Posted on 04/11/2019 1:10:39 PM PDT by johnnyb_61820
This week, WBC fellow Jonathan Bartlett, along with co-author Asatur Zh. Khurshudyan, published a paper showing that elementary calculus contains a longstanding flaw that has been present for over a century. The paper was published in the peer-reviewed journal Dynamics of Continuous, Discrete & Impulsive Systems, Series A: Mathematical Analysis: Mathematical Analysis (DCDIS-A, for short). The journal has been published for a quarter of a century and many major universities across the United States subscribe to it.
The flaw they discovered is one of notation. Now, you may be thinking, how can notation be wrong? Well, notation can be wrong when it implies untrue things, especially when notation exists that implies the correct things.
(Excerpt) Read more at mindmatters.ai ...
Yep, NO flaw found here, either, and I use calculus in my job as an engineer. Who thinks dy/dx is a fraction?
Agreed, I never thought of it that way, just viewed it as a notational convention. You can argue that Δy/Δx is in fact a fraction and that reducing that to the infinitesimal dy/dx doesn’t change the nature of it, but in real life nobody I know thinks of it or uses it that way.
“42”
Shhh! The answer to meaning of Life, the Universe, and Everything is supposed to be a secret.
This question has never been fully answered.
Louis Farrakhan asked, ‘What is so deep about this number 19?’
Book sales?
I doubt it...it seems a whole lot more awkward.
I was trying to derive it by the derivative of the quotient but it doesn’t seem to work for me.
Between this and the college bribery scandal I’ll be able to excuse my piss poor educational performance.
I’m sure this was the part of calculus that just didn’t make sense to me therefor rendering the rest of calculus nonsensical. Never made it to Deferential Equations. You can’t learn 300 pages of calculus in a night, well at least I couldn’t, kept trying though.
As long as the don’t fiddle around with the Einstein notation.
And all this time, (since 1963), I thought I just couldn't understand calculus.
I think it was the professor's fault! He was teaching me a flawed calculus!
No wonder I couldn't get it.
So, to start with, do differentials rather than derivatives (you can probably do it with derivatives, but more steps). So, for instance, d(x^2) = 2x dx.
Now, the quotient rule is d(u/v) = (v du - u dv) / v^2. Therefore,
d(dy/dx) = (dx d(dy) - dy d(dx)) / dx^2
Now, the derivative is the differential divided by dx, so that puts another dx on the bottom
(d(dy/dx))/dx = (dx d(dy) - dy d(dx)) / dx^3
Now, just distribute the numerator and simplify:
(d(dy/dx))/dx = d(dy)/dx^2 - (dy/dx) (d(dx)/dx^2)
d(dy) = d^2y, so
(d(dy/dx))/dx = d^2y/dx^2 - (dy/dx) (d^2x/dx^2)
That’s the new formula.
Actually, the problem with differential equations is mostly that it is poorly taught. There’s actually not a whole lot to know. There’s a couple of basic forms, and just trying to reduce everything to those. Old-school diff-eq books were tiny.
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