How To Integrate The Gaussian Function | HBD Gauss!

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Today is Carl Gauss's 241st birthday. What better way to honor him than to integrate the hell out of the function named after him?
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I just noticed a mistake at 11:16. dx' does not equal dx. dx' = dx/ root b! Sorry about that. So it should be multipled by root b times dx'.

AndrewDotsonvideos
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Fun fact, the Fourier transform of a Gaussian is another Gaussian.

mrnarason
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I came upon this while studying variational approximation. Spent an entire hour integrating it with all the basic calculus I knew. Still got nothing. Had a mental breakdown and then fetched up my old friend from undergrad class at 12am. Ended up giving him brain attacks. Poor man is dying. I have to give him the link to this video. You save lives Andrew. Thank you so much❤️🎉.
Edit: Yes. More math videos please!!!🙏.

addas
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Thank you for posting this, and going through all the algebra so slowly, and step by step. It's the best explanation I've seen so far, I finally get it now.

wolfumz
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Probably one of my favorite videos so far.

semiawesomatic
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When I learn this in school I get bored
But when I find this on Youtube I find it really interesting
how strange

Triadii
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Dude you're so calm in your vídeos it makes me calm, while also learning stuff I find very nice and interesting but don't even need (I study chemical engineering). Anyway, I just discovered this channel and love it. Keep up the amazing work!

MarcoACto
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I myself am in the last year of my high school and I love physics and maths outside the school curriculum and this is probably the best it can get! Love your math and physics videos and keep making more good content Andrew 👍🏻👍🏻

anshchawla
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loved it thank you for taking time out and making these vids. would love to see more math videos

porit
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Really fun! Thanks :) I hope you do more similar math related videos.

Abdullah-emjk
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"Everyone's favourite integral to look up" so true lol 😂

rhosymedra
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I'm in high school and got to know about this Gaussian integral randomly. I surfed through the Internet for the derivation or evaluation but couldn't understand. But After watching your video it's all clear.
Thanks & Keep Uploading.

nobisphysics
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Would it not have been easier to use a gamma function here? To simplify the exponential power issue?
It’s a nice channel you have here though Andrew and I love seeing a physics major discussing rigorous math methods. Keep it up!

utsabdas
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Amazing video! Hoping to see more math related videos in the (near) future :)

gillcallens
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Great work, it was so joyous to learn this incredible beauty👍

sanashabbir
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Just discovered Papa Flammy the other week and now I can get my fix from this channel too!

suhailmall
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I send thanks from Griffiths Intro to Quantum Mechanics 3e problem 1.3

kohenwilliams
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Awww I was looking forward to you integrating the complex probability distribution Gaussian from the Uncertainty Principle's defined momentum spectrum to show us the quantum interference pattern of a particle or a set of particles using their mean value:)

randymartin
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I love how you spun around to represent 2pi.

GabeDT
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Wow..very nice explanation..I would love to see more videos like this ;)

christophebrou