Timeline for How misleading is it to regard $\frac{dy}{dx}$ as a fraction?
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Dec 24, 2011 at 21:09 | comment | added | Will Sawin | If this argument worked, it would work equally well if you weren't moving on a level curve, but were instead following some other path. | |
| Aug 23, 2011 at 22:02 | comment | added | Sridhar Ramesh | The problem here is the unfortunate notation for partial derivatives: the top $\partial U$ represents $dU=U_x dx+U_y dy$ with $dy$ set to zero, while the bottom $\partial U$ represents $dU$ with $dx$ set to zero; the $\partial$ represents a different differential operator in the two cases, even though it is written with the same symbol. This is somewhat orthogonal, though, to the issue of whether it is appropriate to view all these ratio-looking things as ratios; the problem isn't in treating ratio-type things as ratios, but in not notationally distinguishing different operators. | |
| Aug 23, 2011 at 15:06 | history | answered | Steven Landsburg | CC BY-SA 3.0 |