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You are not logged in. #1 20130328 01:54:04
Contour integrationCan somebody explain contour integration to me a little bit? 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 #2 20130328 01:57:40
Re: Contour integrationDo you want to see it work or you want a theoretical discussion? 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. #3 20130328 02:09:02
Re: Contour integrationAn example would be nice. 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 #4 20130328 02:19:17
Re: Contour integrationPlease integrate that. 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. #5 20130328 02:21:54
Re: Contour integrationStefy, check this out: I have discovered a truly marvellous signature, which this margin is too narrow to contain. Fermat Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes Young man, in mathematics you don't understand things. You just get used to them.  Neumann #6 20130328 02:24:54
Re: Contour integration
How do I do that? 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 #7 20130328 02:26:21
Re: Contour integrationGet the poles first. 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. #8 20130328 02:44:33
Re: Contour integrationOkay, that is the easy part. Last edited by anonimnystefy (20130328 02:45:16) 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 #9 20130328 02:46:47
Re: Contour integrationTake the positive 2, do you know why? 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. #10 20130328 02:56:22
Re: Contour integrationNo... 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 #11 20130328 02:57:39
Re: Contour integrationThe limits of integration are positive so we only take the positive poles. 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. #12 20130328 03:05:38
Re: Contour integrationSince when can complex numbers be positive and negative? Do you want their real parts to be positive or...? 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 #13 20130328 03:11:47
Re: Contour integrationI get the poles like this You take the ones that do not have a minus sign in front. See the drawing provided later to tell which poles to 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. #14 20130328 12:19:37
Re: Contour integrationI think those are the 1. and 3. in my list. 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 #15 20130328 21:40:32
Re: Contour integrationNow get the residue of those two poles. This is done in a couple of ways. I prefer the formula. If you like your own way use it. Once you have the residues you are almost done. Tell me when you get mine. 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. #17 20130328 21:57:19
Re: Contour integrationHi; where c is a pole and n is its order. Ex: has 2 poles i and i. To get the residue of i we say n =1 and c = i. The whole formula simplifies to which equals  i / 2 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. #19 20130328 22:17:33
Re: Contour integrationHi;
If you can get it in a week then you will have far surpassed me. I never did get it, despite having it explained to me at least 5 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. #20 20130328 22:33:21
Re: Contour integrationHi bobbym 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 #22 20130328 22:39:13
Re: Contour integrationHi zeta; 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. #23 20130328 22:40:08
Re: Contour integrationpi*sqrt(2)/4? Last edited by anonimnystefy (20130328 22:40:39) 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 #25 20130328 22:43:40
Re: Contour integrationYes, I have. Did you see post #23? 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 