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Joined: Jan 2002
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Joined: Jan 2002
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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.
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Joined: Jul 2000
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Carpal Tunnel
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Carpal Tunnel
Joined: Jul 2000
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TEd
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Joined: Mar 2000
Posts: 11,613
Carpal Tunnel
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Carpal Tunnel
Joined: Mar 2000
Posts: 11,613 |
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!
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Joined: Jan 2002
Posts: 1,526
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Joined: Jan 2002
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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.
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Joined: Jun 2002
Posts: 7,210
Carpal Tunnel
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Carpal Tunnel
Joined: Jun 2002
Posts: 7,210 |
> Smoothing over age and time
I'm getting more wrinkly, so perhaps my t is decreasing.
formerly known as etaoin...
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