| Day |
Week/
Chapter |
Topic |
Assigned/
Due |
| M 8/26 |
1
Chapter 1 |
what do we know about the real numbers? |
Assignment #1 |
| W 8/28 |
|
what do we know about calculus? |
|
| F 8/30 |
Chapter 3 |
metric spaces and normed vector spaces |
|
| M 9/2 |
2 |
no class: Labor Day |
|
| W 9/4 |
|
Early Quiz (30 min)
vector spaces |
A #1 due
Assignment #2 |
| F 9/6 |
|
lp space |
|
| M 9/9 |
3 |
inequalities in normed vector spaces: Cauchy-Schwarz, Young's |
|
| W 9/11 |
|
inequalities cont.: Holder's, Minkowski's |
A #2 due
Assignment #3 |
| F 9/13 |
Chapter 4 |
convergence in metric spaces
open and closed sets |
|
| M 9/16 |
4 |
cont. |
|
| W 9/18 |
Chapter 5 |
continuity |
A #3 due
Assignment #4 |
| F 9/20 |
|
cont. |
|
| M 9/23 |
5
Chapter 7 |
complete metric spaces |
|
| W 9/25 |
|
proofs of completeness |
A #4 due
Assignment #5 |
| F 9/27 |
|
Banach fixed-point theorem |
|
| M 9/30 |
6 |
applications: ODEs, IFSs, Newton iteration |
|
| W 10/2 |
|
cont. |
A #5 due |
| F 10/4 |
Chapter 8 |
totally-bounded sets |
Assignment #6 |
| M 10/7 |
7 |
compactness |
|
| W 10/9 |
|
cont.
review guide for Midterm I |
A #6 due |
| F 10/11 |
|
Midterm Exam I |
Midterm I |
| M 10/14 |
|
chaos
equivalent metrics |
Assignment #7 |
| W 10/16 |
8
Chapter 10 |
sequences of functions |
|
| F 10/18 |
|
uniform continuity/convergence |
|
| M 10/21 |
9 |
a nowhere differentiable function
weierstrauss.m |
|
| W 10/23 |
Chapter 11 |
Weierstrauss theorem
(polynomial approximation in C[a,b])
bernstein.m |
A #7 due
Assignment #8 |
| F 10/25 |
|
overview of integration |
|
| M 10/28 |
10
Chapter 16 |
Lebesgue outer measure m* |
|
| W 10/30 |
|
measure zero sets
Cantor set |
A #8 due
Assignment #9 |
| F 11/1 |
|
m*(I)=length(I) |
|
| M 11/4 |
11 |
m* is countably subadditive
measurable sets
Lebesgue measure |
|
| W 11/6 |
|
m is countably additive
measurable sets form a sigma-algebra |
A #9 due
Assignment #10 |
| F 11/8 |
|
nonmeasurable sets
characterization of Riemann integrability |
|
| M 11/11 |
12
Chapter 17 |
measurable functions |
|
| W 11/13 |
|
simple functions
extended real values |
A #10 due
Assignment #11 |
| F 11/15 |
|
basic construction
Borel's theorem |
|
| M 11/18 |
13
Chapter 18 |
Lebesgue integral (simple; nonnegative measurable; integrable)
review guide for Midterm II |
|
| W 11/20 |
|
monotone convergence theorem |
A #11 due |
| F 11/22 |
|
Midterm Exam II |
Midterm II |
| M 11/25 |
14 |
Fatou's lemma
dominated convergence theorem |
Assignment #12 |
| W 11/27 |
|
no class: Thanksgiving |
|
| F 11/29 |
|
no class: Thanksgiving |
|
| M 12/2 |
15 |
L1 is complete
review guide for Final Exam |
|
| W 12/4 |
Chapter 19 |
approximation in L1
Lp spaces |
|
| F 12/6 |
|
Fourier series
a bit of review |
A #12 due |
| F 12/13 |
|
Final Exam
1:00 pm -- 3:00 pm |
Final Exam |