I love how the video makes you feel smart by hinting at where it’s going so that you figure a lot of it out on your own.

@NazriB

2 жыл бұрын

Lies again? Dark X

@spiderjerusalem4009

10 ай бұрын

yea, pretty much most math books. "as the readers should verify", "it is indeed trivial and shall be left as an exercise to the readers", "the argument will be outlined in exercise (insert number)"

"Might ring a bell"... I see what you did there

@wiseversa5369

4 жыл бұрын

hehehehehehe

@newwaveinfantry8362

4 жыл бұрын

*Laughs in Bell curve*

Dude integrated so hard that his voice changed at 9:35

@newwaveinfantry8362

4 жыл бұрын

"I talked to Barzini."

No word for this great video. Spectacular.

@David_F97

4 жыл бұрын

According to you, there are actually 7 words.

@jadeblades

2 жыл бұрын

@@David_F97 ok

@DiegoMantilla

Жыл бұрын

But you said no word.

@BurningShipFractal

10 ай бұрын

That 7 words doesn’t include

You have transformed the integral into polar coordinates. This is a classic example of how sometimes complex cartesian coordinate integrals can be simplified in polar coordinates.

@rohitjain1455

4 жыл бұрын

Do also read about cylindrical coordinate system

@williamswang7052

4 жыл бұрын

@Kappa Chino laughs in confocal eliptical coordinates.

@chaahatsingh6733

2 жыл бұрын

Hey can you please explain why was the height taken as the function itself ( -e power R2 squared) m

@danipent3550

2 жыл бұрын

One integral is used for area, two for volume, what’s the use of triple integral?

@sample8289

2 жыл бұрын

@@danipent3550 density

I am blown away by the way you simplified it. Pure awesomeness.

@slender1892

2 жыл бұрын

I mean he didnt invent anything its in every calc textbook about integral calculus right

@petachad8463

5 ай бұрын

@@slender1892 stfu bit*h , you probably scored 0 in maths 😂😂

That is stunningly beautiful. One of the best mathematical explanations I’ve ever seen. Well done, sir

This is easily the best video explaining the Gaussian Integral I have ever seen!

I saw Professor Christine Briner from MIT used polar coordinates, double integrals and change of variables to evaluate the Gaussian integral. Now, I see you find the volume under the bell curve by summing tubes(hollow cylinders) whose radii varies from 0 to infinity. I like the geometrical approach to finding the volume of each tube. I find the visual aids intuitive. I think this is a fresh and intuitive way of evaluating the Gaussian integral. Thanks.

This is no random math as your channel name suggests. The geometrical proof is always the most elegant way. I can't skip ads for you. Great content!

thx a lot man. finally a good explanation

@laser4887

6 жыл бұрын

no kidding this is probably the best explaination i found on youtube

Probably the best video on KZread explaining this problem. Thank you!

I have watched a number of clips on the Gaussian Integral, but I like the practical way this has been explained.

THIS IS BEAUTIFUL! This is the best video I’ve seen that talks about this integral.

i find this is the best way to understand what's going on and what is the concept of doing such things with this problem. thanks for making this video.

Thank you for providing with detailed explanation not just formulas, great job!

The best intuitive and clear video ive seen on this topic!

This video randomly popped up on my feed and I am glad that it did. Have been out of touch of mathematics for about 8 years. Brought back a lot of memories.

Very easy-to-digest explanation of a very complex topic. Excellent video!

One of the best explanations I've ever seen...well done!

Beautiful! Congratulations for such a wonderful video and demonstration.

Really great video! Thank you so much for this, I had a really hard time understanding how to integrate wave functions that included this exact integral. Thank you so much!!

An extremely well done video for an extremely beautiful integral.

Just spectacular! Well explained and visualized. Speechless

Came back to this video after taking calc 3 and seeing you explaining the gaussian integral without getting into jacobians and double integral mess is absolutely stunning

This video is AWESOME! I think they skipped this in all my calc classes in college. He makes it so intuitive. I'll def be coming back to this channel

Fantastic video. Kept me entertained with great explanation and graphical representation.

Best explanation I've seen for this integral. Well done sir.

One of my math teachers at university showed this exact method when I studied Applied Mathematics (which was basically "math used for all kinds of real-life things", so it was like a big test of all the students' previous knowledge in other courses), and I was blown away by it.

Absolutely brilliant.... never seen such an explanation. Thanks a lot.

Sehr raffinierte Transformation, die das Problem entscheidend vereinfacht. Das könnte man sogar in einem motivierten Leistungskurs bringen! Super!

This is so beautiful. Amazing explanation, thank you

Simply elegant and brilliant!

I am stunned and amazed with your explanation

OMFG, I hope i could get that video when I started to learn Calculus ... Special Functions(Non-elemental) were such a pain for and after all I just used abstract rules to get them, but omg this interpretation of Gaussian Integral is awesome...

this channel is like sent from god, great video! you deserve a lot more!

Bravo! Best explanation of this integral ever!!!

So in the integral of `e^(-x²)` the simple lack of `·x` is what makes it (almost) impossible to solve? And the whole idea of translating the problem to polar coordinates it what helps to bring that `·x` (or `·r` in this case) back?

@NoobLord98

6 жыл бұрын

Exactly, by multiplying it with itself, but with a different variable, you can turn it into this integral over the entire plane of the function f(x,y) = exp(-x^2-y^2). It is then indeed a smart idea to do a coordinate transform to polar coordinates, doing this transformation then changes the shape and infinitesmal area of the d-bit (no clue what it's called, the dx dy) by an amount according to the jacobian of the transformation (look it up, it's the determinant of a transformation matrix and can be used for any set of coordinates you'd want), this jacobian just happens to be r for polar coordinates, which then makes the entire integral evaluable.

@AuroraNora3

5 жыл бұрын

@@NoobLord98 Alternatively, think of dxdy=dA, a tiny area in the xy-plane caused by changes in x and y. In polar coordinates, a change in r and θ will cause a tiny area of approximately rdθdr which will be equal to dA=dxdy in the limit as they become smaller and smaller. So dxdy=rdθdr

A neat solution with a remarkable result...and with profound real world applications.

Finally i can understand this without polar things. Thank Youuuu. Very Logical and easy to understand. Big much thanks

My first time in your channel. You describe well everything, so I have to subscribe.

Very Good explanation ! Keep sharing such valuable content !

First time I understood this integral. Incredible video

1:25 "might ring a bell" nice pun haha

Thank you. You just earned a subscriber. Looking for more such great content.

I'll just echo what others have typed; this is probably the best explanation on math I've ever had.

Perfect explanation. Big thanks from Germany 👌👌

I am not good at English but this video is one of greatest explanation videos I have ever seen. Thank you very much

Excellent! A very clear explanation, thank you!

Fantastic explanation of a somewhat abstract idea!

Super explanation, this should have more likes and views.

Oh dammit. This is exactly what i needed to answer a question on a paper that was due to 2 days ago. Glad that I understand it now, even if its a little late. Good video!

This is so beautiful and awesome

Hey, thanks for the video, this was an incredibly well-worded demonstration. Can you by any chance tell me what program you used to graph the 3d graph? That would come in pretty handy

@garbanzo2687

4 жыл бұрын

I think it is too late, but i believe he used Maxima

@samuelkitson6946

2 жыл бұрын

looks like MATLAB

This is a great video.... very understandable. A lot of videos go through what to do, but this really helped to visualize it. Thanks, and great job!

very nice video, i like how you explain things, its like how my mind process things exactly thank you

I have watched a lot of videos , but understood nothing. But you explained it perfectly!!

Wow! Great illustration!

You put a lot of effort to make this video!! A great work done!!!!!!!!!!

Brilliant video. Loved it

I didn't see any error function video on youtube which depicts closer picture of the phenomenon than yours. It is the best one the approaching perfection asymptote.

I have seen a couple of videos where this integral is solved by substituting x^2 + y^2 = r^2 and letting dy dx = r dr d(theta) and another one where instead of polar coordinates stuff it goes by substitution y = xt. This is the first time I have seen a visual approach and it's really really good... Much appreciated :slightly_smiling_face:

this is a very great video that helped me understand the gaussian integral and I hereby recommend it to everyone

I love this video and the way you explain

Truly brilliant and magnificent

Can you tell me how you made this video on a white background and what software, editing apps you used

How fun was that! Thanks!

Nice! But one thing, how and why is related de Area of the curve with the volume?

Very nicely done! Thank you!

I always knew to do this by converting to polar form integrating from 0 to 2pi and then 0 to infinity, but this explains where the extra r comes from very well! thank you so much

@MuitaMerdaAoVivo

5 жыл бұрын

In a more mathematical way, the 2pi*r is the jacobian of the substitution and you can calculate it solving the determinant of the jacobian matrix.

Doing this is calc 3 was so amazing for me to see

Such a wonderful integral 👍

Amazing visualization!!!

Thank you so much! This is beautiful!

This is such a good explanation btw

Great teacher! Thank you very much. Keep making maths videos...

Your drawings are absolute **** but they are really doing its job and your explanation is absolutely ace! Really a brilliant video and I am actually here to praise your work, not diss it, because it is simply brilliant! (In case it failed to show, I am actually just making a joke while my real goal is to praise this video. The drawings are crude but they are very successful in conveying the message and your explanation is on 3b1b level in terms of teaching and being understood.)

Amazing, now I know the proof of error function very clearly

Simple and elegant.

Pretty clever way to solve!

pff i love how you just turned one integral into the same integral+another

โอ้วพระเจ้าจ้อดดดด คุณเป็นคนไทยรึนี่ นั่งดูจนจบ สำเนียงโครตเทพ วิชาการ เทพสัด สุดๆครับ ดีใจ กับ อนาคตของชาติจริงๆ

It’s easier too. If you know the gaussian formula, you can moltiplicate and divide that expression for sqrt(2*π*1/2), and drag out the numerator from integral. Now the integral represents the area of a gaussian with mean=0 and variance=1/2 that’s equal 1 and the amount out of integral is sqrt(2*π*1/2), that’s actually sqrt(π). Great video anyway

Beautiful!

This is a great video! Thank you so much!

That video make me remember my first year in college when we were studying electrostatic and electromagnetism 😊😊

@vincentdublin3127

4 жыл бұрын

Is it the electric field of a uniformly charhed disk?

@AymanSussy

4 жыл бұрын

@@vincentdublin3127 Yes those things XD

I listened 9:35 to 9:36 at 25% speed, and I enjoyed it very much!

@glaswasser

4 жыл бұрын

ouuuhhhhfff paaaaaaaiiii

Beautiful.

Congratulations! Very good!

Hi! Nice work dude. How about the integral of e^x2 (z squared) any answer to that?

I was literally just in a lecture for 3D calculus and they introduced polar 3d integrals for the intersecting areas and volumes of sheets and cylinders.

Appriciated! Thanks for the video!

Fantastic It is like... you have to use properties of complex numbers to end out with the error funcion That was very funny to think!!! Thanks a lot for the video!!!

Reminded me of my god damn electrostatics classes haha. Finding the integrands of shapes and stuff... Still have nightmares about it to this day.

Great Explanation.

I love this.Thanks a lot

Beautiful

Brilliant video

fantastic video

my jaw dropped when it came out to be square root of pi!