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You are not logged in. #201 20130805 04:53:31
Re: An Integral and the ComputerTheoretically, Romberg should be much better than Simpson's. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #202 20130805 05:28:19
Re: An Integral and the ComputerBut, it is more complicated to program, though. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #203 20130805 05:44:23
Re: An Integral and the ComputerYou only need one column and the the formula generates all the rest. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #204 20130805 05:46:44
Re: An Integral and the ComputerBut, how do I know how many values to get for the first column? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #205 20130805 05:50:11
Re: An Integral and the ComputerYou do not. But like a difference table how far you go horizontally depends on how tall the first column is. Each column is more and more accurate, so pick a number n and go from there. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #206 20130902 03:26:27
Re: An Integral and the ComputerHi,
J simulation: Code:load 'trig' NB. required for cos samp =: 1000000 NB. the number of samples avg =: +/%# NB. the average function f =: ?samp$0 NB. random numbers in range (0,1) fn =: cos f*pi%4 NB. get the list of cosines after scaling into range (0,pi/4) fn100 =: fn^100 NB. get the 100th power avg fn100*pi%4 NB. Take the average after multiplying (pi/40) ≈ 0.125139 "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #207 20130902 04:14:45
Re: An Integral and the ComputerIsn't o. used for trig functions as well? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #208 20130902 13:18:29
Re: An Integral and the Computertrig functions must be loaded. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #209 20130902 18:21:55
Re: An Integral and the ComputerOnly when monadic. As dyadic, it represents circle functions: http://www.jsoftware.com/help/dictionary/dodot.htm The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #210 20130903 15:56:44
Re: An Integral and the ComputerOkay, thanks, did not see that before! "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #211 20130903 18:59:30
Re: An Integral and the ComputerYou're welcome. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #212 20130903 19:37:48
Re: An Integral and the ComputerIndeed, they are hard to remember and understand. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #213 20130903 19:44:31
Re: An Integral and the ComputerI agree. Fortunately, the tutorials I found on that site are great! The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #214 20130903 20:03:00
Re: An Integral and the ComputerYes, and there are essays in that site with very useful programs! "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #215 20130904 03:44:07
Re: An Integral and the ComputerYes, I've seen them. They are fantastic. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #216 20130904 03:55:15
Re: An Integral and the ComputerOkay, tacit programming is the best part of the language. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #217 20130904 04:00:26
Re: An Integral and the ComputerYes, that is pretty much the reason why I could never do much in it. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment 