Timeline for Do I really need to cover solids of revolution in my Calculus I class?
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Jun 7 at 2:19 | review | Suggested edits | |||
| Jul 31 at 12:46 | |||||
| Jun 6 at 17:17 | comment | added | Cameron Williams | I also did not like volumes in Calculus I in high school. We had one such problem on the AP which was one of few things I got wrong, and it's what landed me at 4 instead of a 5. Now, it's one of my favorite topics to teach because it is a very simple idea (volume is the integral of area) that opens up a lot of doors, plus you can get weird with it and ask very tough questions that stretch their minds. | |
| Feb 11, 2022 at 19:24 | comment | added | John Bollinger | I actually have computed volumes of solids of revolution in my professional life, but since when is "will they have to work similar problems in real life?" the only relevant measure of whether a topic is useful? If it were, then your Calculus classes overall would probably be much smaller. | |
| Feb 11, 2022 at 11:03 | comment | added | Stian | Speaking from anectdotal experience as a receiver; solutions of revolution fundamented my understanding of what integration is and what it does, as the number of dimensions increase. Further on in my non-maths employment it has helped me understand how to quickly model real world phenomena when I know that the phenomena in question is symmetric around an axis... If this had not been taught me, I would have lost interest in maths long before I eventually did (which middle-aged me thinks is a shame) | |
| Feb 11, 2022 at 9:28 | comment | added | preferred_anon | For what it's worth, solids of revolution was the first time I saw a meaningful proof for the volume of a sphere. That sounds significant. | |
| Feb 11, 2022 at 0:00 | comment | added | dan04 | @PeterMortensen: At least here in the US, it's very common for colleges and universities to split the Calculus curriculum into three one-semester courses. Generally speaking, 1 introduces limits and differentiation, 2 introduces integration, and 3 introduces multiple independent variables. | |
| Feb 10, 2022 at 22:29 | answer | added | KCd | timeline score: 22 | |
| Feb 10, 2022 at 17:46 | comment | added | Peter Mortensen | What is "Calculus 1" ("Calculus I"?)? A proper noun? Referring to a particular country or school system? If yes, what country or school system? | |
| Feb 10, 2022 at 17:32 | comment | added | Carson Graham | As a high school student enrolled in calc BC who just recently covered volume of solids, I'd say it was worth doing. The equations are just a bit of algebra on top of the fundementals of integration, and it was a much more concrete use of calculus then the rest of the course so far | |
| Feb 9, 2022 at 14:40 | comment | added | Seth R | I loved it when we covered solid of revolution when I took calculus. It made all the abstract theoretical concepts real. It was an actual practical application. One of our homework assignments was to find objects around the house and figure out their volume using calculus. I actually had fun with it, and over 20 years later I still remember doing that assignment. | |
| Feb 9, 2022 at 1:21 | history | became hot network question | |||
| Feb 8, 2022 at 21:59 | answer | added | guest | timeline score: 1 | |
| Feb 8, 2022 at 21:07 | comment | added | Justin Champagne | Thank you all for the quick and insightful advice! I will certainly be re-evaluating my position on this topic. It's entirely possible that, like Sue VanHattum said, that I've let a previous experience sour my taste for the subject. And thanks for all the wonderful examples and resources! | |
| Feb 8, 2022 at 19:56 | answer | added | Steven Gubkin | timeline score: 42 | |
| Feb 8, 2022 at 19:22 | comment | added | ruferd | According to the AP Calculus Standards, solids of revolution are an "AB" topic. Many people get the impression that "AB topic = Calc 1" and "BC topic = Calc 2," but that might not be the case. When I adjuncted at a community college to teach Calc I, I did not have to do solids of revolution. The layout for me was Limits, Derivatives, applications of derivatives, introduction to integrals up to u-substitution and integrals as "net change." I got the impression "applications of integrals" (finding volumes) was where Calc II started. | |
| Feb 8, 2022 at 18:20 | answer | added | Joseph O'Rourke | timeline score: 14 | |
| Feb 8, 2022 at 17:59 | answer | added | Xander Henderson♦ | timeline score: 12 | |
| Feb 8, 2022 at 17:51 | comment | added | Sue VanHattum♦ | I'm wondering if you're letting a bad experience back when you were a student color your perceptions. | |
| Feb 8, 2022 at 17:39 | comment | added | Dave L Renfro | I would have thought that the skills learned from working with volumes of revolution would be much more useful to engineering majors than (likely "cookbook") approximation methods. You might want to look through some standard (U.S.) 1st/2nd year engineering statics and dynamics texts in your university's bookstore (volumes of revolution ideas are scattered throughout) or visit some of the engineering faculty and talk to them. I suspect learning how to set up definite integrals for various purposes is much more important for those students than methods CAS's can/will-soon take care of. | |
| Feb 8, 2022 at 17:28 | answer | added | Sue VanHattum♦ | timeline score: 7 | |
| S Feb 8, 2022 at 17:17 | review | First questions | |||
| Feb 8, 2022 at 18:06 | |||||
| S Feb 8, 2022 at 17:17 | history | asked | Justin Champagne | CC BY-SA 4.0 |