If you like the videos and would like to support the channel: www.patreon.com/Maths505 You can follow me on Instagram for write ups that come in handy for my videos: instagram.com/maths.505?igshid=MzRlODBiNWFlZA==

Young mathematically talented kids these days are so lucky to have the internet as a resource to keep them stimulated. This kind of video is exactly what I needed as a young teenager.

@Targeted_1ndividual

Жыл бұрын

As a teenage self-proclaimed math goblin / Feynman acolyte, I concur.

@caspermadlener4191

Жыл бұрын

Most of the current IMO participants also watch a lot of math videos. As fourth of Europe at the IMO last year, I am surprised how much there is to learn on the internet.

@mayasudhakar9595

Жыл бұрын

I feel so jealous of them 😁

@slavinojunepri7648

Жыл бұрын

I wish I had access to resources of this king when I was young. I grew in a village with no books and libraries. I barely had a blackboard with some pieces of chalk and a kerosene lamp that hurt my eyes at night during homework. But somehow I took pleasure in math.

@Targeted_1ndividual

Жыл бұрын

@@slavinojunepri7648 where did you grow up?

The more I watch feynmann integration technique videos, the more powerful I become.

@azizbekurmonov6278

Жыл бұрын

Same!!

@Dagestanidude

Жыл бұрын

​@@azizbekurmonov6278 азизбек.не русскоговорящий ты случайно?

@azizbekurmonov6278

Жыл бұрын

@@Dagestanidude Da ya panimayu

@InoueRikako

Жыл бұрын

Lol

@marcokonst4144

Жыл бұрын

Xp farming on this video

It's been 50 years since I've solved a complex integral. This guy moves too fast for me! I'm reminded of my old teacher, and later friend, Wolfram Stadler. Rest in Peace, Wolf.

@blkcat6184

11 ай бұрын

Ditto. Learned how, then never had to use them again. Today, fugetaboutit!

@LetsbeHonest97

9 ай бұрын

sir, may I ask what you studied and what you did in your professional career? I'm planning to get back to grad school for math and computing

@kwgm8578

9 ай бұрын

@@LetsbeHonest97-- If you're asking me, I earned an undergrad in EE in 1980 and a master's in CS in 1984. Go and do it as soon as you can -- school gets more difficult as you age.

@LetsbeHonest97

9 ай бұрын

@@kwgm8578 absolutely ... Will do asap

@kwgm8578

9 ай бұрын

@@LetsbeHonest97 Good luck to you!

So to sum it up and generalize: Craftily plug in a parameter a so the derivative of the integrand with respect to a is simpler, now you have I(a) and you're looking for I = I(a0) Derive the integral with respect to the parameter making sure swapping places between the integral and the derivative is allowed (check convergence) Make your way towards an explicit expression for I'(a) Integrate I'(a) yielding an extra constant in the I(a) expression Determine the constant by plugging in I(a) a nice value for a making it trivial to compute Replace a by a0 and voilà, I(a0) à-la-Feynman, serve hot with a light Chianti.

@brendawilliams8062

Жыл бұрын

No wonder they use a math sign language. What a ride!

@rondovk

8 ай бұрын

Hero

@TheChrisSimpson

7 ай бұрын

My summary: Find someone better at math than me and ask them for help. Maybe I'll find this guy's email somewhere...

@mq-r3apz291

5 ай бұрын

We makin it outa Cornell wit dis one😎

Love how you talk about mathematics with passion while solving :)

My favorite aspect of Feynman is that, while he was certainly a genius, he has a big dose of ordinary guy that we can relate to. I'm not in his league by a long shot, but I bet it would have been a blast to hang out with him.

@JgHaverty

9 ай бұрын

With respect, what are you talking about lol? 😂 Feynman's brilliance was only matched by his ego and capability to be a complete asshole. His lecture series are engaging and make him out to be what youre trying to portray, but the reality of his personality was quite a bit more grim in both nature and circumstance of his life. He was a good teacher; as that tied into his work, but no you really wouldnt want to be "buds" with him and he most certainly is not a strong candidate for representing the "every man". Sorry to burst your bubble; but best to keep his legacy wrapped in his brilliance and contributions to science as a whole, not his personality.

@TheSireverard

8 ай бұрын

Surely you're joking, Mr Feynman... ;)

@jamesedwards6173

8 ай бұрын

JgHaverty, spoken like a true ignoramus.

@jamesedwards6173

8 ай бұрын

@@TheSireverard, and also "What Do You Care What Other People Think?"

@JgHaverty

8 ай бұрын

@jamesedwards6173 what the hell are you talking about? Hahaha

Excellent work, a good way to check the answer is by plotting the function (e^-x^2)*sin(x^2)/x^2 and estimating the area from 0 to infinity under the curve. The function is > 0 from x=(0 to 1.722), and the function is almost zero for x=(1.722 to 2.35) and then zero for all values of x>2.35. You can approximate the area under the curve as a right tringles with sides of 1 and 1.722. The area for that right triangle is (1x 1.722)/2=0.861. The exact answer per the video is 0.806626.

epic , thank you for making this technique so clear

Absolutely beautiful. Thank you for sharing!!

This is AMAZING!! Thank you for your great video. I think I lack some basic techniques regarding imaginary number but except that everything was super clear and easy.

This was amazing, really gotta use it instead of by parts. Thanks a lot !

You're doing really good content. Please, moreeeeee Feynman Integrals!!

Been waiting for an explanation of my favorite’s, Feynman, noble prize topic.

Beautifully done video!

Noticing that d/dx(-exp(-x^2)/x) = 2exp(-x^2) + exp(-x^2)/x^2, I went for an integration by parts, which also works nicely, but is less elegant I admit. I found amusing that in that case, the result appears in the form of sqrt(Pi/sqrt(2))(cos(Pi/8) - sin(Pi/8)). After multiple careful checks for mistakes, I eventually realized it is actually the same result as in the video!

@yogsothot

Жыл бұрын

In the video is =d/da[sin((ax²) dx =f of d/da X² ½-a The -exp =to its integral, but its sin8 and exp

Wow yes this is so intuitive and elegant and beautiful and I totally followed you the whole way along

@maths_505

8 ай бұрын

Thanks so much 😊

Did it (after seeing video) with the a on the exponential term.....follows pretty much the same route except using the Im operator as sin(x^2) is a constant. Other than proving Im(sin(x^2) = 0) over the range, pleasingly we get the same answer.

As someone who failed their A level maths almost forth years ago, I found this video utterly fascinating and understood (or rather, could follow) practically none of it . . . .

Very cool! Thanks for sharing.

We used to study similar integrals using the residue theory in the complex field and the polar coordinates.

Cool video. :D Another way I think you could do is using my #1 favorite method, ha ha. Once you've differentiated and the integrand is in the cosine form, use Euler's definition to re-write cos. Then you have a sum of integrals of exponentials. Then the trick is, make a u subsitution for the argument of the exponential, that puts the integrals into the form of a Euler's integral definition of gamma. The power of u allows you to determine each z.

This may be one of Feynman’s integration techniques (he has several and needed them to perform integrations necessary to compute Feynman diagram calculations) but it isnt the one he was most famous for…. Integrating by analogy with finite summations and vice versa. This particular technique, or parts of it (particularly integration by differentiating under the integral sign) is discussed in Engineering Mathematics Advanced texts such as Sokolnikoff & Sokolnikoff . This particular calculation is a bit more involved as complex variables are introduced

Amazing! I solved this by defining an I(a,b) equal to the integral with a parameter inside the e and the cos. Then differentiating partially and adding to get a first order PDE. Then conjugating and using partial integration to get the required result! Your method is much slicker, as you just took the real part rather than dealing with the whole complex function!… 😂

@zed_961

6 ай бұрын

It's crazy

Been listening to the Feynman audiobook ("Surely...") and Feynman was a PLAYA wowwww. Dude got around! And then he talks about this, so I had to look it up. I've only taken Calc 1, so this is way beyond me but fun to watch. I'll have to watch more videos to understand it better.

Beautiful!

Great video. Thank you

This makes me want to learn complex analysis. Great video considering I still understood most of it

Can't wait to learn all this it seems interesting enough 🙂

very perfect, I tried to do it myself and needed the video again and again. But now I got it all. See research gate if you are missing 2 or 5 steps in between.

Amazing content!

Very nice presentation.

Just infinitely beautiful!

@maths_505

10 ай бұрын

SUIIIIIIIIIIIIIIII

very nice effort. good luck

Brilliant! Thank you.

Wow. This technique is amazing. Maybe not even among the top 10 achievements of Richard Feynman but still fantastic!

Wonderful!

What a beautiful integral! You might also be able to solve this same integral using residues/contour integration.

Nice integral! I wonder if it's solvable putting the a parameter into the exponential instead? Seems like you should end up at the same place. To solve the constant of integration you would need to let a tend to Infinity instead of setting it to zero, and the rest should be the same.

@patrick-kees8962

Жыл бұрын

I'd imagine you'd get issues with the fact you'd still have the sin and therfore a complex exponential which makes things more complicated

@GilbertoCunha-tq2ct

Жыл бұрын

@@patrick-kees8962 I believe it would still work if you consider the Imaginary part of the integral instead of the Real part

Thank you Sir for your best explanation and working out of the problem🥰😍🤩

@maths_505

9 ай бұрын

Thank you for the nice comment

Beautiful solution

Once upon a time I would have been able to reproduce this. Now I am just watching and thinking wow.

You are mad man indeed ... You mad a great Difference. So clever...❤❤❤❤❤

nice demonstration 👍

beautiful

I love this video!!

I understood it but it still made my head spin!

Thanks you , greeting from Argentina.

I came up with this myself in college. I hadn't known until now that this Feynman guy stole it.

@maths_505

Жыл бұрын

😂😂😂

@RohanDhandr8

Жыл бұрын

I completely believe you

This is sheer brilliance. I found something with a similar message, and it was beyond words. "The Art of Meaningful Relationships in the 21st Century" by Leo Flint

Very awesome technique, I love it - great👌

Why did we stop? application of a formula for the cosine of double angle shows that sin(pi/8) equals sqrt(2-sqrt(2))/2 ... which allows us to simplify the entire answer to sqrt( pi (sqrt(2) - 1) / 2) ; that final formula does not use any trig functions (sin,cos,etc). Just a thought :)

Awesome!

Wonderful 🎉❤

I like the pace, you don't go at a snail's pace like some others. Great job!

Great video, primers are so much better than triggers

Around minute 10, you can just use the fact that 1-i has angle -π/4 so the square root has half that, and multiplying by i rotates it by π/2 meaning that the new real part(cosine) is the old imaginary part(sine). Just seems slightly easier and more intuitive than the algebraic argument.

@georgemaclaurin3705

9 ай бұрын

Instead of -pi/4 i used 2pi-pi4=7pi/4 which is the same but got different answer. 😢

I feel that im evolving after watching this!!

The square root in complex numbers has two solutions. You also have e^7pi/8 as solution

How does any of this help me order coffee?

technically you also have to ensure that the differentiation and integration are interchangeable (which is not true in general for integrable functions) which can be quite tedious, especially when working with improper integrals

@thomasdalton1508

Жыл бұрын

He covered that in the video, albeit somewhat handwavingly.

@egdunne

Жыл бұрын

@@thomasdalton1508 Yes. The handwaving ignored the potential problem at the left-hand side, where x=0 and x^2 is in the denominator. It's fine, but should be addressed.

@thomasdalton1508

Жыл бұрын

@@egdunne It doesn't need to converge at x=0 does it? The integral is from 0 to infinity, so it needs to converge on the *open* interval (0, infinity). The boundary points don't matter.

@evertvanderhik5774

Жыл бұрын

Mathematicians will worry about that, physicists not so much.

@thomasdalton1508

Жыл бұрын

@@evertvanderhik5774 Physicists might not worry about proving rigorously that it converges appropriately, but they need to worry about whether it does or not otherwise they'll get the wrong answer. You can determine that using rules of thumb rather than a rigorous analysis, but you have to do it.

Inspiring

There is no reason for this thumbnail to go so hard

I'm one of the very unlucky ones who are incapable of math beyond basic algebra but am fascinated by it. I watched the entire video despite understanding nothing. I'm not sure if this is just an elaborate form of self-harm...

@Amb3rjack

Жыл бұрын

Absolutely. I feel exactly the same!

I have a great integral as an idea for a video The integral from 0 to ∞ of e^(A(x^B)) Where A and B are any complex numbers except the values of divergencey and to find what are they

Nice video!

It would be easy for me to love mathematics if my teachers were like you!

The derivative of x squared is 2X

Why choose to throw alpha into the sine function as opposed to the x^{2} in the denominator or the exponent exp{-x^{2}} in the numerator?

amazing

My AP calculus BC brain has expanded… glad i’m pursuing a stem major 😃

@JgHaverty

9 ай бұрын

Eh this is pretty entry level stuff on tbe grand scheme of things. If you really want to "expand your brain", go noodle around feynman diagrams; with regards to path integrals and quantization 😅. If you REALLLY wanna see where this rabbit hole can go, then go over neutron transport while youre there 😂 Recommend calming the hubris of your AP calculus class. The reality is if youre pursuing a degree in engineering, physics, or whatnot; your best interest is actually not using AP credits for anything other than humanities. Encumbent on what programs you narrow down and get accepted to of course [if your program only requires calc 1, then yes of course use your ap credit in that capacity]. Its a good path to be on; just take it in stride. That said, AP credits are kind of useless beyond gpa padding and i dont understand why highschools put so much weight on them in the first place..

¡¡¡Brillante!!!

sin(pi/8) is easy to calculate: sqrt((sqrt(2)-1)/sqrt(2))/sqrt(2). Hence, we can simplify the result: I = sqrt(pi/2) * sqrt(sqrt(2)-1)

I just want to know which drawing tablet do you use for mathematics and which app (on Android Tablet I suppose) ?. Thank you very much. And great content!

damn this is great

Genius!!! Dick Feynman is awesome

Nice video. What application and writing device(pen) are you using to write so nicely math?

@kenfrank2730

8 ай бұрын

I would like to know also.

Good job

Honestly, using Re on euler's theorem that way is more impressive than feynman's technique, imo. That's precisely the sort of chicanery that i started to love these subjects for! edit: first time I saw that integral was statistical mechanics and the professor just gave the formula without proof or derivation. In numerical methods we got to see montecarlo integration, and that's probably my favourite integration method. Didn't see any of this in complex variables, which I went on to fail.

Calling it Feynman's technique makes it appear as though it took centuries to develop it, when in reality this is also known as Leibniz's rule after one of the creators of integral calculus, so it was actually known pretty much since integration became a thing.

@csharpmusic9866

8 ай бұрын

Hey, just to add to your knowledge the lebinitz rule basically deals with differentiating a function under integration, whereas Feynman's techinque is a way to find definite integrals of non integrable functions by introduction of a parameter while 'using' the lebinitz rule as a smart tool and hence " lebinitz rule is different from Feynman's techinque, one helps the other."

@epikherolol8189

3 ай бұрын

Nah Leibnitz rule is different.

Just another example of why we should be having people take complex analysis

An integral of a complex function equates to a real number.

Brilliant

When you set up the steps wrong and start trying to solve this on your calc test

At 5:00. This integral can be determined easily by switching to a 2D integral in polar coordinates. No need to use formulas from books.

Where did the pi under the first radical come from in the last line? Shouldn't it just be root 2 of root 2 multiplied by sin pi/8?

3 months ago I understood none of these.Now I finally understand it

@maths_505

2 ай бұрын

Hell yeah 🔥

I'd like to ask what's the device you record on? 👀

There are two points at which the technique used here needs further explanation: where the derivative of the integral becomes the integral of the derivative of the integrand, and the reason given is because the integrand is clearly bounded; the more crucial point is where part of the integrand is replaced by the real part of a complex term, and it is then assumed that integrating the integrand with the full complex term and then, when the integration is done, taking the real part, so discarding the imaginary part, is an equivalent result to integrating without the complex term replacement - that is quite an assumption since throughout the subsequent manipulations of the complex terms some real terms become imaginary and some imaginary terms become real, so some imaginary terms contribute to the real result, but the technique seems to rely on the imaginary part of the original complex replacement having no effect on the real part.

As Feynman once told us at Cal Tech, "F... the 2pi".

Wouldn’t the constant of integration be part of the argument of Re() because the integral da was within Re()?

Please tell me why we take just real part in 3:43. I see that we need just cos but I do not undersfand how can we ingore sin part of Eular formula.

can u make a video about the feynman technique itself ?

This is wizardry 😮😮

Nice video and cool trick. I've never seen integrals written like a rho though. ;) Good job though.

Kept wondering how to do this...simple.

Which app you use for writing please tell me

Why Am i loving watching integration videos

@Jorgensen07

8 ай бұрын

U r from India bro ?

@maths_505

8 ай бұрын

You have been chosen.....

Interesting... but of course, *one must know _when and where_ it is true that _each step is valid_ if one is to apply the technique more generally. Which makes me wonder: How would 3Blue1Brown explain this?

Awesome.