1/13-1/16

Operators on inner product spaces.

Axler p113-134

Chap 5, sec 5-6 in Treil.

homework 1

We settled on Sundays 7-8 PM for help sessions. I'm working on the room right now—hopefully 125 Hayes-Healy, same as last term.

1/19-1/23

Spectral Theorems for normal and self-adjoint operators

Axler p135-147

6.1-6.2 in Treil

homework 2

Starting Monday, class will meet 8-9:15 MW instead of 8:30-9:20 MWF. So you rise earlier to get Fridays off.

The (new) Notre Dame Association for Women in Math Club is having meets this Thurs, Jan 22, at 4:15 PM in Reckers cafe, in the area across from where you order. 

My penance.

1/26-1/30

Polar and singular value decomposition

6.3-6.5 In Treil

homework 3

While I've been plugging Axler's treatment of operators on inner product spaces, I think Treil's presentation is about equally good on this week's material.

Here's an entertaining article about the use of eigenvectors in Google's pagerank algorithm.

Here's the mathematica file (with some annotation) from my in class demo on 1/28.

2/2-2/6

1^st order ordinary differential equations.

Pages 4-19 in Terrell's notes

homework 4

My notes on the existence/uniqueness theorem for 1^st order ODEs.

The dfield applet for drawing direction fields (courtesy Polking et al)

2/9-2/13

Higher order linear ODEs

Pages 25-37 in Terrell's notes

homework 5

Here's a little note about existence and uniqueness that should be helpful for the last homework problem this week.

2/16-2/20

Higher order linear ODEs (continued)

homework 6

2/23-2/27

Linear systems of ODEs

Indedependent subspaces: section 4.1.2 on page 101 in Treil. Also 8.3.2 for generalized eigenvectors.

Systems of ODEs: Pages 37-42, 57-68 in Terrell's notes

homework 7 (updated with two new probs on 3/18)

We'll have a class on Friday 2/27 to make up for missing next week.

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.

You can find pplane (for drawing vector fields and solution curves of 2 x 2 autonomous systems at the same place as dfield

3/2-3/6

No class this week. However, if you're looking for things to think about, here's a review sheet for the midterm. And from anonymous students who've gone before you, a little gallows humor.

3/16-3/20

Back to basics—more about vector spaces

Fields are discussed in section 1.1 in Hoffman-Kunze (on reserve in math library).

The Wikipedia article on the subject is pretty nice, too.

homework 7 (updated with two new probs on 3/18).

Midterm exam Wednesday 3/18, at 7 PM in 129 HH. Review in class on 3/18.

I'm opting not to lecture on the proof of the existence/uniqueness theorem for ODEs, but you're still welcome to read my notes on the subject.

3/23-3/27

product and quotients of vector spaces

Appendices A.4 and A.5 of Hoffman and Kunze discuss equivalence relations and quotient vector spaces.

homework 8

3/30-4/3

Quotient vector spaces

homework 9

4/6-4/9

polynomials and invariant subspaces

Some notes of mine on canonical forms. These are still evolving somewhat.

homework 10 (not collected until Wed 4/21)

4/12-4/17

Canonical forms

There will be no help session Easter Sunday. Instead, there will be a help session Monday 4/13 (tentatively) at 7 PM in Hayes-Healy 117 (note the room, too, is different than usual).

4/20-4/24

Canonical forms

homework 11 (last one!)

Here's the Mathematica example I went through in class on 3/25. I'll expand on this example more during Monday's lecture.

4/27-4/29

Everything else

Here's a review sheet for the final exam. Since the final will deal with material from last semester, I thought you might also like to have a look back at last semester's final.

Don't forget to fill out course evaluations!

I'll hold office hours 3-5 Tues May 5 and 10-12 Wed, May 6. The hours on Tuesday will be for my other class, too, so don't be surprised if you find unfamiliar faces in my office when you arrive—just knock and announce yourself, so I don't neglect you.