Laplace Transform: Gaussian Bell Curve ℒ{e^(-t^2)} - The [ Complementary ] Error Function

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Today we are going to explore yet another laplace transform! We are going to end up with a non-elemntary analytical function by using 2 methods: Inspection and Taylor Series Expansion. Enjoy! =)

[zuccx]

Switched to porn because the intro was easier to explain to my parents.

[rot]

This video contains:
- autism (50%)
- actual maths (40%)
- memes, asmr and youtube poop (10%)
Gotta love papa❤

[orangeguy]

you can accomplish the same result using feynman integration ;)

You get F'(s) related to F(s) when you expand the integral using integration by parts. Then you're left with a first order linear differential equation which is solvable to exactly what you got.

[paolofernandofloresrivera]

WOOOOW YOU HAVE NO IDEA HOW HELPFUL IS THIS TO ME

[chandankar]

As long as the radius of convergence is 'infinute' I dont think 's' has no restrictions.

[The_Professor_S_]

It looks like YouTube’s notification system is taking a lesson from the error function, because I still haven’t gotten a notification. Maybe it forgot to apply the Laplace Transform?

[david-ytoo]

1:49 now I might ask myself what methods you use to factor because that's not a minus sign

[thelightningwave]

Let's now mesh two hard things from college based mathematics, which are The Laplace transform and the Gaussian integral into one. So, Papa Flammy are the next 2 topics to be meshed for a video going to be curvature with complex analysis?

[ronanglemusic]

2:30 wait what? I didn’t know this was an advanced class. That’s tough pre knowledge

[juanignaciodiaz]

Instead of having the limit as τ approaches infinity you could rewrite the last integral as from 0 to inf minus from 0 to s/2 that way you get a nicer expression

[abdullahm]

😂

I don't know if I like more the hilarious part of you or your brilliant explanations

[herlanggaizul]

Hey, what's the name of soundtrack your opening video papa ?

[KidNamedVashin]

Thanks, intro played while I was in calc 2

[alexismiller]

Hey look I'm really tired and i'm nearly postmortem. Can somebody pls explain to me why the integral of the polynomial at 7:54 isn't just equal to infinity?

[eashanshenai]

8:33 I don't think s can be negative one because then you would be dividing by zero in the denominator

[duggydo]

Flammable Maths every time the Notification Bell sounds, my Curve Transformers into La Place.

[wahyuhidayat]

Papa is back...I like to watch your video.

[yodaadoy]

Ooo nothing like math to finish a good day strong! Thanks papa <3

[frozenmoon]

Dirty, papa! I mean, you do realize that only a girl could feel affection for 7 seconds of such an intro.

[somewhatblankpaper]

4:05 Nani? You just assumed my gender


Joke aside, that was a lovely and spicy transform; however, I've only understood 50% of the steps because I need more Math training and omega-3 shakes to get my brain shredded and swoll to fully grasp your steps.