Proof of the Convolution Theorem

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Proof of the Convolution Theorem,
The Laplace Transform of a convolution is the product of the Laplace Transforms, changing order of the double integral, proving the convolution theorem,

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this guy is a genius.we spent more than two weeks in lectures studying laplaces but i couldnt understand anything...the moment i watched videos from this guy hahahaha i bet im now a genius..lol...thanks lots

munashekaks

please do more differential equations. I took that class and learned a lot in a small amount of time, and now its all gone. we spent like two weeks on all of laplace, convolution, dirac's delta function, and a whole lot of stuff that required much more than two weeks to get into.

gerardogutierrez

Man, what a huge video... Great work! But I found it a lot simpler going "backwards", using the subtitution theorem for multivariable integration and changing the integrating region from (R+)^2 to {(x, y) | 0<x and 0<y<x} using the transform f(x, y)=(x+y, y) with inverse g(t, v)=(t-v, v). Everything simplifies inmidiatly and the jacobian of f is 1.

HeraldoS

convolution is the worst notation ever, change my mind. as someone who is almost always typing math, * meaning multiplication should be standard, its been this way since like prealgebra, so this is like changing the meaning of + to be subtraction to me. this notation is the biggest middle finger for anyone who types math all the time and honestly i came up with a better notation for that, f(t)*_{(a, b)}g(t)=∫_a^b f(u)g(t-u)du.

aneeshsrinivas

Thank you! You've explained this so clearly.

oybekkhakimjanov

I have been trying to prove this theorem myself for about a month now because I could honestly not find proof anywhere and just seeing this video in my recommended made me smile so widely I already smashed that subscribe button. I'll be watching your videos from now on my dude. :D

novanecros

I found it, Convolution, Thank you... you are a blessing

nomvuseleloh

2:55 the function graph looks like end brace you draw (using Laplace transform you should put input in braces)

P.s. yea my English is very bad

JordHaj

Are you going to explain the deconvolution too?

edwardalexis

Such an elegant proof of Convolution theorem using the unit step function.✨️

AakashSingh-ewkz

you can actually do u=t-v, du=dt after changing variables, and the integral will work very nicely without any unit step functions.

randomguy-gi

11:03 Not all those functions are continuos in the interval. Namely the u(v-t) function is not. Which makes the whole thing not continuous at v=t. But I get it what you mean. The u function is not continuous, but can be integrated in that period

Alkis

1:25 did my man just say Calculus 3? How the fuck is the american system so slow? Everything he has ever said is "Calculus 2" is taught in calc 1 or before here

Eknoma

Around 15.00, I'm confused because there were two e functions... and they merged into one function? The Laplace definition gives e^-vs(F(s)), so when you replace it back into the integral, wouldn't it give e^-s(t+v)?? Great videos! I love them and they've been so helpful for me!

morganrogers

I cannot follow what he is doing. Will have to look at this video more than once. HE knows what he is doing, but I do not.

calvinjackson

when u introduce at start u(tau-t) t acts as constant (t=a )
at start but at end in u(t-tau) you choose tau as constant (tau=a) and t as variable, please explain this ambiguity ???

UETLHRCED

Wow. Genius. Keep producing content like this

MuhammadWaleed-fn

I don't know why, but this is still easier than algebra

ehmchris

Wait... what happened to the e^(-st) (right after the "note")?

simdriver

I'm a little confused here at 6:33. Isn't u(3-v) the mirror over the vertical axis of u(v-3)?

TawpeeBoyshuck

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