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You are not logged in. #126 20130727 02:45:17
Re: An Integral and the ComputerI meant that I would be happy if I knew how the program is the same as drawing quadratics. '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 #127 20130727 02:46:20
Re: An Integral and the ComputerYou see each interval? 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. #128 20130727 03:06:59
Re: An Integral and the ComputerK Thanks '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 #129 20130727 10:49:32
Re: An Integral and the ComputerGo here when you have a chance. 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. #130 20130727 19:38:52
Re: An Integral and the ComputerGreat! '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 #131 20130727 20:40:56
Re: An Integral and the ComputerVery nice animations don't you think? 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. #132 20130727 22:30:32
Re: An Integral and the Computeryep and they are created with Mathematica? '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 #133 20130727 22:44:32
Re: An Integral and the ComputerYes, it appears so. Do you have a little bit better idea of what has been done. 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. #134 20130727 23:04:00
Re: An Integral and the ComputerIs it the same as the formula? how? '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 #135 20130727 23:08:26
Re: An Integral and the ComputerMost likely yes. All the formulas for Simpson's rule basicaly do the same thing. There may be different rates of convergence to the answer. There are many variations to each formula, I have just shown you one. This is a huge field. 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. #136 20130728 00:04:42
Re: An Integral and the ComputerOk.. '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 #137 20130728 00:26:45
Re: An Integral and the ComputerThere are higher quadrature formulas then Simpson's. I used to use Weddle's Rule and Bode's. They are even higher, they are 5th or 6th order fits. In any case all those formulas, quadratics, cubics, quartic have all been invented by mathematicians of the past. They are all called Newton  Cotes formulas. 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. #138 20130728 00:34:06
Re: An Integral and the ComputerOh, '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 #139 20130728 00:37:30
Re: An Integral and the ComputerYes, but since we are talking about numerical work I can tell you that they suffer from some problems which is the reason that lower order quadrature formulas trap, and simpsons are preferred. 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. #140 20130728 00:43:05
Re: An Integral and the Computerare they? why? '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 #141 20130728 00:45:31
Re: An Integral and the ComputerBecause they have smaller coefficients (2 or 4 ) and therefore less susceptible to roundoff error. 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. #142 20130728 00:49:51
Re: An Integral and the ComputerI am still not ok with the error calculation '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 #143 20130728 00:51:06
Re: An Integral and the ComputerOn which one? We will do one when you wake up. 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. #144 20130728 13:46:30
Re: An Integral and the ComputerThat formula with 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 #145 20130728 14:32:44
Re: An Integral and the ComputerYou mean that 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. #146 20130728 16:06:15
Re: An Integral and the ComputerYikes! I meant this! '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 #147 20130728 16:51:58
Re: An Integral and the ComputerOkay, the first thing you do is plot the second derivative of the function and see where the absolute value is a maximum. We see that occurs at x = 0. Do you follow? 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. #148 20130728 17:43:16
Re: An Integral and the Computeryes, but what is the function? cos(x)^100 ? '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 #149 20130728 18:00:25
Re: An Integral and the ComputerThat is the integrand, what we are integrating. The error requires the second derivative. That is what the graph 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. #150 20130728 18:04:17
Re: An Integral and the Computerokay. Why do we check on the second derivative for the 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 