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#201 2013-08-05 04:53:31

bobbym
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Re: An Integral and the Computer

Theoretically, Romberg should be much better than Simpson's.


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.

#202 2013-08-05 05:28:19

anonimnystefy
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Re: An Integral and the Computer

But, it is more complicated to program, though.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#203 2013-08-05 05:44:23

bobbym
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Re: An Integral and the Computer

You only need one column and the the formula generates all the rest.


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.

#204 2013-08-05 05:46:44

anonimnystefy
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Re: An Integral and the Computer

But, how do I know how many values to get for the first column?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#205 2013-08-05 05:50:11

bobbym
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Re: An Integral and the Computer

You do not. But like a difference table how far you go horizontally depends on how tall the first column is. Each column is more and more accurate, so pick a number n and go from there.


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.

#206 2013-09-02 03:26:27

gAr
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Re: An Integral and the Computer

Hi,

Can anyone tell how to find the value of the following integral upto four significant digits with the help of a computer but not a readymade CAS?

J simulation:

Code:

load 'trig'            NB. required for cos
samp =: 1000000        NB. the number of samples
avg =: +/%#            NB. the average function
f =: ?samp$0           NB. random numbers in range (0,1)
fn =: cos f*pi%4       NB. get the list of cosines after scaling into range (0,pi/4)
fn100 =: fn^100        NB. get the 100th power
avg fn100*pi%4         NB. Take the average after multiplying (pi/4-0)

≈ 0.125139

which is close enough!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

#207 2013-09-02 04:14:45

anonimnystefy
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Re: An Integral and the Computer

Isn't o. used for trig functions as well?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#208 2013-09-02 13:18:29

gAr
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Re: An Integral and the Computer

trig functions must be loaded.
o.n is pi times n.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

#209 2013-09-02 18:21:55

anonimnystefy
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Re: An Integral and the Computer

Only when monadic. As dyadic, it represents circle functions: http://www.jsoftware.com/help/dictionary/dodot.htm


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#210 2013-09-03 15:56:44

gAr
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Re: An Integral and the Computer

Okay, thanks, did not see that before!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

#211 2013-09-03 18:59:30

anonimnystefy
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Re: An Integral and the Computer

You're welcome.

The functions are hard to remember.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#212 2013-09-03 19:37:48

gAr
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Re: An Integral and the Computer

Indeed, they are hard to remember and understand.
Anyway, it's good and quick once we get a hang of it. Their documentation is good, but scattered. They need to reorganize that.
E.g. I had to search for quite a long time to find how to change the array values


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

#213 2013-09-03 19:44:31

anonimnystefy
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Re: An Integral and the Computer

I agree. Fortunately, the tutorials I found on that site are great!

How good are you with tacit expressions?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#214 2013-09-03 20:03:00

gAr
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Re: An Integral and the Computer

Yes, and there are essays in that site with very useful programs!

I'm still learning. Are you too trying out J?


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

#215 2013-09-04 03:44:07

anonimnystefy
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Re: An Integral and the Computer

Yes, I've seen them. They are fantastic.

I have learned a bit about it, I was amazed by how simple and complex it looks at the same time. Also, the tacit programming part of J caught my eye. I haven't done much in it though.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#216 2013-09-04 03:55:15

gAr
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Re: An Integral and the Computer

Okay, tacit programming is the best part of the language.

But needs much practice to know the rules and use it efficiently.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

#217 2013-09-04 04:00:26

anonimnystefy
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Re: An Integral and the Computer

Yes, that is pretty much the reason why I could never do much in it.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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