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You are not logged in. #1 20060701 09:32:30
understanding macluarin polynomials. A peak under the hoodMy calculus book explained how to form macluarin polynomials but said nothing on why they work. Over the past couple days I've been turning it over in my head trying to figure it out. I haven't found a proof but its begining to make sense. I thought it might make an intresting discussion for anyone who has never seen the proof or is not advanced enough to understand it yet. Last edited by mikau (20060701 09:40:48) A logarithm is just a misspelled algorithm. #2 20060701 11:11:23
Re: understanding macluarin polynomials. A peak under the hoodTo me the biggest mystery is still why its characteristics at f(0) can be used to determine its behavior anywhere if its approximated to enough terms. Like I said, if the function matches the behavior at zero to such a high degree, then its behavior for other numbers relatively close to zero can't be too far off. Still I'm trying to find an argument for why it works for other area's just because we matched its behavior in one particular spot. (0). A logarithm is just a misspelled algorithm. #3 20060702 00:21:18
Re: understanding macluarin polynomials. A peak under the hoodVery interesting mikau. I like analogies and things that are not complete proofs because they help you to remember the equations and it's a big step toward understanding something. What is your favorite usage of maclaurin series? What is a usage of maclaurin that is too hard to use? igloo myrtilles fourmis #4 20060702 08:17:39
Re: understanding macluarin polynomials. A peak under the hoodI suppose my favorite usage would be for approximating sine and cosine, as I am always infatuated with trig functions. Last edited by mikau (20060702 09:07:41) A logarithm is just a misspelled algorithm. #5 20060705 06:27:11
Re: understanding macluarin polynomials. A peak under the hoodCool man, have a nice fourth in NJ. I'm in NH. igloo myrtilles fourmis #6 20060705 06:55:37
Re: understanding macluarin polynomials. A peak under the hoodI'm not in NJ, I'm in PA. A logarithm is just a misspelled algorithm. #7 20060705 10:10:51
Re: understanding macluarin polynomials. A peak under the hoodI'm in NJ! Cool, were all in about the same area (of the globe). "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #8 20060705 10:58:41
Re: understanding macluarin polynomials. A peak under the hoodthat must mean New Hampshire isn't far from pennsylvannia.... Last edited by mikau (20060705 10:59:34) A logarithm is just a misspelled algorithm. #9 20060706 07:03:47
Re: understanding macluarin polynomials. A peak under the hoodYeah New York and Vermont separate NH and PA. igloo myrtilles fourmis #10 20060707 00:23:41
Re: understanding macluarin polynomials. A peak under the hoodGood Job, Mikau! X'(yXβ)=0 #11 20060707 03:39:10
Re: understanding macluarin polynomials. A peak under the hoodI think my book stated the error is always less then or equal to the value of one additional term. (one term greater then the last term you used). I think this applied to all convergent series' as well but I"m not sure. A logarithm is just a misspelled algorithm. #12 20060709 01:55:29
Re: understanding macluarin polynomials. A peak under the hoodAbout the error I guess your book uses a limit proof. A limit proof itself implies locally being virturely the same the numerator ( the error) is little enough to match the little denominator (x displacement), before both getting zero. So your book may give after the proof an example evaluating f(a+0.m) by macluarin series of f starting from a. X'(yXβ)=0 