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You are not logged in. #26 20130723 23:31:10
Re: An Integral and the ComputerIs the formula same as filling it up with trapeziums? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #27 20130723 23:32:17
Re: An Integral and the ComputerYes, they are rectangles with a triangle on top. 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. #28 20130724 00:46:07
Re: An Integral and the ComputerHmm... 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #29 20130724 04:31:35
Re: An Integral and the ComputerI already do: with that we can answer the question. 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. #30 20130724 11:26:08
Re: An Integral and the ComputerBut we still do not know n! 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #31 20130724 11:28:02
Re: An Integral and the ComputerThose are well known from books on numerical analysis and elsewhere. I believe it is derived from the Taylor series. We are going to compute n using that formula! 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. #32 20130724 11:28:41
Re: An Integral and the ComputerDefine error before that. Last edited by Agnishom (20130724 11:29:54) 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #33 20130724 11:29:33
Re: An Integral and the ComputerYou have defined 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. #34 20130724 11:32:48
Re: An Integral and the ComputerI do not understand the formula at post 29, what did you put between f''() 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #35 20130724 11:37:17
Re: An Integral and the ComputerHi; Remember we are in computer land here, not in the real world. Throw your pencil and paper out the window but make sure you do not hit anybody with them. Maxima or any other CAS can get that second derivative immediately and in this field you are encouraged to use it. If you can not do the differentiation what then? We will talk about that at the end. Let us not be slowed down by side issues of differentiation or computing numbers. These are tasks unrelated to what the question is. 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. #36 20130724 11:59:14
Re: An Integral and the ComputerI wrote the function and I am getting 0.12501848174018745 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #37 20130724 12:02:24
Re: An Integral and the ComputerHi Agnishom; 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. #38 20130724 12:04:01
Re: An Integral and the ComputerCode:>>> from math import cos >>> def integrate(f, a, b, n): s = 0 for k in xrange(1, n): s += f(a + ((k*(ba))/n)) s += 0.5*(f(a) + f(b)) s *= (ba)/n return s >>> f = lambda x: (cos(x))**100 >>> integrate(f, 0, (3.141592653589793/4),1000) 0.12501848174018745 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #39 20130724 12:08:09
Re: An Integral and the ComputerHaha!
Post that in help me and I will work with you on it there.But let us proceed quickly and smoothly to our goal of getting a trapezoid rule 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. #40 20130724 12:11:23
Re: An Integral and the Computer
_ 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #41 20130724 12:17:33
Re: An Integral and the ComputerThat is very good! and the somewhat enigmatic statement
How do we use 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. #42 20130724 12:21:02
Re: An Integral and the Computer
Nope. I have not. What is error? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #43 20130724 12:30:10
Re: An Integral and the ComputerYou said 4 significant figures. Since we have an estimate given for the integral, that implies an error of .00005 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. #44 20130724 12:31:30
Re: An Integral and the ComputerOk, what about xi? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #45 20130724 12:35:09
Re: An Integral and the Computerxi is a value in the closed interval a,b that maximizes the value of error. Let's see how to compute 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. #46 20130724 12:37:31
Re: An Integral and the ComputerHmm 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #47 20130724 12:55:15
Re: An Integral and the ComputerIt looks terrible.. 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #48 20130724 13:07:42
Re: An Integral and the ComputerYes and the error estimate is wildly inaccurate so we will do it the old fashioned way. When you ran your routine for n = 4 what did you get? 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 20130724 13:09:48
Re: An Integral and the ComputerI did not run the routine for n=4 ever 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #50 20130724 13:12:51
Re: An Integral and the ComputerCan you do it now? 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. 