Timeline for How misleading is it to regard $\frac{dy}{dx}$ as a fraction?
Current License: CC BY-SA 3.0
30 events
| when toggle format | what | by | license | comment | |
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| Oct 11, 2021 at 12:51 | comment | added | BCLC | how is this on-topic on maths of? sounds like it is more on topic on maths se or maths education se. | |
| Jun 25, 2020 at 14:36 | answer | added | johnnyb | timeline score: 7 | |
| Feb 21, 2020 at 17:14 | history | edited | YCor |
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| Feb 21, 2020 at 8:52 | answer | added | Enrique Macias | timeline score: 0 | |
| Nov 2, 2017 at 5:41 | comment | added | Neo M Hacker | I thought it's rigorously correct to assume it is a ratio of differentials, where dy is defined as a change in y along the tangent line at (x,y). dy = f'(x) dx. Where dx is the change in x, and dy is the corresponding change in y along the tangent with slope f'(x) at x. Quote from Calculus with Analytic Geometry by George F. Simmons II edition on the notation dy/dx in dy/dx = f'(x) (9): "The new feature of equation (9) in our present discussion is that now the Leibniz symbol on the left not only looks like a fraction but is a fraction." Is the text book wrong? | |
| May 14, 2016 at 20:58 | comment | added | user21349 | Since this is not a research-level question, it's not surprising that the same question has been asked on math.SE and has received much better answers: math.stackexchange.com/questions/21199/… | |
| Sep 19, 2015 at 20:38 | history | protected | Lucia | ||
| Jan 13, 2015 at 12:40 | answer | added | Boggie Georgiev | timeline score: 5 | |
| Jan 13, 2015 at 9:56 | answer | added | Namo | timeline score: -2 | |
| Oct 8, 2013 at 0:20 | comment | added | Suvrit | No longer relevant; it has received enough good answers already... | |
| Oct 7, 2013 at 21:00 | review | Close votes | |||
| Oct 8, 2013 at 0:38 | |||||
| Oct 7, 2013 at 20:42 | comment | added | Gerald Edgar | Teaching Calc I for the first time: Do not deviate from the textbook. Not even one tiny bit. Not even by an infinitesimal dx. | |
| Feb 29, 2012 at 21:57 | comment | added | Joël Cohen | I would argue that the notation actually leads students to make fewer mistakes. In my experience, students who do not use this notation have trouble computing the derivative of the reciprocal of a function (the formula $(f^{-1})'(y) = \frac{1}{f'(f^{-1}(y))}$ is cumbersome compared to $\frac{dx}{dy} = \frac{1}{\frac{dy}{dx}}$), or performing a change of variable in an integral. | |
| Sep 19, 2011 at 17:39 | vote | accept | Frank Thorne | ||
| Aug 24, 2011 at 6:41 | comment | added | user13113 | Dorais: how much of that do you think is because the notation is inherently difficult, and how much the students are left to learn it by osmosis while being instructed they're "supposed" to think of all of the variables as being functions of some other designated variable? | |
| Aug 24, 2011 at 3:38 | answer | added | Alexander Woo | timeline score: 9 | |
| Aug 23, 2011 at 18:05 | comment | added | Robert Israel | See also math.stackexchange.com/questions/46530/… | |
| Aug 23, 2011 at 17:54 | comment | added | Michael Hardy | I entirely disagree with François G. Dorais about this. See my answer below. | |
| Aug 23, 2011 at 17:51 | answer | added | Michael Hardy | timeline score: 28 | |
| Aug 23, 2011 at 17:43 | comment | added | Mark | My answer for a different question exemplifies one possible danger of taking such notation for granted: Suggestions for good notation | |
| Aug 23, 2011 at 17:37 | answer | added | David Milovich | timeline score: 9 | |
| Aug 23, 2011 at 15:11 | answer | added | Jim Conant | timeline score: 55 | |
| Aug 23, 2011 at 15:10 | answer | added | john mangual | timeline score: 14 | |
| Aug 23, 2011 at 15:06 | answer | added | Steven Landsburg | timeline score: 29 | |
| Aug 23, 2011 at 14:33 | answer | added | Steve Huntsman | timeline score: 12 | |
| Aug 23, 2011 at 14:21 | comment | added | François G. Dorais | Whether or not it can be viewed as a fraction, I think $dy/dx$ is a poor choice of notation for Calc I. The problem is illustrated by the need for the parenthetical remark "under appropriate conditions" in your third paragraph. Using $dy/dx$ means that students have to struggle with both the notion of derivative and the intricacies of the notation. Unfortunately, the notation is so prevalent that it is unreasonable to postpone the notation until Calc III or Diff Eq, where it actually comes in handy. Oh well... | |
| Aug 23, 2011 at 14:08 | answer | added | Pietro Majer | timeline score: 15 | |
| Aug 23, 2011 at 13:48 | answer | added | Neil Strickland | timeline score: 62 | |
| Aug 23, 2011 at 13:41 | comment | added | user11000 | Couple of related posts of possible interest @ math.se: math.stackexchange.com/questions/21199/is-dy-dx-not-a-ratio math.stackexchange.com/questions/21869/… | |
| Aug 23, 2011 at 13:23 | history | asked | Frank Thorne | CC BY-SA 3.0 |