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

[@zuccx99]

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

[@neilgerace355]

He's just there to repair her fridge ... That kind of thing?

[@zuccx99]

@@neilgerace355 Yeah.

[@rot6015]

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

[@paolofernandofloresrivera6244]

WOOOOW YOU HAVE NO IDEA HOW HELPFUL IS THIS TO ME

[@PapaFlammy69]

:)

[@orangeguy5463]

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.

[@abdullahm4830]

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

[@chandankar5032]

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

[@duggydo]

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

[@david-yt4oo]

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

[@david-yt4oo]

2:14 close call

[@KidNamedVashin]

Thanks, intro played while I was in calc 2

[@ronanglemusic1993]

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

[@herlanggaizul6965]

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

[@simon_vezina]

We want to know!!!

[@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?

[@akirakato1293]

@@PapaFlammy69 lambert function and linear algebra meshed together please

[@yodaadoy2863]

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

[@The_Professor_S_]

It looks like KZbin’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?

[@wahyuhidayat7042]

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

[@juanignaciodiaz28]

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

[@alexismiller2349]

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?

[@sergiokorochinsky49]

yes, but then you have and infinite sum of alternating sign... inf-inf+inf-inf+... He is far far away from solving the problem. Actually, aproximating the function with a Taylor series around zero, and then integrating the aproximation all the way to infinity, is a really bad idea.

[@alexismiller2349]

@@sergiokorochinsky49 Thank you so much, I understand what he was going for. I have never hitherto seen a sum of infinite alternating numbers

[@eashanshenai4980]

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

[@DendrocnideMoroides]

how would it be dividing by zero in the denominator??

[@danrain12345]

You know what’s funny is that I literally just did this exact thing the other day just for the hell of it

[@Ryan_Perrin]

This was one good boi

[@somewhatblankpaper1423]

4:05 Nani? You just assumed my gender REEEEEEEEEEEEEEEEEEE!! 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.

[@atrimandal4324]

Normie👏Meme👏

[@frozenmoon998]

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

[@neilgerace355]

4:50 can you please explain what the problem is, or link to one of your several videos? I have a mental blank.

[@ElDiarioLudita]

U got that flammy

[@martinzone8153]

Guys, can u recommend a channel a level bellow this one. I'm familiar with and relatively good in calculus I, II and III (casual time killing use), this german dude is funny but is hard to follow his thoughts. Where should I start, some introductory course in linear algebra?

[@Gustavo_0107]

U should make ur videos wearing an ahegao hoodie

[@schokoladenjunge1]

Would be less pornographic than the intro

[@connorshea9085]

Go to jail

[@okoyoso]

Does flammable come from fellow mathematicians?

[@The1RandomFool]

Who else replayed the first 5 seconds of the video repeatedly?

[@PapaFlammy69]

:D

[@somewhatblankpaper1423]

Should I buy Euler's formula V2 or Euleroid (I have a limited budget cauz I'm broke)? Both look fucking op and memeful. Bruh, I'd suggest you to design a t-shirt (or shirt) in which you blend hentai (or anime meme) and math. I feel like that's going to be a revolutionary product. Regardless, should I get Euler's formula V2 or Euleroid?

[@somewhatblankpaper1423]

@@PapaFlammy69 Actually, I've decided to buy Euleroid because it seems like a more unique and original meme from your channel. Btw, I've introduced 2 of my friends from the math department to your channel and they insta-liked it and they also plan to get some merch (they are richer than me).

[@Mystery_Biscuits]

Integral of e^2x * tan(x) dx ?

[@Mystery_Biscuits]

Damn I don’t even remember writing this. Pre-covid comments hit different ngl

[@hoodedR]

Can you pls make a vid on that result you used (involving the erf..I think bprp made a vid on it but not that specific integral)

[@sergiokorochinsky49]

72 comments and only one person noticed the problem of evaluating the polynomial at infinity... hmmmm...

[@oni8337]

you mean at 8:10?? yeah i was wondering why he said tau has an infinite radius of convergence because you would have to plug in inf on tau as the upper bound

[@amirb715]

mmmm....why don't you just use Leibnitz rule and calculate the Taylor series of that function of (s/2) directly term by term? I mean, if you let f(s) = \int_{s/2}^\infty \exp(-\tau^2) , then you should be able to directly calculate the Taylor series of f(s) by calculating f'(s=0), f''(s=0), f'''(s=0),etc...using the leibnitz rule. As a start f'(s=0)=-1/2, ....

[@mrandersonpw53]

Papa Flammy prerequisites: complex analysis, at least Bprp prerequisites: breath, at most

[@dr.merlot1532]

Flamm, do you know what the solution to Poisson equation is with density "right hand side " a gaussian? Ans: It's you boi Error function. en.wikipedia.org/wiki/Poisson%27s_equation

[@tifnatandmat]

Yass Papa

[@leafbaguette]

I believe your final result was in error

[@Assault_Butter_Knife]

Never call me a flammer ever again

[@emperorpingusmathchannel5365]

Yo gib shoutout pls

[@pappaflammyboi5799]

Well let's be super mathematically accurate here, Pi and e don't have closed forms either...

[@pappaflammyboi5799]

Unless I didn't catch the sarcasm, in which case I just flammable flamed myself...

[@FGj-xj7rd]

Laplace? The triangle squared boi?

[@davidsonjoseph8991]

Laplacian*

[@FGj-xj7rd]

Nah, for us normies is a "triangle squared".

[@FGj-xj7rd]

@@PapaFlammy69 Ay, I am proud normie ☺

[@davidsonjoseph8991]

Spicy normies, I bestow upon you delta, Δ²

[@Broody90]

Intähgaral

[@harrygreen9804]

Erf(X) is the hottest sigmoid

[@harrygreen9804]

Mfw sign(x)=(Erf(x))^n lim n -> infinity

[@AlterRektMLG]

Le

[@charliesuarez1033]

Those fat sigmas look thicc

[@sahilbaori9052]

mfw adds