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You are not logged in. #26 20130328 22:45:14
Re: Contour integrationAh ha, you did not see post #24... 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. #27 20130328 23:01:41
Re: Contour integrationYou edited it after I posted. 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 #28 20130329 10:16:24
Re: Contour integrationDitto! Are you clear on the contour integration. Want to do another? 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. #29 20130329 10:19:09
Re: Contour integrationWait, that's it? Are you sure? When I looked at some videos, I found that they split the integral into several integrals along the contour path... 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 #30 20130329 10:20:16
Re: Contour integrationI am not following you? What integral? 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. #31 20130329 10:46:25
Re: Contour integrationThe contour integral. As far as I know tthe original integral and the contour integral are not the same. 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 #32 20130329 10:49:09
Re: Contour integrationI am sorry, I am still not following. The original integral? 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. #33 20130329 10:51:29
Re: Contour integration
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 #34 20130329 10:52:26
Re: Contour integrationDid we not get the right answer? 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. #35 20130329 10:54:01
Re: Contour integrationBut, where did we use the contour integration? 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 #36 20130329 10:57:54
Re: Contour integrationWe considered the poles that were inside the contour, see the graph of the imaginary points. 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. #37 20130329 10:59:28
Re: Contour integrationOk. And why did we take those two poles and not the other two? 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 #38 20130329 11:08:14
Re: Contour integrationGood question. See rule one of my signature. 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. #39 20130329 11:14:48
Re: Contour integrationOk, but, why did I see some examples done with a rectangle path instead of a semicircle? 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 #40 20130329 11:22:21
Re: Contour integrationThat I do not know. But this I do know: One thing at a time! 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. #41 20130329 19:27:34
Re: Contour integrationAs I understand it if the integral is from ∞ to + ∞ you take all the poles. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #42 20130329 19:47:15
Re: Contour integrationHi; 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. #43 20130329 22:04:26
Re: Contour integrationHi 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 #44 20130329 22:19:47
Re: Contour integrationIsn't that just the standard way of evaluating a limit with an infinite endpoint? It is more like a definition than a means to computation. 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. #45 20130329 22:30:14
Re: Contour integrationNot exactly. I will try posting later what I mean, when I get on my laptop. 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 #46 20130329 22:37:46
Re: Contour integrationOkay, but chances are it will be one of those methods mathematicians love but does not do anything. 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. #47 20130329 23:26:24
Re: Contour integrationHere is what he did: And, when we let R go to infinity, the second integral becomes zero and you get the value of Last edited by anonimnystefy (20130329 23:28:35) 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 #48 20130330 03:33:54
Re: Contour integrationThose integrals look difficult the residue way does not require you to do the integral. 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. #49 20130330 12:28:17
Re: Contour integrationBut, are sure it always gives a correct solution? Last edited by anonimnystefy (20130330 12:42:08) 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 #50 20130330 13:07:53
Re: Contour integrationThe residue method? I know it does for rational functions. And how come you are not sleeping at this late hour? 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. 