What is the derivative of this function

>>8382449
boner distribution

Isn't that the Dirac Delta function? If it is, than it's 1.

>>8382449
Heaviside function is the integral....

>>8382452
>>8382461
Undergrads spotted.

Zero everywhere except at the origin where it is not differentiable

>>8382449
[eqn]\delta'(x) = i \int t \exp(i t x) \mathrm{d} t[/math]

>>8382449
[math]\delta'[/math]

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>>8382493
>[eqn] [/math]

>>8382449
"""""""function"""""""

>↑
What did he mean by this?

>>8382503
just integrate my shit up f.a.m.

>>8382452
I hope you're trolling anon

>>8382500
>"""""""function"""""""
rofl its a function you moron.

>>8382500
https://en.wikipedia.org/wiki/Dirac_delta_function

>>8382449
[math] /delta' [/math] is the linear map on the space of differentiable functions given by
[math] \delta'(f)=-f'(0)[/math]

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>Dirac Delta "function"

that's not a function

>>8382670
>From a purely mathematical viewpoint, the Dirac delta is not strictly a function, because any extended-real function that is equal to zero everywhere but a single point must have total integral zero

>>8382723
But what's wrong with that? f(x)=0 is a function with an integral of 0

>>8382727
The Dirac distribution doesn't have a null integral ya git

>>8382723
>Integral of zero means it's not a function

Shut the fuck up

>>8382449

3

>>8382449
https://en.m.wikipedia.org/wiki/Unit_doublet

It's called the unit doublet, and like the Dirac delta, it's not a proper function but a distribution. Intuitively it's like the point-dipole in physics.

>>8382732
>he doesn't know the integral is 1
wew

>>8382730
>The Dirac distribution doesn't have a null integral ya git
? the picture of the OP shows a function thats 1 at 0 and 0 everywhere else.
its not the dirac distribution

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>Unit_doublet

>>8382742
The delta function is commonly represented as an arrow, where the arrow's height is equal to the value of the integral (in this case 1).

>>8382742
That would be the Kronecker Delta as used in signal processing :^)

>>8382742
>? the picture of the OP shows a function thats 1 at 0 and 0 everywhere else.
How is freshman year?

I was in a workshop where we were learning about the Dirac Delta and one of the postgrad assistants kept insisting to me that its value was 1 at the origin.

>>8382770
It's 1/p where p is the width of the function, the area is 1

>>8382750
>How is freshman year?
do you think the image shows the delta function?

>What is the derivative of this function

The distribution that makes the product rule under the integral true.

>>8382723
This.

Goodman, Introduction to Fourier optics 3rd edition bitch

bitch

why does nobody here /ref/

>>8382791
It is the common representation for it, yes.

>>8382798
>giving reference for basic math
wew

>>8382816
bitch i could reference everything I post. information is useless unless you can verify it.

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>>8382828
>referring a fucking physics book for distribution theory

>>8382449
ZIPPY ZAP THAT AINT CRAP

>>8382811
>It is the common representation for it, yes.
no? show me 3 textbooks using that representation!

>>8382863
Not that guy but how else would you represent it

any other representation would have width which is unacceptable.

>>8382863
why would I do that?

>>8382863
are you one of those "muh rect function limit" fags

>>8382865
>how else would you represent it
suggestive: as a line at 0 heading towards infinity.
for the purists: not at all.

>>8382889
>for the purists: not at all.
but purists understand that all functional representations are just as conventional you dip

>>8382685
>"From a purely mathematical viewpoint, the Dirac delta is not strictly a function,"

The limit at 0 is clearly 0, but the value obviously is not. Even if it were a function, or if we stretched what we meant by "function," it wouldn't be continunous, and thus wouldn't be differentiable. Asking for this """"function""""'s derivative makes absolutely [math]0[/math] sense.

>>8382735
THANK YOU

Now how about the second derivative? Just a function [math]u_2(t)[/math] s.t. [math](x * u_2)(t) = \dfrac{\text{d}^2x}{\text{d}t^2}[/math]? How would such a function behave around zero? Is there a general way of telling how all derivatives of the Dirac delta function behave around zero?