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#126 2013-07-26 04:45:17
Re: An Integral and the Computer
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'
I'm not crazy, my mother had me tested.
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#127 2013-07-26 04:46:20
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#128 2013-07-26 05:06:59
Re: An Integral and the Computer
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'
I'm not crazy, my mother had me tested.
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#129 2013-07-26 12:49:32
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#130 2013-07-26 21:38:52
Re: An Integral and the Computer
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'
I'm not crazy, my mother had me tested.
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#131 2013-07-26 22:40:56
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
Very nice animations don't you think?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#132 2013-07-27 00:30:32
Re: An Integral and the Computer
yep 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'
I'm not crazy, my mother had me tested.
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#133 2013-07-27 00:44:32
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#134 2013-07-27 01:04:00
Re: An Integral and the Computer
Is 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'
I'm not crazy, my mother had me tested.
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#135 2013-07-27 01:08:26
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#136 2013-07-27 02:04:42
Re: An Integral and the Computer
Ok..
How can I fit a cubic or biquadratic there instead of a quadratic?
'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'
I'm not crazy, my mother had me tested.
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#137 2013-07-27 02:26:45
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#138 2013-07-27 02:34:06
Re: An Integral and the Computer
Oh,
'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'
I'm not crazy, my mother had me tested.
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#139 2013-07-27 02:37:30
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#140 2013-07-27 02:43:05
Re: An Integral and the Computer
are 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'
I'm not crazy, my mother had me tested.
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#141 2013-07-27 02:45:31
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
Because 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#142 2013-07-27 02:49:51
Re: An Integral and the Computer
I 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'
I'm not crazy, my mother had me tested.
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#143 2013-07-27 02:51:06
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
On which one? We will do one when you wake up.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#144 2013-07-27 15:46:30
Re: An Integral and the Computer
That 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'
I'm not crazy, my mother had me tested.
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#145 2013-07-27 16:32:44
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
You mean that one?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#146 2013-07-27 18:06:15
Re: An Integral and the Computer
Yikes!
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'
I'm not crazy, my mother had me tested.
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#147 2013-07-27 18:51:58
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
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?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#148 2013-07-27 19:43:16
Re: An Integral and the Computer
yes, 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'
I'm not crazy, my mother had me tested.
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#149 2013-07-27 20:00:25
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: An Integral and the Computer
That 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#150 2013-07-27 20:04:17
Re: An Integral and the Computer
okay. 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'
I'm not crazy, my mother had me tested.
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