#Calculus? Fourier + Eigenfunctions

44 messages · Page 1 of 1 (latest)

smoky berry
tawny muskBOT
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still galleon
# smoky berry

correct me if I am wrong but isn't this just a straightforward computation question?

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you compute all the f_n first then try to determine what the series looks like

smoky berry
still galleon
smoky berry
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bet, give me a sec

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didnt seem to be simplifying fn much

still galleon
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huh...

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I find it quite difficult to read

smoky berry
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apologies. Process wise though, fn is the integral of f(x)*u_n(x) ?

still galleon
smoky berry
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just split the integral accordingly and by parts the first one. Not sure if I can find a nicer form for sin((n-1/2)pi/2) or cos((n-1/2)pi/2)

still galleon
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did i miss something?

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,w plot 3/2 - 2x

cursive roverBOT
smoky berry
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skipped a line, when subbing in x = 1/2 in 2nd integral, get another term. I just combined them

still galleon
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also is it normal that f is not continuous?

smoky berry
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yeah, hence fourier

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i figured it was just straight computation but even just computing fn i hit a wall

still galleon
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yeah I can see why

still galleon
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i was expecting -1/2

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ah wait no i missed a factor 2

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stupid me

smoky berry
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all good. Just dont know if im acc doing any of this right

still galleon
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let's see what wolfram thinks

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,w int (3/2 - 2x) cos((n-1/2) pi x) from 0 to 1/2

cursive roverBOT
still galleon
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,w int 2 cos((n-1/2) pi x) from 1/2 to 1

cursive roverBOT
still galleon
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Let's see if that checks out

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bro

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guess i'll get some paper

smoky berry
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😭

still galleon
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I was able to identify some terms but the coefficients don't match

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nah bruh i throw the towel

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💀

smoky berry
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nw

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anyone else may know?

eager raptorBOT
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@smoky berry

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