Timeline for Why do we teach calculus students the derivative as a limit?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Nov 11, 2010 at 15:21 | comment | added | Steven Gubkin | @Jeff: The MO question I linked to shows that for C^\infty functions, these axioms do characterize differentiation. | |
| Nov 4, 2010 at 18:12 | comment | added | Jeff Strom | I don't claim these properties fully characterize differentiation. I've toyed with adding a "uniform convergence" type axiom, but not for Calculus 1 purposes. Unfortunately, all of my analysis knowledge is half-remembered, so I'd have to sit down and think about this, and I have not found the time yet. | |
| Nov 4, 2010 at 14:23 | comment | added | Steven Gubkin | See this MO question: mathoverflow.net/questions/44774/… | |
| Nov 4, 2010 at 3:01 | comment | added | Steven Gubkin | So see that I can get more than polynomials: By using the chain rule and the product rule I can actually get any algebraic function. But I still do not see how to get any transcendental function. | |
| Nov 3, 2010 at 15:41 | comment | added | Steven Gubkin | Is there really a unique equivalence relation satisfying these rules? I do not see how these rules could ever access a function which is not a polynomial. If not, saying that you can define f'(a) to be the slope of the tangent line at x=a presupposes that you have chosen one of the many equivalence relations which satisfy these properties. | |
| Oct 19, 2010 at 14:11 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Oct 9, 2010 at 1:27 | history | edited | Jeff Strom | CC BY-SA 2.5 |
added 628 characters in body
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| Sep 27, 2010 at 17:12 | comment | added | Mark Meckes | I second Deane's comment. | |
| Sep 27, 2010 at 14:20 | comment | added | Deane Yang | This is very nice. | |
| Sep 27, 2010 at 13:58 | history | answered | Jeff Strom | CC BY-SA 2.5 |