Here are my notes from and office hours: Note Mar 25, 2020

Here is the link to the video of the lecture: https://www.dropbox.com/s/eu8257lh2hbt2aj/Lecture%2020200325.mp4?dl=0

Here is the link to the video of office hours: https://www.dropbox.com/s/57r5zjw2e1xnq7v/Office%20Hours%2020200325.mp4?dl=0

I’m not sure whether I actually succeeded in recording the session today (sometimes it takes Webex some time to make the videos available). I’ll post the video link here if and when it’s available.

As of right now, in-person classes at CityTech are still scheduled for Monday. Edit: we will not hold in-person classes next week; classes will officially move online next Thursday. More details will be posted when they are available but you can see the Chancellor’s message here. For now, assume that you will be learning the following material yourself, at least initially. More details will posted as soon as they are available. Stay healthy!

For Monday’s lesson, we’ll finish Section 3.7 Improper Integration and cover Section 6.3 Taylor and Maclaurin Polynomials. I’ll include some material here in case we end up needing it. Quiz #5 next Wednesday will cover improper integrals of type 1.

Section 3.7 Improper Integration

We have covered most of the material from Section 3.7, but we still need to see examples of what we called “improper integrals of type 2.” The Webwork deadline has been change  to Tuesday, March 17 at 11:59pm Tuesday, March 24.

Remember, improper integrals of type 1 are those where one or both of the limits of integration are infinite; improper integrals of type 2 are those where the limits of integration are finite, but there’s a vertical asymptote between the limits of integration.

In the textbook, you can find the improper integrals of type 2 by scrolling to the subsection heading Integrating a Discontinuous Integrand. Here is a video illustrating some examples of type 2 improper integrals.

Edit 3/22: Raisa and I talked about this example over email, so I thought I’d share it with the class: Improper integral example

Edit 3/23: Here are my notes from office hours. They’re very messy and might not make sense to someone who wasn’t there! I plan to record office hours in the future. Mon March 23 Office Hours

  • Textbook homework: P. 343: 347 – 373 odd
  • Webwork Improper Integrals due Tuesday, March 17 Tuesday, March 24
Section 6.3 Taylor and Maclaurin Polynomials (part 1)

Your textbook is a little unusual in that it covers two topics: Taylor/Maclaurin polynomials and Taylor/Maclaurin series in the same section. For Monday, we’ll look only at the subsections Taylor Polynomials and Taylor’s Theorem with Remainder (stop before the subsection Representing Functions with Taylor and Maclaurin Series). We’ll cover the rest of section 6.3 later in the semester.

Edit 3/19:

  • This video provides a great introduction to Taylor polynomials and Taylor series. Watch up at least the first 14 minutes and 30 seconds.
  • See this example and this example (both videos are under 5 minutes).

Here are a few videos describing Taylor and Maclaurin polynomials and some examples. 

Here are some interactive graphs where you can see graphs of the first few Taylor polynomials for

  • $f(x)=\ln(1+x)$ centered at $x=0$ (link)
  • $f(x)= \cos(x)$ centered at $x=a$; you can change the value of $a$ to see how the polynomials change (link)

Toggle the graphs on and off by clicking the circles on the left-hand side of the screen.

  • Textbook homework:P. 578: 118—123 all, 125, 127, 28, 133, 135
  • Webwork Taylor Polynomials due Sunday, March 22 Sunday, March 29