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Previous Thread Next Thread Print Thread Mild derivative amusement. #154151 01/20/2006 2:32 PM Joined: Jan 2002 Posts: 1,526 Virginia, USA TheFallibleFiend veteran TheFallibleFiend veteran Joined: Jan 2002 Posts: 1,526 Virginia, USA 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. Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: Mild derivative amusement. #154152 01/20/2006 3:30 PM Joined: Jul 2000 Posts: 3,467 Marion NC TEd Remington Carpal Tunnel TEd Remington Carpal Tunnel Joined: Jul 2000 Posts: 3,467 Marion NC Jerk! TEd Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: Mild derivative amusement. #154153 01/20/2006 3:45 PM Joined: Mar 2000 Posts: 11,613 Louisville, Kentucky Jackie Carpal Tunnel Jackie Carpal Tunnel Joined: Mar 2000 Posts: 11,613 Louisville, Kentucky 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? Harvard Edit--dang, Ted, you snuck in while I was still researching! Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: Mild derivative amusement. #154154 01/20/2006 4:34 PM Joined: Jan 2002 Posts: 1,526 Virginia, USA TheFallibleFiend veteran TheFallibleFiend veteran Joined: Jan 2002 Posts: 1,526 Virginia, USA 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. Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Re: Mild derivative amusement. #154155 01/20/2006 4:48 PM Joined: Jun 2002 Posts: 7,210 Vermont Buffalo Shrdlu Carpal Tunnel Buffalo Shrdlu Carpal Tunnel Joined: Jun 2002 Posts: 7,210 Vermont > Smoothing over age and time I'm getting more wrinkly, so perhaps my t is decreasing. formerly known as etaoin... Copy Link to Clipboard Share Post on Facebook Share Post on Twitter Moderated by  Jackie  Hop To General Topics ------  Information and announcements  Q&A about words  Wordplay and fun  Words and languages in schools  Miscellany  Weekly Themes  Looking for (writers, speakers,... (Old) Weekly themes. (have been... ------  Words from medicine  Beheading words  Meta-words  Words from classical mythology  Animal Safari  Words with unusual etymologies  Eponyms or words derived from p...  Loanwords from German  English as a global language Print Thread Switch to Threaded Mode Show Likes Link Copied to Clipboard View Profile Private Message Website Follow User Forum Posts Like Summary View Profile Private Message Follow User Forum Posts Like Summary View Profile Private Message Follow User Forum Posts Like Summary View Profile Private Message Website Follow User Forum Posts Like Summary View Profile Private Message Website Follow User Forum Posts Like Summary

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