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#26 2014-02-20 15:19:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

Yes, but what has that have to do with pizza?


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.

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#27 2014-02-20 15:21:37

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: Fourier series

Nothing. We are making gel candles for school project. Why is a gel candle considered a good gift?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#28 2014-02-20 15:23:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

Because the people who sell the materials say so.


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.

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#29 2014-02-20 15:33:26

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: Fourier series

Why is it not?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#30 2014-02-20 15:35:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

What makes anything a good gift?


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.

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#31 2014-02-20 15:37:46

ElainaVW
Member
Registered: 2013-04-29
Posts: 270

Re: Fourier series

That pizza sounds good:)

Have you covered the least squares - orthogonality property of these approximations?

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#32 2014-02-20 15:38:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

Hi EVW;

Not yet on both!


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.

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#33 2014-02-20 15:41:30

ElainaVW
Member
Registered: 2013-04-29
Posts: 270

Re: Fourier series

That post earlier about .999999... it does sound like that guy you told me about:(

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#34 2014-02-20 15:43:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

Read the other ones, have you?

These fits are both least square and orthogonal. This makes them very desirable. Along with the periodicity property.


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.

Offline

#35 2014-02-20 16:00:07

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: Fourier series

bobbym wrote:

What makes anything a good gift?

I've no idea


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#36 2014-02-20 16:04:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

Do you agree with her that is GiB over 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.

Offline

#37 2014-02-20 16:09:47

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: Fourier series

bobbym wrote:

Do you agree with her that is GiB over there?

Sounds like good news but when did ElianaVW tell that?

Last edited by Agnishom (2014-02-20 16:10:46)


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#38 2014-02-20 16:11:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

Post #33.

I have to go eat now, we will continue later. Have a good day at school.


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.

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#39 2014-02-20 16:16:07

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: Fourier series

That is not likely to be GiB He does quality posts.

By the way, today is the last day of my secondary schooling


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#40 2014-02-20 21:17:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

I never saw him ever do a quality post.

Let's do the fourier series for x^2.

f[x_] := x^2;

a0 = 1/(2*\[Pi]) Integrate[f[x], {x, -\[Pi], \[Pi]}];
a[n_] := 1/\[Pi] Integrate[f[x] Cos[n*x], {x, -\[Pi], \[Pi]}];
b[n_] := 1/\[Pi] Integrate[f[x] Sin[n*x], {x, -\[Pi], \[Pi]}];

All the b's are zero and

a0 + a[1] Cos[x] + a[2] Cos[2 x] + a[3] Cos[3 x] + a[4] Cos[4 x]

yields:

Plot[{x^2, \[Pi]^2/3 - 4 Cos[x] + Cos[2 x] - 4/9 Cos[3 x] + 1/4 Cos[4 x]}, {x, -\[Pi], \[Pi]}]

quite a good fit as you can see below.

View Image: 2014-02-21_011246.gif

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.

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#41 2014-02-21 22:31:23

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: Fourier series

Thanks, I tried that. Do you have an exercise for me?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#42 2014-02-21 23:46:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

Did you get the same answer?


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.

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#43 2014-02-21 23:58:07

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: Fourier series

I just copy pasted what ever you wrote. What answer?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#44 2014-02-22 00:06:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

Okay, you are ready to stand on your own two feet.

Please get the Fourier series of

[I made a small edit to the problem.]


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.

Offline

#45 2014-02-22 01:04:47

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: Fourier series

In[61]:= a[0] + a[1] Cos[x] + a[2] Cos[2 x] + a[3] Cos[3 x] + 
 a[4] Cos[4 x] + a[5] Cos[5 x] + a[6] Cos[6 x] + a[7] Cos[7 x] + 
 b[0] + b[1] Sin[x] + b[2] Sin[2 x] + b[3] Sin[3 x] + b[4] Sin[4 x] + 
 b[5] Sin[5 x] + b[6] Sin[6 x] + b[7] Sin[7 x]

Out[61]= 2/\[Pi] - (2 Cos[2 x])/(3 \[Pi]) - (2 Cos[4 x])/(
 15 \[Pi]) - (2 Cos[6 x])/(35 \[Pi]) + Sin[x]/2

It is not really a good fit still


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#46 2014-02-22 01:45:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

Please post a picture of the fit.


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.

Offline

#47 2014-02-22 02:02:21

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: Fourier series

I'll but now it'll be done by GNU Plot rather than M because now I am running Linux


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#48 2014-02-22 02:13:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

Okay, lets see the plot of both functions superimposed on each other.


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.

Offline

#49 2014-02-22 02:29:35

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: Fourier series

I am getting this error in my CAS sad

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plot2d: expression evaluates to non-numeric value somewhere in plotting range.

'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#50 2014-02-22 02:33:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Fourier series

Take a look at mine in the blue and yours in the black. What do you notice?

View Image: 2014-02-21_011246.gif

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.

Offline

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