Differentials for Dummies

By -
This is (I think) too good to be hidden as comment #3 under “An Uncomfortable Teacher”.

Here’s something I handed my calculus teacher in high school:

Solve: A d2y/dx2 + B dy/dx + C y = 0

Multiplying through by dx2:
A d2y + B dy dx + C y dx2 = 0

This is a quadratic in dx:
dx = (-B dy +/- sqrt(B2 dy2 – 4AC y d2y)) / 2C y

Therefore
dx/dy = (-B +/- sqrt(B2 – 4AC y d2y/dy2)) / 2C y

But d2y/dy2 = d/dy (dy/dy) = 0

dx/dy = (-B +/- sqrt(B2)) / 2C y = (-B +/- B) / 2C y

dx/dy = 0 OR (-B/C) (1/y)

Therefore
EITHER x is constant (highly doubtful)
OR x = (-B/C) log y + K
IN WHICH CASE y = exp((-C/B) (x – K)) = K’ exp((-C/B) x)

Done!

Needless to say, I did not receive a convincing explanation of why this derivation was invalid.

Comments

  1. Bob Murphy9:45 PM

    Wabulon,

    I used to think I was a geek.

    ReplyDelete
  2. Anonymous9:00 PM

    My favorite bit is: "EITHER x is constant (highly doubtful)"

    ReplyDelete

Post a Comment

Popular posts from this blog

Libertarians, My Libertarians!

By -
Cruel to be kind means that I love you . Because, while I think you are mistaken, your hearts are in the right place -- yes, even you, Silas --  unlike some people . This Breitbart fellow (discussed in the link above), by all appearances, deliberately doctored a video of Shirley Sherrod to make her remarks appear virulently racist, when they had, in fact, the opposite import. I heard that at a recent Austrian conference, some folks were talking about "Callahan's conservative turn." While that description is not entirely inaccurate, I must say that a lot of these people who today call themselves conservative give me the heebie-jeebies.
Read more

"Pre-Galilean" Foolishness

By -
 I am currently reading The Master and His Emissary , which appears to be an excellent book. ("Appears" because I don't know the neuroscience literature well enough to say for sure, yet.) But then on page 186 I find: "Asking cognition, however, to give a perspective on the relationship between cognition and affect is like asking astronomer in the pre-Galilean geocentric world, whether, in his opinion, the sun moves round the earth of the earth around the sun. To ask a question alone would be enough to label one as mad." OK, this is garbage. First of all, it should be pre-Copernican, not pre-Galilean. But much worse is that people have seriously been considering heliocentrism for many centuries before Copernicus. Aristarchus had proposed a heliocentric model in the 4th-century BC. It had generally been considered wrong, but not "mad." (And wrong for scientific reasons: Why, for instance, did we not observe stellar parallax?) And when Copernicus propose...
Read more