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You are not logged in. #11601 20130628 17:10:59
Re: Linear Interpolation FP1 FormulaSuppose you had the integral So now we let: We have and Adding these two equations yields: Thus, #11602 20130628 17:24:10
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. #11603 20130628 17:27:42
Re: Linear Interpolation FP1 FormulaUnfortunately it doesn't seem to work nearly as often as one would like! #11604 20130628 17:33:45
Re: Linear Interpolation FP1 FormulaIt is a trick and as such you use it when you can. 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. #11605 20130628 17:40:56
Re: Linear Interpolation FP1 FormulaThat's the thing when you learn a new trick... you want to use it on everything but really it will only work on a few problems. #11606 20130628 17:47:45
Re: Linear Interpolation FP1 FormulaI think it was Alan Turing along with Alonzo Church that proved a long time ago that for an infinite number of problems you will require an infinite number of methods. 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. #11607 20130628 18:37:09#11608 20130628 19:02:15
Re: Linear Interpolation FP1 FormulaSupposing you want to evaluate this integral: you might first embed it into a whole family of integrals called y. you could now work it like this. Factor: Now you have solved for the family y in terms of a useful recurrence relation. 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. #11609 20130628 19:20:27
Re: Linear Interpolation FP1 FormulaThat is impressive. A question like that came up in my STEP III exam  except we had a trig version. #11610 20130628 19:29:10
Re: Linear Interpolation FP1 FormulaWhen I first saw it I loved it and tried to find more of them. But they are few and far between. 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. #11611 20130629 06:33:50
Re: Linear Interpolation FP1 FormulaDo you use a CAS for almost every integration problem you encounter? #11612 20130629 08:40:27
Re: Linear Interpolation FP1 FormulaIf I am doing an integration problem where there is something I need to learn how to do then I do it by hand no matter how long it takes. If someone is asking a question I will do it by hand for them and then use the CAS to check. 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. #11613 20130629 19:11:19
Re: Linear Interpolation FP1 FormulaI understand what you mean. And there are also lots of problems that CAS's give oddlooking answers for, and many integrals that they cannot do (yet can be done on paper). A lot of integrals in STEP were like that. #11614 20130629 19:18:28
Re: Linear Interpolation FP1 Formula
A CAS does not mean you shut your brain off. Sometimes you have to help him along. With practice you will find that the number of integrals, sums, DE's , limits and simplifications you can do will increase by a factor of 10. 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. #11615 20130703 18:03:23
Re: Linear Interpolation FP1 FormulaI was just looking at my UCL course and it appears that you can't go down the computational route without sacrificing the pure maths route... I can either fit into one category or the other! #11616 20130703 19:34:55
Re: Linear Interpolation FP1 FormulaWho ever said you needed UCL to teach you computational math or any other type. They are mostly just good for supplying you with credentials and reputation. Like all the other things in life you will have to teach yourself. 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. #11617 20130703 19:41:58
Re: Linear Interpolation FP1 FormulaOK, but the problem is that if I do not take some computational modules then I won't be allowed to take other ones the next year (they claim I would not have the prerequisite knowledge). #11618 20130703 19:47:46
Re: Linear Interpolation FP1 FormulaThey are a product of self understanding. If you are forced down that road and that just might be the case you will have the satisfaction of knowing you are unique. If a hundred of them come out of some university they may not be fragmented but they are also bereft of imagination. All one hundred will be mirror images, all exactly alike. 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. #11619 20130704 21:35:26
Re: Linear Interpolation FP1 FormulaYes, I do not want to be like that. But, hopefully my passion will never dwindle. #11620 20130704 22:21:38
Re: Linear Interpolation FP1 FormulaThen if they will not teach then you will still find a way to learn. 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. #11621 20130704 23:47:59
Re: Linear Interpolation FP1 FormulaHopefully the quality of teaching won't affect it too much. #11622 20130704 23:51:43
Re: Linear Interpolation FP1 FormulaIf you can decide what you most likely want to be then choose the one that fits that best. 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. #11623 20130704 23:56:23#11624 20130704 23:58:37
Re: Linear Interpolation FP1 FormulaNot necessarily, although that would certainly be a way to decide. Even as a lifelong hobby. 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. #11625 20130705 00:19:12 