In approximately 1971 I attended a seminar by Feynman on the PCT theorem at UC Berkeley. The auditorium had sliding black boards as in this video except that they were huge and heavy and so they hung from pulleys with one of the boards serving as the counterweight for the other. Feynman, upon sending up one of the boards to write on the other said to the audience "Oh look. I don't have to do any work." Laughter from the all-physicist audience.
Gaussian represents some sort of symmetry which in 3-d can be built up by infinitely many slices of "disks". With that, it, no wonder, is somehow related to Pi.
Hahahha yeah, that was indeed funny. More so. I don't think its so much of Kqnt trying to destroy traditional metaphysics than it is him being irresponsible epistemology
Hi there, dude. Love your vids. At minute 14, what if the parameter "a" is negative? Wouldn't it lead to a non convergent integral? Brilliant! Keep going.
I allays wondered what π have to do with this integral The moment i saw Invers tan i felt it Thank you very much 🥰 finally a solution that i can understand I am a high school student by the way
*Papa* ... I miss you and your Math .... Therefore I'm here, because your old videos are still great. Thank you *Papa Flammy Mathy* . *Papa's Ways, Is The Best* . Your Hagoromo Chalk and Your black jacket 😂
I LOVE YOU Watching you do this is very satisfying. Where did you learn these techniques? In graduate courses? I'm an engineering student but these techniques are never mentioned in my calculus classes.
I have learned how to solve exponential equations lately. I faced a problem that required a substitution t=2^x and t ended up being negative. Well, no problem, complex numbers helped me and I got the result. My teacher had never heard about such a thing. Note she has a masters degree. Thank you, mathematicians of UA-cam.
@@SirDerpingston e^[-(x)^2] is a famous function because 1.) It is the general shape of bell curves used in statistics and 2.) It's integral is non-elementary, which I find pretty interesting
I found the general method, it is more geometric it change I(x) to (I(x))^2=I(x)I(x*)=I(x)I(y)=V(x,y) so we need to integrate z(x,y)=e^((-a)(x^2+y^2)), plot on 3 dimension the integral basically is finding the volume between z(x,y)=e^((-a)(x^2+y^2)) and z(x,y)=0 we found symmetry around z axis, so we change the coordinate to cylindrical coordinate the original integral=z(x,y)dxdy=e^((-a)(x^2+y^2))*dx*dy intergral after=z(R,angle)dRd(curve)=e^((-a)R^2)*dR*(Rd(angle)) the additional R from d(curve) made the integration solvable them I(x)=(I(x)I(y))^0.5, solved I still like your method more Your method is much easier to understand
Lord Kelvin's definition of a mathematician: Someone to whom Int[-infty, +infty] exp(-x^2) dx = sqrt(PI) is as obvious as 2+2=4. (Said before Russell and Whitehead rendered 2+2=4 non-obvious to anyone.)
Don't you have to use uniform convergence in order to interchange integral and limit at 13:25? Because that's not allowed in general. For example, observe the integral from 0 to 1 of n*x^(n-1) dx and let n go to infinity.
Damn this is awesome. Verstehe nur manche sachen nicht ganz mit dieser Partiellen Ableitung das wurde mir zu schnell aber sonst hammer video. Das liebe ich so an mathe. Richtig komplizierte Integrale und dann so eine schöne Antwort 👍
Hey I just wanted to ask about when you are solving for the c value, you don't touch the variable u even though it is dependent on t. As I recall, t is equal to zero, and u is equal to x/t, which would make u undefined. I would just like to ask how it still works even though that part is unresolved. Thank you so much for your effort and I'm loving your videos!! There really is a uniqueness to your videos that I don't think I've ever seen except kind of in Faculty of Khan, who is just pure salt and no more. This really blew my mind on several levels, so I'll use papa flammy's method every day in my calculus class, referring to it with that name every time because there is no other more beautiful way to describe it.... I don't know how but I'm going to try anyway XD.
also i think it is important to remember that "to the minus 1" doesn't mean "1 over" but "inverse". It just happens that the inverse of simple numbers is also denoted as "1 over"
now I know why my professor don't want to proof this in class XD the way is kind of tricky for me, especially the the integral at the last part vanish when t close to infinity. I was like "wait, whaaaat?"
Actually, I got a little feedback I don't really have too much talent in calculation. So yeah, I ran into a lot of issues in learning. The good thing is I would know exactly what it takes for a normal person to understand this kind of proof. When I'm trying to understand any proof and analysis, I always struggle in why do this now, why do that now, and somehow it just work out. In this kind of situation, I usually would look the proof several times to find reasons to makes the method make any sense. But sometimes it just really hard to figure it out. But only by doing this I can really apply this method (or even figuring out a method) in other problem. My suggestion is make a summary after the derivation, going back and explain why do this now, why do that now. But this might be why watch you derive is better than on textbook. Sorry for bad grammar, English is not my native language. I hope this will help you out:)
great video! where would you say is the best university in germany for mathematics? (im currently learning german so hopefully the language of study wont be a problem)
This was super cool. However I have a problem: You introduced u as x/t and then you treated u as a separate variable, for example, when you took the limit as t goes to infinity. Are we allowed to do that? I mean you got to the correct answer, so I suppose there must be some validity in what you have done...
Dont say that - you easily get correct results from doing wrong maths, so your question is legit. My guess looking at it would be that you got lim t²(u²+1) = lim t² = inf (because lim u²t² = constant) and lim u²+1 = 1 and thats why he doesnt even mention that u = u(t).
In the beginning of the video you state that a is in the real numbers, but later on you use that the limit of t -> infinity of e^(-at^2) = 0. If a is negative, this does not hold anymore. The proof still holds for a>0 of course and it is still beautiful. Do correct me if I'm wrong though.
Partial derivative, t and +c: Hey Me: Have mercy please Them: There is no mercy Also the only thing in this that makes sense is dt/dt=1, the rest just makes no sense, sik why calculus was even a thing, like it makes no sense
In approximately 1971 I attended a seminar by Feynman on the PCT theorem at UC Berkeley. The auditorium had sliding black boards as in this video except that they were huge and heavy and so they hung from pulleys with one of the boards serving as the counterweight for the other. Feynman, upon sending up one of the boards to write on the other said to the audience "Oh look. I don't have to do any work." Laughter from the all-physicist audience.
10:41 the best thing to do as a german... xDDD
DON'T MENTION THE WAR!!!! :)
Godwin point my bois
Maks not C!
As a german, and behalf of all Germans
We will remember this flamy, and so will the wall street journal
14:29 This is outrageous
Gaussian represents some sort of symmetry which in 3-d can be built up by infinitely many slices of "disks". With that, it, no wonder, is somehow related to Pi.
I just discovered this channel and I freaking LOVE IT. Flammable Maths is awesome!!!
Flammable Maths enjoying is an understatement! :D
*Sips* Reminds me of the time when Kant tried to destroy traditional metaphysics
Hahahha yeah, that was indeed funny.
More so. I don't think its so much of Kqnt trying to destroy traditional metaphysics than it is him being irresponsible epistemology
Thank you... It is helpful in solving quantum mechanics problems
10:04 mah boi's board has been possessed by Papa's soul.
14:14 OMG that celebrity's name is Sharukh Khan and my mother was his fan and that's why she named me Sharukh. Coincidence? I think not.
Ok but it works only if a>0 !!
Or Re(a)>0
@@aidankwek8340 Integral wont converge in all cases
I like how in these older videos you make a few more mistakes, still the content is great do like it very much! Papa bless
:)
2:59 the CHEN LUUU!
14:13 Great picture of Dr. Peyam.
Is he Shahrukh Khan from India?
@@all462 yuuup
Nothing less than a cool video! Haven't learnt some of these integration techniques yet, so I know how I'm gonna spend this evening!
Alright,I wont be going to school now...Watching ur videos is enough
lol
You are a genius. Period. Just shared this video with 5 others
Hi there, dude. Love your vids. At minute 14, what if the parameter "a" is negative? Wouldn't it lead to a non convergent integral? Brilliant! Keep going.
yes, a>0 is required!=)
13:37 This limit, we'll dominate :)
1337
Subbed and favorited immediately upon seeing "Papa Leibniz". Haven't even watched the video yet and I still can't do calculus.
Greetings from America and Africa! Have a Flammable day, bro! 😊🙌🏽🎊
Thanks for this video man! Keep going u are the best
Had to come over here and hand out a like, just because of the title.
:D
i like how it sounds like a youtube apology video in the beginning
Making a bit complicated but I love your approach ...
Oh my god!!! Gauss could be angry :v.
Just amazing!
That's some nasty integral
At 7:48
Don't forget the negative sign my boys!
Jens : 'My girls' are smart. Only boys need a reminder!
😂
:D
I allays wondered what π have to do with this integral
The moment i saw Invers tan i felt it
Thank you very much 🥰
finally a solution that i can understand
I am a high school student by the way
Mathematics sounds so much better on chalk than a marker board
*Papa* ...
I miss you and your Math ....
Therefore I'm here, because your old videos are still great.
Thank you *Papa Flammy Mathy* .
*Papa's Ways, Is The Best* .
Your Hagoromo Chalk and Your black jacket 😂
Nice picture of Dr Peyam
AndDiracisHisProphet where?
AndDiracisHisProphet nvm got it at 14:14
@@blackpenredpen That's actually the Indian actor Shah Rukh Khan
PHYSICS STUDENTS: change to polar coordinate plane --> done
I am from india....this concept come so many times in gate exam ...tq brother...🙏🙏
i got asked to solve this for an interview and i am going to use this next time i get asked to BLOW SOMEONE'S MIND.
Extremely a mad genius
I LOVE YOU
Watching you do this is very satisfying. Where did you learn these techniques? In graduate courses? I'm an engineering student but these techniques are never mentioned in my calculus classes.
I have learned how to solve exponential equations lately. I faced a problem that required a substitution t=2^x and t ended up being negative. Well, no problem, complex numbers helped me and I got the result. My teacher had never heard about such a thing. Note she has a masters degree. Thank you, mathematicians of UA-cam.
where do you find such thorny integrals? I'm looking for some hardcore calculus questions...
@@SirDerpingston e^[-(x)^2] is a famous function because 1.) It is the general shape of bell curves used in statistics and 2.) It's integral is non-elementary, which I find pretty interesting
@@PapaFlammy69 , that's the only way to really LEARN , DO & UNDERSTAND maths ... !!! ... & you also 'did well' , so thanks !
@@SirDerpingston michael penn on yt and this channel have some meaty integrals
This could also be solved for by using the gamma function (a lot easier imo)
Man you're so cool and handsome
If a
I found the general method, it is more geometric
it change I(x) to (I(x))^2=I(x)I(x*)=I(x)I(y)=V(x,y)
so we need to integrate z(x,y)=e^((-a)(x^2+y^2)), plot on 3 dimension
the integral basically is finding the volume between z(x,y)=e^((-a)(x^2+y^2)) and z(x,y)=0
we found symmetry around z axis, so we change the coordinate to cylindrical coordinate
the original integral=z(x,y)dxdy=e^((-a)(x^2+y^2))*dx*dy
intergral after=z(R,angle)dRd(curve)=e^((-a)R^2)*dR*(Rd(angle))
the additional R from d(curve) made the integration solvable
them I(x)=(I(x)I(y))^0.5, solved
I still like your method more
Your method is much easier to understand
1:32 We call that bad boy "you""? OK, if you insist.
Thanks for the video!
lol, you approach the problem of interchanging various limiting processes as every professional analyst I know: "just fuck it"
but the video and technique are lit af
nice approach.
You look angry in the video debut 😂😂 I like you 🔥
You know what would actually be good, is if you can use guassian blurs to do filters instead of IIR/FIR if you can just increase the fall off!!!
"is nothing else but", is nothing else but, "is just".
ie. "is nothing else but" simplifies to "is just".
XD Sorry I couldn't resist a silly joke. :P
Are you interested only in real/complex analysis? What about Abstract Algebra, Combinatorics, Topology, Number Theory etc...?
At 2:00, how did we know to square the I(t) integral? Like, trying to solve it, what clues are there that this is a useful step?
i love you papa flammable maths;
Lord Kelvin's definition of a mathematician:
Someone to whom Int[-infty, +infty] exp(-x^2) dx = sqrt(PI) is as obvious as 2+2=4.
(Said before Russell and Whitehead rendered 2+2=4 non-obvious to anyone.)
It must be so fascinating, any dislike in your videos i guess, thats a proof that your channel its a lot useful, fellow :)
Whoa that is overkill :0
yas! :D But so damn cool! :D
Wow really awesome
if Gauss revives and sees this bad boi he will get mad indeed :v
NICE! I only missed what if a
why does he feel like crying but resisting it the best he can
Me after watching the first episode of Rick and Morty
Lovely stuff
Don't you have to use uniform convergence in order to interchange integral and limit at 13:25? Because that's not allowed in general. For example, observe the integral from 0 to 1 of n*x^(n-1) dx and let n go to infinity.
great video!
I know that pi is half a circumference. was he talking about circles?
San Samman a circle is 2pi radians, radians is standardized in the unit circle so it’s just 2pi
4:10 MY EYEBALLS!!!
Damn this is awesome. Verstehe nur manche sachen nicht ganz mit dieser Partiellen Ableitung das wurde mir zu schnell aber sonst hammer video. Das liebe ich so an mathe. Richtig komplizierte Integrale und dann so eine schöne Antwort 👍
you could do it in one action by dividing and multiplying by the root of A and substituting A under the differential
Nice video! Why did you use the same letter (I) for constant and for function?
Is it possible to evaluate integral e^-(x^3) 0 to infinity the same way?
Hey I just wanted to ask about when you are solving for the c value, you don't touch the variable u even though it is dependent on t. As I recall, t is equal to zero, and u is equal to x/t, which would make u undefined. I would just like to ask how it still works even though that part is unresolved.
Thank you so much for your effort and I'm loving your videos!! There really is a uniqueness to your videos that I don't think I've ever seen except kind of in Faculty of Khan, who is just pure salt and no more.
This really blew my mind on several levels, so I'll use papa flammy's method every day in my calculus class, referring to it with that name every time because there is no other more beautiful way to describe it.... I don't know how but I'm going to try anyway XD.
Why tan^{-1}(x)? Why? arctan(x) is so much better ! tan^{-1}x=1/tan(x)=cotan(x) ! Other than that, great video.
context, my friend
also i think it is important to remember that "to the minus 1" doesn't mean "1 over" but "inverse".
It just happens that the inverse of simple numbers is also denoted as "1 over"
inverses are just weird in trigonometry. go look up:
pre algebra.
I'm kidding 😂
Good morning to you too my flammer
now I know why my professor don't want to proof this in class XD the way is kind of tricky for me, especially the the integral at the last part vanish when t close to infinity. I was like "wait, whaaaat?"
Actually, I got a little feedback
I don't really have too much talent in calculation. So yeah, I ran into a lot of issues in learning.
The good thing is I would know exactly what it takes for a normal person to understand this kind of proof.
When I'm trying to understand any proof and analysis, I always struggle in why do this now, why do that now, and somehow it just work out. In this kind of situation, I usually would look the proof several times to find reasons to makes the method make any sense. But sometimes it just really hard to figure it out. But only by doing this I can really apply this method (or even figuring out a method) in other problem.
My suggestion is make a summary after the derivation, going back and explain why do this now, why do that now. But this might be why watch you derive is better than on textbook. Sorry for bad grammar, English is not my native language. I hope this will help you out:)
*Link in the description to the corresponding video* 😂😂😂 Yes bro
Brilliance incarnate.
7:30 The u=x/t therefore it is dependent on t, how could you ignore the chain rule in the partial differentiation step?
genius papa
Legends only know that he was earlier known to be "Fapable maths"😂😂😂
I'm starting to think that in germany it's always morning
Papa Bless
Papa's way is the best
Can you calculate
fx= (1/2)*sqrt(1-x^2);
Integral(f'/sqrt(1+(f')^2))dx
Use any method to achieve this?
Eliptic curve length?
What can be done about the quotient of two of them? Like one integrated until 3 and other until 5, or so?
Hello. I'd like to ask why u was considered a constant at 7:15 when u was defined as x/t. Thank you.
Just watch this impressive Math channel ua-cam.com/channels/ZDkxpcvd-T1uR65Feuj5Yg.html
great .thank you .... is x variable real or complex ?
I've gotta know, what song do you use whenever you introduce the problem?
3:08 There is just one term there equal to exp(-at^2) by the usual fund. thm. of calculus.
great video! where would you say is the best university in germany for mathematics? (im currently learning german so hopefully the language of study wont be a problem)
From what I've heard TU Munich is the best.
I know my 10 times tables 😱
Can you solve the integral of x².e^2x² dx from -infinite to +infinite?
why is the comments section blocked for the new videos, does any one know???
Shouldn't the domain of a be a>=0? If a∞) doesn't converge, right?
yas!
@@PapaFlammy69 Thanks for quick answer, Papa Jens
14:16 Did you consider the case which a
fellow mathematicians
fllow mathemacians
flow mathemains
flo mathmans
flo mamans
flo amas
fl amas
flamas
= flammers
This was super cool. However I have a problem:
You introduced u as x/t and then you treated u as a separate variable, for example, when you took the limit as t goes to infinity.
Are we allowed to do that? I mean you got to the correct answer, so I suppose there must be some validity in what you have done...
Dont say that - you easily get correct results from doing wrong maths, so your question is legit. My guess looking at it would be that you got lim t²(u²+1) = lim t² = inf (because lim u²t² = constant) and lim u²+1 = 1 and thats why he doesnt even mention that u = u(t).
In the beginning of the video you state that a is in the real numbers, but later on you use that the limit of t -> infinity of e^(-at^2) = 0. If a is negative, this does not hold anymore.
The proof still holds for a>0 of course and it is still beautiful.
Do correct me if I'm wrong though.
Holy, you looked so tired 2 years ago!
Das gefällt mir.
At 12:00, if we make t = 0, doesn't that mean u = x/0 which isn't allowed?
You are awesome
One may achieve the same result as your application of the Leibniz rule by simply applying the fundamental theorem of calculus.
Hey, I want to know whether this integral could be solved or not(integral from 1 to inf(lnx / (x^x)))
Partial derivative, t and +c: Hey
Me: Have mercy please
Them: There is no mercy
Also the only thing in this that makes sense is dt/dt=1, the rest just makes no sense, sik why calculus was even a thing, like it makes no sense
Dimensional analysis ist dæ wæ