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I 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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,957

You see each interval?

Each color is an interval. Simpsons rule chooses the two endpoints of the interval and the midpoint and fits a parabola through them.

Later on I will show you an excellent page that will show what I mean. For now, sleep.

**In mathematics, you don't understand things. You just get used to them.**

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K 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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Go here when you have a chance.

http://math.fullerton.edu/mathews/a2001 … ature.html

Click them all but make sure you get both Simpson's rules. You will see all the major forms of quadrature.

**In mathematics, you don't understand things. You just get used to them.**

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Great!

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Very nice animations don't you think?

**In mathematics, you don't understand things. You just get used to them.**

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yep and they are created with Mathematica?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Yes, 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.**

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Is it the same as the formula? how?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Most 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.**

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Ok..

How can I fit a cubic or biquadratic there instead of a quadratic?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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There 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.**

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Oh,

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Yes, 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.**

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are they? why?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Because they have smaller coefficients (2 or 4 ) and therefore less susceptible to roundoff error.

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I am still not ok with the error calculation

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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On which one? We will do one when you wake up.

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That formula with xi

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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You mean that one?

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Yikes!

I meant this!

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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Okay, 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?

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yes, but what is the function? cos(x)^100 ?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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That is the integrand, what we are integrating.

The error requires the second derivative.

That is what the graph is.

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okay. Why do we check on the second derivative for the error?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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