Proof of the Convolution Theorem :: Laplace Transforms

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Here we prove the Convolution Theorem using some basic techniques from multiple integrals.

We first reverse the order of integration, then do a u-substitution. These two techniques should be very familiar from multivariable calculus.

I hope seeing the proof of the convolution theorem helps you gain greater understanding of the idea behind why it works!

It's super easy to use and now you know why it works!

Post any questions you have below and I'll try to answer the best I can!

Thanks for watching! -j Dub
  1. Jonathan Walters
  2. Proof of the Convolution Theorem
  3. Convolution Theorem
  4. Laplace Transforms
  5. Laplace Convolution
  6. Convolution Laplace
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Комментарии
Автор

The exact proof was asked in our exam today, could do it just because of you, thank you

dikshaarora
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This is very nice, you have explained it better than my professor. Thank you! 👍

martinxiang
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anyone else looks at the sum of independent random variables differently?

MACC-gkui
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So simple and concise. Thanks for making this video.

BlueEdgeTechno
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Thanks for this simplified explanation

Error-tblu
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on 1:48 could you please explain how could we just simply take exp(-st) in the integral and f(r) out from the integral? Is it because since we switched integral order which makes these two functions to constants so we can just move in and out in the integral?

tuntapatsirikup
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Tq sir but how to use this theorem at any questions..plz help me sir...🙏🙏

divyadubey
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Great job man. Very much Appreciated from India ❤️

SayandeepBMSCE