Solving the Gaussian Integral the cool way

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Күн бұрын

Check out MAPLE LEARN ►www.maplesoft.com/products/le.... Try out the limited trial version of Maple Learn
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My video on the "normal" way to solve the Gaussian Integral using a double integral in polar coordinates ► • The Gaussian Integral ...
In this video we're going to see a different trick to be able to solve the Gaussian Integral utilizing Feynman's trick of introducing a parameter.
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Пікірлер: 72

@bryangough6424 Жыл бұрын

Hello Dr. Trefor! I am an undergraduate student who loves your videos a lot. I have been struggling in my current major and really not felt confident in my studies. I think your videos have helped convince me that my passion lies in mathematics instead of the subjects I have pursued so far. Thank you so much for your content!

@DrTrefor Жыл бұрын

That's so kind of you to say, good luck!

@grahaml6072 Жыл бұрын

Wish I had KZfaq and channels like this when I was an undergraduate student. Unfortunately that was 30 years ago.

@ShanBojack Жыл бұрын

man i have a similar story

@agutilinus2828 11 ай бұрын

@@DrTreforhi

@fordtimelord8673 11 ай бұрын

@@grahaml6072 Same here. These KZfaq professors that share their knowledge, intuition and joy of a subject or problem are an incalculable blessing to mankind.

@212ntruesdale Жыл бұрын

Who in the world is brilliant enough to come up with this?! I feel really smart just being able to understand what’s happening! There’s clever, and then there’s CLEVER. Know your station!

@DrTrefor Жыл бұрын

so clever!

@caryfitz Жыл бұрын

I really liked this. Feynman's technique has always been obscure to me. Your description was revelatory! Thank you very much!

@DrTrefor Жыл бұрын

Thank you! Isn't it cool?

@ajb16384 4 ай бұрын

I have an extreme love for math and I just discovered this channel. This is an absolute goldmine. Thank you Dr. Trefor

@Valori_4 9 ай бұрын

Hello! I'm currently 12 year's old studying in 6th grade but I'm a very curious person in learning mathematics and physics so I chose you to teach to solve this infamous Gaussian Integral Hope when I get older I'll find a new invention like any other scientist's ❤ Thanks to you for your video's You got a new sub❤

@ryemiranda6800 9 ай бұрын

Same im 13 and in algebra 1

@Valori_4 9 ай бұрын

@@ryemiranda6800❤

@kasg8427 Ай бұрын

I am 9 year old

@slavinojunepri7648 11 ай бұрын

Wonderful proof. Thanks for sharing.

@johnchessant3012 Жыл бұрын

Wow, up until today I only knew the polar coordinates way of solving the Gaussian integral!

@umairbutt1355 7 ай бұрын

This was my first proof of the gaussian that I came across and it blew my mind (I didn't study multi-variate calculus yet). Does anyone know the original author of this proof?

@monke9865 Жыл бұрын

Interestingly there is another way to compute this integral using single variable calculus, with strong geometric flavor. Consider F(r)= int _{x^2+y^2

@AssemblyWizard Жыл бұрын

This is multivariable..

@user-cg7gd5pw5b 3 ай бұрын

Thanks, I've done multiple exercises where they give the developed derivative and you have to climb back to the Gaussian integral, and was always wondering how people found this kind of expressions in the first place.

@aweebthatlovesmath4220 Жыл бұрын

Nice video! it's always good to solve a problem in more then two ways. i mean all and all it's not the answers that make math interesting it's the way we do math!

@DrTrefor Жыл бұрын

Absolutely, and we often get stuck only knowing the "normal" way things are done

@marylinebentzinger7378 Жыл бұрын

Can somebody explain why we introduced y and why when we introduced the new variable y, we set the top border to one?

@DrTrefor Жыл бұрын

It's just a change of variables y=x/t. Specifically when x=t for the upper bound, in the new variable y=t/t=1. The point of this change of variables was to get the parameter t out of the limits of integration and into the integrand.

@marylinebentzinger7378 Жыл бұрын

@@DrTrefor thank you so much, it seems so easy right now, you must have a gift for maths

@monsterhunter8595 Жыл бұрын

Nice

@MurshidIslam Жыл бұрын

Shouldn't it be −arctan 1 + arctan 0 + C at 7:26?

@balubaluhehe2002 Жыл бұрын

It should've been, because there was a negative sign at the front, but -0 or +0 didn't change the final result at all.

@DrTrefor Жыл бұрын

Oops, good catch. Yes irrelevant for the end result:)

@josafajunior5425 Жыл бұрын

7:25 That signal it's wrong? Don't changed because is zero, but should be +arctan(0)?

@EdoardoDAurelio Жыл бұрын

That Englishal it's wrong too lol

@foysalsahriar5608 11 ай бұрын

Hi, Really nice video! I was wondering if I can help you edit your videos and also make highly engaging shorts out of them.

@tg0406 4 ай бұрын

I remember solving this using power series and differential equations

@alebaldus9229 Жыл бұрын

Grazie.

@DrTrefor Жыл бұрын

Thank you so much!

@airman122469 Жыл бұрын

Before the video started: “Feynman technique?” Video starts: Feynman technique.

@user-rq6gd8yy2t Жыл бұрын

What A WAY😮😮😮😮

@strikerstone 8 ай бұрын

Really fun if you understand imo

@andrewharrison8436 Жыл бұрын

50 years ago I felt that integration was a black art. If anything videos like this confirm it. Love the way that the annoying C that crops up in any integration turns out to be the part that carries the result from the doable integral to the unknown one. I will probably watch this again to see exactly when you hid the rabbit in the top hat.

@DrTrefor Жыл бұрын

Ha ya it really is tbh, so many cool tricks to learn

@samtux762 2 ай бұрын

Neat approach. But I wouldn't dare to repeat it and would go for the classic switch to polar coordinates. But, I am not in math (was in chemistry), so this isnot my field.

@samtux762 2 ай бұрын

Integrals arenot my jam and are not a part of my work. But I added your channel to my watch list. This "I will just use Feinman approach and square" came out of the blue. Brain massaging. Love it.

@ahmedyacine5661 Жыл бұрын

This guy here is so nice

@sandorszabo2470 Жыл бұрын

Tricky solution! However it is not the "Feynman's trick". This method was known earlier. Only Feynman was the person who used a lot to simplify the calculation of many complicated integral.

@MooImABunny Жыл бұрын

Gozeean integral. Hey look, it's Dr. Chreethaw, he's gonna us Mothimautecs

@joelchristophr3741 9 ай бұрын

Sir i dont understand one thing .. that is how did you assume that f(t) is a square of that integral initially?????

@umairbutt1355 7 ай бұрын

It's not an assumption. It's a definition for f(t). Now, the question of WHY such a function f(t) was defined in order to get to the gaussian is the really interesting question 😅😅

@joelchristophr3741 7 ай бұрын

yeah... i understood.. thankyou :) @@umairbutt1355

@egor.okhterov Жыл бұрын

Why?

@Sciensistbikon 9 күн бұрын

Feynman integral !?

@user-xo5th3cm5k 2 ай бұрын

11 12 22 4..

@ViralShorts_2323 Жыл бұрын

What is the need of taking partial derivatives?

@DrTrefor Жыл бұрын

It's just a partial because the integrand is a function of both x and t

@ViralShorts_2323 Жыл бұрын

@@DrTrefor Dear Sir, don't we concern with 't' only?

@gnarlybonesful Жыл бұрын

disappointed you didn't prove the limit was 0 and instead justified it by looking at a graph!

@mariostelzner4530 Жыл бұрын

WHY BUST YOUR BRAIN TRYING TO REFIGURE OUT SOMETHING THAT'S ALREADY BEEN SOLVED. AHAHAHA AHAHAHA LOL

@Ben-rd3mg 3 ай бұрын

Such an evil way to solve it

@avinashyadav8314 Жыл бұрын

No offence but Polar coordinates were much better 🫠

@DrTrefor Жыл бұрын

ha, I like both!

@billcook4768 Жыл бұрын

No, no, no. In order to truly be “cool”, you have to use Taylor series. It’s like a law or something. Then again, for the life of me I don’t see a Taylor expansion so maybe there is no official cool method :)

@DrTrefor Жыл бұрын

Taylor series is all good, but the question becomes for definite integrals what does that series sum to? We might get that it converges but harder to know in general if there is a nice answer for the sum

@grahaml6072 Жыл бұрын

1st

@monsterhunter8595 Жыл бұрын

Haha

@grahaml6072 Жыл бұрын

@@monsterhunter8595 I don’t know why people do that and post they first but this just happened to be the only time I have ever been first so I thought what hell I will look like an idiot like all the others 😀

@DrTrefor Жыл бұрын

ha, nice one!

@diezelvh4133 6 ай бұрын

So, if you're technically first, is every other comment under your first comment first also? ...