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Fourier Transform - Wave Equation Help Reaching f(x-ct)

Math notation confusion Thu 27 Aug 01:27:33 2020 No.12052877 View Reply Original Report

Quoted By: >>12052883

Here is my rough work. I cannot figure out how to turn the last integral into f(x-ct) what am i missing? Thanks in advance.

Math notation confusion

Math notation confusion Thu 27 Aug 2020 01:30:09 No.12052881 Report

Quoted By:

Of course the BS is sideways. Fuck i am stupid, my bad senpai. Someone please help me with the last step.

Anonymous

Anonymous Thu 27 Aug 2020 01:30:21 No.12052883 Report

Quoted By: >>12052891

>>12052877
Just like, use the definition of the fourier transform my guy

Math notation confusion

Math notation confusion Thu 27 Aug 2020 01:33:33 No.12052891 Report

Quoted By: >>12052895

>>12052883
Yeah, truly helpful. Fuck you.

Anonymous

Anonymous Thu 27 Aug 2020 01:35:38 No.12052895 Report

Quoted By: >>12052911 >>12052916

>>12052891
??? It's literally just the definition
We have
$ \int^\infty_{-\infty} e^{i \omega (x - c t)} \hat{f} (\omega) d\omega = \int^\infty_{-\infty} e^{i \omega x'} \hat{f} (\omega) d\omega = f(x') = f(x-ct) $
with $x' = x-ct$ , where we used the definition of the inverse Fourier transform in the second equality

Math notation confusion

Math notation confusion Thu 27 Aug 2020 01:40:31 No.12052911 Report

Quoted By:

>>12052895
Well, fuck. You are right.

Math notation confusion

Math notation confusion Thu 27 Aug 2020 01:41:38 No.12052916 Report

Quoted By: >>12052942

>>12052895
Is it possible to even show this by splitting the integral and evaluting it from - infinity to zero then from 0 to infinity? I should get the same result correct?

Math notation confusion

Math notation confusion Thu 27 Aug 2020 01:47:51 No.12052932 Report

Quoted By: >>12052948

Give me more insight! Don't answer and run! I need conversation! I get the substitution. I just want to know I would actually evaluate it...not use the definition?

Anonymous

Anonymous Thu 27 Aug 2020 01:49:37 No.12052942 Report

Quoted By:

>>12052916
yes,
$ \int^0_{-\infty} + \int_0^{\infty} = \int^{\infty}_{-\infty} $
should always hold if there are no singularities in the integrand at 0

Anonymous

Anonymous Thu 27 Aug 2020 01:50:33 No.12052948 Report

Quoted By: >>12053019 >>12053027

>>12052932
holy shit mate, you are actually retarded
how exactly to you plan to integrate f(x)? you don't know what that function is

read more examples

Math notation confusion

Math notation confusion Thu 27 Aug 2020 02:20:37 No.12053019 Report

Quoted By:

>>12052948
I wasn't planning on integrating the lefthand side you fucking dolt.

Math notation confusion

Math notation confusion Thu 27 Aug 2020 02:21:49 No.12053027 Report

Quoted By:

>>12052948
Anyone who says "mate" is a literal cum guzzling faggot. So your opinion literally doesn't matter. You are a negative nancy too, calling someone who is a biologist in an applied PDE class a retard. Go fuck a Kangaroo or whatever you Aussie fags do in your free time in the Outback.

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