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Re: [Phys-L] calc probs --> real-world physics deliverables



On 12/21/2013 01:31 PM, Paul Lulai wrote:
i like the kids to get some basic practice with the general
relationships before they try to apply them to deeper settings.

I don't know whether the following example is the sort of
thing that is being requested, or the exact opposite. Doing
the calculus is super-easy ... just differentiating the 1/x
function ... but /understanding/ why that's what you need to
do is a hurdle for lots of people.

Anyway, here's the example:
a) Consider the black-body spectrum(or almost any spectrum)
in terms of power per unit frequency. Find "the" peak of
"the" spectrum.
b) Now consider the same spectrum in terms of power per unit
wavelength. Find "the" peak of "the" spectrum.
c) Observe that the two peaks do not occur at the same place!
Specifically,
λ_peak < c / f_peak
and
f_peak < c / λ_peak

This is discussed in lurid detail, with diagrams, at
http://www.av8n.com/physics/black-body-notes.htm#note-shifty-denom

===

More generally, this is yet another example of why you should
plot every distribution two ways: Once as the /density/
distribution and again as the /cumulative/ distribution. This
applies to probability distributions as well as all sorts of
spectral distributions.

So ... my example is representative of a huuuge category of
examples that use calculus in an important way. Knowing how
to differentiate 1/x is not important; you can look that up
if you have to. What's important is knowing that the density
distribution is the derivative of the cumulative distribution,
and that both are useful.

=======================

Even more generally, this document
http://www.av8n.com/physics/black-body-notes.htm

is an example of how a physicist can make himself useful in the
real world. Here's the story: Some buddies of mine have a real-
world high-tech application that involves using an infrared
pyrometer. They are smart guys in their field, but they're not
physicists, and they had half a dozen misconceptions about how
the pyrometer works. None of the misconceptions was particularly
deep; just little things like assuming that the black-body
spectrum would be sharply peaked at some frequency. However,
when you add all the misconceptions together they led to seriously
incomprehensible results. It was the sort of situation where the
usual engineering approach did not work, because fixing any one
thing didn't yield any improvement. There were just too many
misconceptions in series.

So I spent a couple of hours talking to the guys and then wrote
up a brief memorandum, not even a set of answers but more of a
guide to how to think about the issues.

This memorandum bears little resemblance to the "lab reports" that
students are required to do in school, but it is a 100% genuine
example of the sort of "deliverable" that gets delivered in the
real world.

The hard part of preparing a memorandum like this is figuring out
which questions need answering. Once you know what the questions
are, any physicist on earth can find the answers. The trick is
talking to the guys long enough to figure out what the real issues
are. There are a million things that could go wrong, and you have
to figure out which ten of them actually went wrong.