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You are not logged in. #176 20130804 01:45:15
Re: An Integral and the ComputerYes. Would you change the title of this thread to 'An Integral and the Computer' or something more interesting 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #177 20130804 02:21:37
Re: An Integral and the ComputerHi; 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. #178 20130804 03:32:36
Re: An Integral and the ComputerHm, what about Romberg? 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 #179 20130804 03:40:17
Re: An Integral and the ComputerRomberg uses the trapezoidal rule and then generates an array of values. Hopefully with each column being more accurate because each column is a higher and higher Newton Cotes. 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. #180 20130804 03:42:36
Re: An Integral and the ComputerSo, how is each value generated, exactly? 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 #181 20130804 03:47:43
Re: An Integral and the ComputerIt uses something called Richardson's Extrapolation to do that. I generally do not use it for anything but sequence acceleration and I am not sure how it does that either. 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. #182 20130805 00:54:31
Re: An Integral and the ComputerThe original integral to a 100 places (with trap): Requires n=215004709762716014868701639070092447035983684173824 according to the error estimate. Last edited by anonimnystefy (20130805 00:55:36) 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 #183 20130805 00:57:01
Re: An Integral and the ComputerI would not recommend the trap rule for that many digits of precision. 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. #184 20130805 00:58:14
Re: An Integral and the ComputerWith what did you compute that? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #185 20130805 00:59:15
Re: An Integral and the ComputerHe used the big boy on the block, M! 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. #186 20130805 01:08:38
Re: An Integral and the ComputerI do not recommend it either. Just look at how large n it took! Last edited by anonimnystefy (20130805 01:09:01) 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 #187 20130805 01:10:26
Re: An Integral and the ComputerYou do not believe that M actually did anything that many times?! 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. #188 20130805 01:22:32
Re: An Integral and the ComputerOf course not! Nothing can do something like that that many times. What I do not know is what it did. Last edited by anonimnystefy (20130805 01:22:58) 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 #189 20130805 01:26:24
Re: An Integral and the ComputerUsed acceleration techniques. What command did you use? 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. #190 20130805 01:31:07
Re: An Integral and the ComputerSum. Last edited by anonimnystefy (20130805 01:31:28) 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 #191 20130805 01:37:49
Re: An Integral and the ComputerOkay, that uses lots of acceleration making that command fast. 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. #192 20130805 02:08:55
Re: An Integral and the ComputerYes, thought it was something like that, but that number is still very large. Maybe it has to do with the fact that it all of them are very very small. 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 #193 20130805 02:14:35
Re: An Integral and the ComputerWhat is very small? 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. #194 20130805 02:16:28
Re: An Integral and the Computer(Cos[x])^100. 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 #195 20130805 02:19:46
Re: An Integral and the ComputerIf you used Sum he probably was able to do the definite summation and get a closed form. 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. #196 20130805 02:25:13
Re: An Integral and the ComputerIt seems it really does have a closed form for the sum! 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 #197 20130805 02:26:05
Re: An Integral and the ComputerThat would account for the speed and accuracy. 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. #198 20130805 02:33:20
Re: An Integral and the ComputerI'm now trying to implement the Simpson's rule in M. 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 #199 20130805 02:37:32
Re: An Integral and the ComputerShould not be difficult. Nice clean formula for math style. 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. #200 20130805 04:49:53
Re: An Integral and the ComputerYes, it is a pretty one. Unlike Romberg... 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 