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#126 2013-07-26 04:45:17

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#127 2013-07-26 04:46:20

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#128 2013-07-26 05:06:59

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
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Re: An Integral and the Computer

K Thanks smile


'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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#129 2013-07-26 12:49:32

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#130 2013-07-26 21:38:52

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

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

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#131 2013-07-26 22:40:56

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#132 2013-07-27 00:30:32

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

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

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#133 2013-07-27 00:44:32

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#134 2013-07-27 01:04:00

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

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

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#135 2013-07-27 01:08:26

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#136 2013-07-27 02:04:42

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

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

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#137 2013-07-27 02:26:45

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#138 2013-07-27 02:34:06

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

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

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#139 2013-07-27 02:37:30

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#140 2013-07-27 02:43:05

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

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

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#141 2013-07-27 02:45:31

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#142 2013-07-27 02:49:51

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

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

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#143 2013-07-27 02:51:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#144 2013-07-27 15:46:30

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

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

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#145 2013-07-27 16:32:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

Re: An Integral and the Computer

You mean that one?


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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#146 2013-07-27 18:06:15

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

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

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#147 2013-07-27 18:51:58

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

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?

View Image: 2013-07-27_234737.gif

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

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#148 2013-07-27 19:43:16

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

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

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#149 2013-07-27 20:00:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,766

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#150 2013-07-27 20:04:17

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

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

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