Class 11: Index Theory

Before class, watch the lecture material linked below

Then post questions or comments (or respond to others) on Piazza (access via Canvas or from the direct link on the course page)

Check yourself via Check Yourself 11 (by 11:59pm on Wed Oct 7th)

In class, we'll work on examples of these ideas: 2Dindex.pdf

After class, complete the homework

For a nice summary of index theory see Chapter 6 of Wiggins, 2nd edition

Note: Index theory works only in 2D.

V01 (St) | Global picture from index theory (00:21 to 9:31) | 9 min

V02 (St) | Index theory examples (9:36 to 17:07) | 8 min

V03 (St) | Useful properties of the index (17:07 to 37:30) | 20 min

V04 (St) | Index of a point (37:30 to 46:43) | 9 min

V05 (St) | Theorem about closed trajectories (46:43 to 55:38) | 9 min

V06 (St) | Extra index theory thoughts (55:38 to 1:05:00) | 10 min

V07 (St) | Intro to isolated closed trajectories: limit cycles (1:05:30 to end) | 8 min

Video:

Steve's entire lecture

Sarah Iams