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You are not logged in. #8226 20130222 01:20:00
Re: Linear Interpolation FP1 FormulaHi; 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. #8227 20130222 01:54:05
Re: Linear Interpolation FP1 FormulaI sort of miss her in a friend sort of way, not a romantic sense. You know, just having someone to talk to... #8228 20130222 02:01:31
Re: Linear Interpolation FP1 FormulaShe will be back soon, so relax and do some math. 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. #8229 20130222 02:05:55
Re: Linear Interpolation FP1 FormulaYes, I have read that  but basically I just found the Fourier series of x/2, differentiated both sides and let x = 0, pi/6, and other values which resulted in 1/2 = 1  1 + 1  1 ... etc. but I don't know if that type of manipulation is valid. If I'm getting Grandi's series on the RHS, then that means the Fourier series doesn't converge at those points...? #8230 20130222 02:08:35
Re: Linear Interpolation FP1 FormulaRemember the Grandi does not converge. It is convergent in a Borel sense. Which loosely means we would like it to converge to 1 / 2, here are the usual methods. Last edited by bobbym (20130222 02:08:59) 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. #8231 20130222 02:12:27#8232 20130222 02:25:37
Re: Linear Interpolation FP1 FormulaHi; Last edited by bobbym (20130222 02:26:31) 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. #8233 20130222 02:27:58
Re: Linear Interpolation FP1 FormulaOkay, so we cannot just differentiate a FS and expect everything to work out... so, if my FS is 2piperiodic (say, over the integral [pi,pi], then does it converge for all values of x, pi < x < pi? (My original FS for x/2, not the differentiated one) #8234 20130222 02:28:34
Re: Linear Interpolation FP1 FormulaSorry, just saw your edit... #8235 20130222 02:33:34
Re: Linear Interpolation FP1 FormulaHi;
At 0 it is the Grandi Series.
Fourier series do not always converge. Last edited by bobbym (20130222 03:06:05) 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. #8236 20130222 03:47:34
Re: Linear Interpolation FP1 FormulaSo how do we know for certain whether or not the Fourier series for a particular function converges or not? I did read somewhere that it 'almost completely' converges in the interval... #8237 20130222 03:55:05
Re: Linear Interpolation FP1 FormulaYou mean dorms?
Except at discontinuities which is quite often because those are the type it is often used on.
No, Gibb's shows it will not always converge in the interval. To really know would require in a practical sense numerical experimentation. Else, you would need Harmonic analysis. I choose the first one. 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. #8238 20130222 04:06:37
Re: Linear Interpolation FP1 FormulaEither halls of residences or just flats provided by UCL, on their campus. #8239 20130222 04:07:05
Re: Linear Interpolation FP1 FormulaHarmonic analysis looks interesting but difficult too, I doubt I will understand much of it... #8240 20130222 04:08:06
Re: Linear Interpolation FP1 FormulaIt is hard. I do not get it either. Worse, I have never found a book that was willing to explain it. 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. #8241 20130222 04:12:49
Re: Linear Interpolation FP1 FormulaI think it is offered as either a third year course or a graduatelevel course. I don't know what the prerequisites are though... #8242 20130222 04:19:39
Re: Linear Interpolation FP1 FormulaFrom a practical standpoint you can use the idea of probably convergent except at jump discontinuities. 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. #8243 20130222 04:24:26
Re: Linear Interpolation FP1 FormulaBut even if I get a prettylooking series, it means nothing mathematically, because it requires proof of the convergence... #8244 20130222 09:20:48
Re: Linear Interpolation FP1 FormulaNot necessarily, Sometimes you can use a truncated part of a divergent series for real numerical work. 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. #8245 20130222 09:37:07
Re: Linear Interpolation FP1 FormulaDo you have an example? #8246 20130222 09:41:45
Re: Linear Interpolation FP1 FormulaFacebook got hacked yesterday or this morning. 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. #8247 20130222 09:42:53
Re: Linear Interpolation FP1 FormulaReally? It says she updated 23 hours ago (21:40ish on the 21st of Feb)... which would coincide with when she returned to London. #8248 20130222 10:10:10
Re: Linear Interpolation FP1 FormulaFound a photo of her and her BF cuddling, from 3 days ago. I guess we know what decision she made... I would not be surprised if she decides not to contact me again. Oh well. #8249 20130222 11:14:31
Re: Linear Interpolation FP1 FormulaCuddling? I thought she was the other way. It is a real shame that the story of Pinocchio is not true. Could you imaging how many big noses there would be? 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. #8250 20130222 11:26:01
Re: Linear Interpolation FP1 FormulaYep. I suppose it just reinforces the fact that I shouldn't get involved with her and just keep her as a friend or acquaintance. My time will hopefully come soon, just with another woman. She might not exist but I won't lose hope, hope makes the journey worthwhile. 