• Announcements: The next homework set (HW8) is available online, and due on April 20. Note that this is 2 weeks from today, in keeping with the original Spring Break from the pre-pandemic calendar. Although CUNY has "cancelled" Spring Break due to the "recalibration period", since we worked through the recalibration period, I am extending the deadline for HW8 by one week (hence to April 20), and will be posting online lectures as follows: Lecture 21 by April 20, and Lecture 22 by April 22. These lectures will likely be available online sooner than these dates, and you may work through them whenever is most convenient for you (but, at the latest, on these indicated dates). In this way, you can choose whether to allow yourself a Spring Break, or instead work through the Spring Break having twice the usual amount of time to go through the same amount of material. Either way, you can pick what is most convenient for you, both options are equally fine for me, as long as you deliver HW8 by April 20. As always, if you have any questions, please send me an e-mail!

• Basic properties of double integrals Download file or watch below

• Example of computing volume using a double integralDownload file or watch below

• Another example of computing volume using a double integral (careful: only one order of integration is feasible!) Download file or watch below

• Lecture Notes (static file from above videos): PDF file

• Alternative Lecture Notes (from last year): PDF file

• External link 1 (highly recommended, has many further examples!): Paul's Online Notes about General Double Integrals

• External link 2 (same as External link 5 of Lecture 19): PatrickJMT computing a double integral by switching order of integration, very similar to last example I did above (video): Watch on YouTube

• External link 3 (same as External link 6 of Lecture 19): PatrickJMT computing a few more double integrals (video): Watch on YouTube