d/dt - thanks and summary

[JIMCHEVAL -at- AOL -dot- COM]

I got a variety of responses to the question I tossed out in passing
on d/dt.  Thanks to:

cwrites -at- usit -dot- net (Brad Connatser)
chuck -dot- melikian -at- exgate -dot- tek -dot- com
xrm -at- email -dot- msn -dot- com (Richard Mateosian)
wdhanig -at- rice -dot- edu (Walter Hanig)
JohnG -at- mikohn -dot- com (John Gilger)

Since someone else may actually encounter this term, but also because the
following is a neat illustration of different styles of explaining complex
info in simple terms, I've included a summary of the responses below.

Jim Chevallier
North Hollywood

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d/dt is not a stat term. It simply is a rate of change. For example,
lets say the voltage in a circuit changed from 1 volt to 5 volts in 32
milliseconds. The rate of change would be 4V/32ms or 125V/s. The "d" stands
for Delta (change). The ratio is read "Delta V over Delta T (for time)."


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The least geekoid description of d/dt I can think of:

d/dt describes how fast (or slow) something changes.

or

The rate of change of <whatever> with respect to time.

Ex. 1

dx/dt = speed when x represents position or in simpler terms, distance
traveled.

For example, if you travel 5 miles in 1 minute, your speed (rate of change
of position) = 300 mph.

Ex. 2

dv/dt = acceleration where v represents speed.

If your speed is constant (whether 0 mph or 17,000 mph), acceleration is
zero. If your speed changes, you have acceleration.

Think of it as rate of change with respect to t. For example, if
your distance (m, in miles)traveled as a function of time (t, in
hours) is

                  m = 30 t

Then (d/dt) m (or dm/dt, as it's usually written) is your speed,
namely 30 mph in this case.  ...RM

The d in the numerator (on top or to the left of the virgule) stands for
"change in" (it's math shorthand for lower case letter delta).

The dt in the denominator (on the bottom or to the right of the virgule)
stands for "change in time."

So, d/dt means the change in something compared to (or divided by) a change in
time.

For example, d/dt of position means the change in position divided by the
change in or amount of time. In other words, speed.

The notion of change in one quantity divided by or with respect to the change
in another quantity is one of the bases of differential calculus.


It means the change in the observed data as time passes.  The most familiar
version is speed, i.e., miles per hour.  If you look at an object and
establish where it is located, then look at it again in an hour and find out
that it is 10 miles away from its former location, you can determine that
its speed is 10 miles per hour.

Mathematicians, being lovers of obscure symbols, chose the Greek letter
"delta" (Latin 'd') to mean "change."

So what all this means is that d/dt is short hand for "change over a period
of time."
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