Many people realize that the first derivative of position wrt (with respect to) time is called velocity and is represented by the symbol v and that the second derivative wrt time is called acceleration, denoted by the symbol a. Probably fewer people know that there is a technical name for the third derivative wrt time which I'll leave to the sufficiently curious reader to google.
Homo Loquens??
derivatives I actually understood pretty much all of this page except for the equations--I can't do any math where I don't know what the symbols mean. In x'(t) = 3t^2 + 2, I have no idea what ' and ^ mean.
Another site has me wondering about something, and if anyone can give me a brief layman's definition, I sure would appreciate it: what is meant by
Smoothing over Age and Time?
HarvardEdit--dang, Ted, you snuck in while I was still researching!
In x'(t) = 3t^2 + 2
x'(t) means the first derivative of x with resepct to t.
That is, the rate at which x changes as t changes.
x''(t) would be the second derivative.
x'''(t) would be the third.
The caret symbolizes exponentiation which is difficult to represent on a computer otherwise. In mathematica, it might be possible to do it. I'm not sure. Old versions of basic used "**", so one would write x'(t) = 3*t**2 + 2 where one asterisk denoted multiplication and two exponentiation.
As that page was not written for a program, but for a human to read, he left out the single asterisk, because most people would understand that better.
Smoothing in relation to functions means trying to come up with parameters that make a function more "natural" looking. There's an art to it, as well as a science. We had to do splines in graduate numerical analysis, which is trying to find a smooth curve to fit n points. I haven't used it since, but I'm vaguely aware that they use splines in some kinds of graphics applications.
Smoothing over age and time should be a property of a function that gets smoother as t increases.
> Smoothing over age and time
I'm getting more wrinkly, so perhaps my t is decreasing.