Timeline for Why is differential calculus often presented before integral calculus?
Current License: CC BY-SA 4.0
8 events
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| Jul 8, 2021 at 13:26 | comment | added | Steven Gubkin | @user615 I agree this argument is not excruciating at all for us, but I think it would require at least a 50 minute lecture to reach 1/4 of the average freshman calculus population. You may also be interested in this: mathoverflow.net/questions/114738/… | |
| Jul 7, 2021 at 15:37 | comment | added | DKNguyen | @JohnOmielan Ah, yes. One of those classes. I took one of those once. Apparently I did astonishingly well, but I remember nothing from it and always felt I deserved 20%. | |
| Jul 6, 2021 at 20:38 | comment | added | John Omielan | @DRF (cont.) going from about $100$ to $50$. Also, the average mark on the first midterm was only about $20$%! The course continued to teach derivatives and then, near the end, showed with the FTC that, for most cases, integrals can, at least in theory, be calculated as anti-derivatives. Interestingly, I guess because they didn't want to bell-curve too much or fail too many students, the final exam had very few questions covering the first part of the course, with most of it being instead about derivatives & calculating standard integrals. | |
| Jul 6, 2021 at 20:38 | comment | added | John Omielan | @DRF Regarding "Also just the definition of a Riemann integral is pretty hard", I grew up in Ontario, Canada back when they still had a grade $13$. In that year, we were taught about the basics of limits, derivatives and then integrals, mainly as anti-derivatives. However, at the University of Waterloo, in a first year advanced honors calculus course I took, the instructor started with the historical background of integrals, & then the theoretical aspects of Riemann integrals. Although this class consisted of many of the top math students from Canada, about half dropped out fairly early, ... | |
| Jul 6, 2021 at 18:41 | comment | added | DRF | Also just the definition of a Riemann integral is pretty hard. I realize that calc students don't usually do proper proofs/definitions anyway, but you need a (proper) generalized definition of a limit if you want to define a Riemann integral. My experience that your normal calc student never even understands the basic limit definition. Which I think is another reason the order is what it is. You never actually learn differential calculus you learn a new kind of arithmetic. | |
| Jul 6, 2021 at 18:37 | comment | added | DRF | You still have to do limits first though if you want real integral calculus and not just numerical math. Also limits that are much much harder than anything calc students normally cover. | |
| Jul 6, 2021 at 14:17 | comment | added | Steven Gubkin | Another issue is the ordering of corequisite courses. A student taking physics at the same time might need to understand velocity as the derivative of position before they get to integrals later. So making a change in the "standard curriculum" forces potentially unwelcome changes to courses in other departments. There is just a ton of institutional inertia to doing anything different with a calculus course. | |
| Jul 6, 2021 at 14:00 | history | answered | Steven Gubkin | CC BY-SA 4.0 |