Topics, reading and homework assignments are given below. As I did last semester, I will update this page
very often. It is your responsibility to check it frequently to
see what's going on in class. In particular, you will find all
new homework assignments here, and soon after you turn in an
assignment, I will post solutions for you to look at.
|
Dates |
Topics |
Reading |
Homework |
Miscellaney |
|---|---|---|---|---|
|
1/18-1/20 |
Where we left off: Isometries and unitary operators |
5.6 and 5.7 |
Homework 1 and tex source |
|
|
1/23-1/27 |
Schur representation and the spectral theorems |
6.1-6.2 |
Homework 2 and source |
|
|
1/30-2/3 |
Polar and singular value decompositions |
6.3-6.4 |
Homework 3 and source |
I'll be away at meeting all week this week. Martha Precup will lecture in my place. Turn in hwk 2 to her on Wed. |
|
2/6-2/10 |
First order ordinary differential equations |
Pages 1-6, 12-17, 21-28 in Terrell's
notes Apostol, Calc I also has sections on ODEs |
Homework 4 and source |
My notes on the existence/uniqueness theorem for 1st order ODEs. The dfield applet for drawing direction fields (courtesy Polking et al) Math for Everyone talk, Thursday February 9 at 5:00PM in 105 Jordan Hall: |
|
2/13-2/17 |
Existence/uniqueness Autonomous first order eqns |
My notes on
existence/uniqueness. |
Homework 4a and source |
I'll be away on Friday 2/17. I'll make that class up later in the term. |
|
2/20-2/24 |
Autonomy (ct'd) Higher order linear ODEs |
Pages 35-37 and 43-53 in Terrell's notes |
Homework 5 and source |
|
|
2/27-3/2 |
Linear systems of ODEs |
Pages 54-62 and 83-95 in Terrel's notes | Homework 6 (I won't pick this one up. It just has some more ODE probs you can use for practice) |
Unfortunately, Terrell's notes don't treat matrix
exponentiation. He pursues a slightly different approach to
solving linear systems of ODEs. If you happen to be taking
Connoly's class simultaneously with this one, then you probably
own Apostol vol 2, which does discuss matrix exponentiation, so
you might look there. Review sheet for the midterm exam pplane is a program for drawing direction fields for autonomous 2x2 systmes of ODEs. |
|
3/5-3/9 |
More linear systems, the exponential map |
A correct proof for the fact about exponentials of sums See Polking, Boggess and Arnold (on reserve in the math library) chapter 9 for more about linear systems of ODEs. |
Homework 7 and source |
Math for Everyone talk, Thursday March 8 at 5:00PM in 105 Jordan Hall: Discovering Origami Theorems Amanda Serenevy, Riverbend Community Math Center Midterm exam, Thursday 3/8 from 6:15-8:15 in Jordan |
|
3/19-3/23 |
Inhomogeneous linear systems of ODEs; Autonomous 2x2 systems. Quotients and direct sums of vector spaces |
Polking, Boggess and Arnold chapter 10 gives a nice tour of autonomous systems Some notes by Santiago Canez about quotient vector spaces, and a couple of pages by me about equivalence relations |
No new hwk this week! |
|
|
3/26-3/30 |
Quotients and direct sums (ct'd) | My notes on canonical forms for linear operators, sections 1 and 2 |
Homework 8 and source |
I'd be grateful for any feedback
concerning my notes. Please tell me if you see typos, find some
point confusing, etc, etc. |
|
4/2-4/4 |
Polynomials |
My notes, sections 1 and 3 |
Homework 9 and source |
Since I'm introducting a lot of new terminology lately, you might enjoy hearing some of it used. You won't be sorry you clicked. |
|
4/11-4/13 |
Primary decomposition of operators |
My notes, section 4 |
Makeup lecture on tensor products, Tuesday 4/10 5-7 PM in HH 127. |
|
|
4/16-4/20 |
Cyclic decomposition of operators |
My notes, section 5 |
Homework 11 and source |
This week's math for everyone talk has been rescheduled for next week. The other details remain the same. Here is the mathematica file that I showed you in class on Wed 4/18 |
|
4/23-4/27 |
Matrix Lie Groups Infinite dimensional vector spaces |
Mitchell Faulk will tell us about Matrix Lie Groups and their Lie Algebras on Monday 4/23. Here is the paper he wrote to accompany the lecture. I just posted a substantial revision of my notes about canonical forms. Math for Everyone talk, Thursday April 26 at 5:00PM in 127 Hayes-Healy: An invitation to Analytic Combinatorics Mark Ward, Purdue University |
||
| 4/30-5/2 |
Projective spaces Optimization |
Final exam Tues 5/8 from 8-10 AM in 125 Hayes-Healy (our usual classroom). Here's a review sheet. |