# Math Fascinates: But differential equations sucked

Why couldn’t I have one of these when I was in college?

I ran across this video by chance, made in August last year.  The narrator shows how differential equations and integrals were solved before digital computers were invented.

If all mathematics and calculus (and other sciences) were explained as clearly and simply as this young man does it, there would be more people in STEM.

1. Allison says

What he’s described at the beginning is the standard explanation of
what integration is, and if you didn’t get that in the first few weeks
(Granted, bad teaching seems to be the rule rather than the
exception in math.)

It’s interesting, but what’s missing is the connection between what
he shows and actually solving differential equations (as opposed to
calculating the values of certain integrals.) For example,
the differential equations that describe the motions of the
planets etc. in the solar system. To solve those equations,
you’d need all the stuff that you get in a 1- or 2-semester
course on Ordinary Differential Equations, and there’s no
way you could begin to explain it in a 10-minute video.
And you’d need to know all that before you could begin to
design an analog computer to solve it.

Note when you build an analog computer, that computer will only
solve _one_ set of differential equations. If you decide you need to
solve a slightly different one, it’s back the machine shop.
The advantage of an analog computer (or a program for a digital
computer) is that, once you’ve built one, such as for a bombsight,
people don’t have to know any math to use it to solve the same
set of equations over and over again.

BTW, people were solving differential equations by hand centuries
before analog computers existed, and the methods digital computers
use to solve them are pretty much just automation of those methods.

2. jrkrideau says

Why couldn’t I have one of these when I was in college?

You would have needed a forklift to carry it?

The narrator really does a good job.

3. Peter B says

Analytical chemists use a simple trick to integrate. They run a solution through a column that separates the various constituents into multiple peaks while recording on a strip of paper. They then cut the curve out and weigh the paper. Microgram weight measurements are not a problem.

For good fractional ppm measurements, the chemist will add a measured small amount of that which is to be measured and make a new curve. (That method also helps identify which peak belongs to the item of interest.)

4. says

It’s very hard to build a compact mechanical computer. If you make the parts too small they’re just not stiff enough to work properly.

And I would imagine that e.g. the mentioned fire control computers require quite a bit of maintenance.