Announcements

If you are interested in learning more about operator norms, please review Lecture 7 in the 510 lecture notes. The basic idea is that a matrix is simply a linear operator, and hence the metric on our underlying Hilbert space induces a norm on that operator. For example, consider operator

$A:X\to Y$

The operator norm is just

$\begin{aligned} \|A\|_{\text{op}}&=\sup_{\|x\|=1}\|Ax\|\\ &=\sup\left\{\frac{\|Ax\|}{\|x\|}:\ \ x\neq 0, \ x\in X\right\} \end{aligned}$

For example, if $A$ has as its domain $(\mathbb{R}^n,\|\cdot\|_2)$ and as its co-domain $(\mathbb{R}^n,\|\cdot\|_2)$, then the operator norm is simply the induced 2-norm or maximum singular value. If $A$ has as its domain $(\mathbb{R}^n,\|\cdot\|_1)$ and as its co-domain $(\mathbb{R}^n,\|\cdot\|_1)$, then the operator norm is simply the induced 1-norm or maximum $\ell_1$-norm of the columns.

One can also mix and match norms on domain and co-domain. For example, if $A$ has as its domain $(\mathbb{R}^n,\|\cdot\|_1)$ and as its co-domain $(\mathbb{R}^n,\|\cdot\|_2)$, then the operator norm is simply the maximum across the column’s $\ell_2$-norms.

This is a recommendation on how to watch M2-RL2. This video is ~1hour long. It has three concise parts however.

• Part 1: 0 – 17.5mins: Introduction to spectral theorems on stability
• Part 2: 17.5 – 39.5mins: Numerical integration and connections between DT and CT stability spectral properties.
• Part 3: 39.5 – 59.5mins: Linearization of nonlinear systems and stability via Hartman-Grobman.

You can break this up into roughly three equal parts and watch them this way.

Homework 1 has been posted. It is due 2022-01-16 at 11:59PM.

EE/AA 510 is a required pre-requisite course. You must have taken it to be able to enroll and take this course. If you have not taken this course, you make consider signing up for ME547 instead.

You should also feel free to reach out to Prof Ratliff with questions.

Lecture notes for EE/AA 510 can be found here. It will be assumed that you have mastered this material.

We’re excited to be working with you this quarter, even as we are still slugging through the pandemic! This course will be taught in a ‘flipped’ style organized into modules. This means you will watch pre-recorded videos for each module that are between 15-35mins long. The schedule will be posted to this website. During the in-class sessions will we have a very brief high level review of concepts and then solve problems related to those concepts. There will also be time for you to ask questions. Some of these sessions will be over zoom (you are always welcome to join via zoom if you, say, need to quarantine) and some will be in person.

The class will have weekly homework starting in week 2. These homeworks will be ‘self-graded’. The purpose of self-grading is to 1. Incentivize you to review your homework solutions. I have found this to be instrumental in making sure students’ understanding of topic is solidified, and retention is improved. 2. Give you the opportunity to earn full-credit on the homework. We will select 1-2 homework problems per assignment to hand grade. More detail on self-grading can be found on the homework link.

All in-class sessions will be recorded as well. Office hours will be over zoom. We will also have a discord that we will use for discussion related to lectures and homework.

To prepare for the quarter, we recommend familiarizing yourself with the Syllabus to learn about how the course will run online. You can also check out the Staff Page to meet the instructional team, or the Calendar to get a preview of the topics we’ll cover. Other content such as projects and exercises will be published here as they are released during the quarter.

We’re looking forward to meeting you! Please reach out to the staff if you have any questions or concerns about the quarter.