3.2,3.3 HW 7 Due Wed, 3/30 solutions |
| 3/28 | There will be a short quiz on this day. (Here is the solution). Limits of functions Class Notes |
more on function limits, continuity. Class Notes |
Abbot: section 4.1-4.3 HW 8 Due Wed, 4/6 solutions |
| 4/4 | Continuous functions. Class Notes |
Uniform continuity, the Intermediate Value Theorem. Class Notes |
Abbot: section 4.4-4.7 HW 9 Due Wed, 4/13 solutions |
| 4/11 | There will be a short quiz on this day. (Here is the solution). Derivatives Class Notes |
More on derivatives, Darboux's theorem, the Mean Value theorem Class Notes |
Abbot: section 5.1-5.3 HW 10 Due Wed, 4/20 solutions |
| 4/18 | L'Hopital's rule, a nowhwere differentiable function. Class Notes |
Area, integration Class Notes |
Abbot: section 5.3-5.4, 7.1-7.2 Wu: 4.7,6.5 HW 11 Due Mon, 5/2 solutions |
| 4/25 | Riemann sums, the fundamental theorem of calculus Class Notes |
trigonometry Class Notes |
Abbot: section 7.3-7.5 Wu: Chapter 1 |
| 5/2 | review for final. Here is the final that I gave in 2017; keep in mind that ours will differ. Here are the solutions. Class Notes, courtesy Stephanie. |
more review | |
| 5/9 | Final Cumulative Wednesday, May 11, 5:30pm, Physics P-130. |