Category: Class Agendas (Page 3 of 9)

Class Info

• Date: Mon Nov 13
• Meeting Info: 10a-11:40a, N719

Announcements

Exam #2:

• Our 2nd midterm exam will be tomorrow, Wednesday Nov 15
• See this post for a list of topics and review exercises for the exam
• Please work through on those review exercises, which I will collect later in the semester as a HW assignment

Topics

We reviewed the topics that will be on the exam, in particular partial fractions and volumes of revolution. We reviewed Quiz #3, and set up a couple of the suggested exercises from the Final Exam Review sheet:

We also revisited the topic of improper integrals, although this will not be on tomorrow’s exam:

We closed with an application of improper integrals to “an infinite” volume of revolution–“Gabriel’s horn“:

Class Info

• Date: Wed Nov 8
• Meeting Info: 10a-11:40a, N719

Announcements

WebWork:

• “Applications – Volumes of Revolution” (due Friday Nov 9)

Exam #2:

• Our 2nd midterm exam will be Wednesday (Nov 14)
• See this post for a list of topics and review exercises for the exam
• Please start working on those review exercises, which I will collect later in the semester as a HW assignment

Topics

We reviewed the last exercise on the “Volumes of Revolution” WebWork, which asked for the volume of a torus:

We found that setting up an integral for this volume is rather complicated, but in fact it’s quite straightforward to find the volume if we “cut” the torus and “unwrap” it–so that we see that it has the same volume as a cylinder. Here is an illustration (from this website) of what we discussed, and what I tried to draw on the board:

We then did some additional examples of improper integrals. We revisited the improper integral we calculated on Monday, which “converges” to a finite number, even though we are integrating over an infinite interval:

You can also see that example in this PatrickJMT video:

We contrasted this with the improper integral of 1/x over the same interval, which we saw diverges to infinity. That example is worked out in Sec 3.7 of the textbook:

You should also read Example 3.48, which is an improper integral for a volume of revolution via the disk method!

Class Info

• Date: Mon Nov 6
• Meeting Info: 10a-11:40a, N719

Announcements

WebWork:

• “Applications – Volumes of Revolution” (due Friday Nov 9)

Topics

We recapped how to set up integrals for areas between curves, and for volumes of solids of revolution:

We set up an example from the WebWork that that involves calculating a volume using cylindrical shells, and also looked at an example from the textbook (Example 2.15 from Sec 2.3):

We then introduced “improper integrals”–where we integrate over an infinite interval, using a limit: