Gauss, Riemann, Dirichlet, and Euler start a mathematics fight club where you beat people to death with integrals. The last man standing was papa flammy, and he wasn't even part of the club
14:18 Sure you can get that result from other integrals. For example, integral(pi/e · dx) defined from 0 to 1. I'm just being annoying ;P Great video! Really enjoyed it!
For engineers: Wolfram Mathematica gives the right answer instantly. When you're in a hurry, of course. If you have some time, try it with the residue theorem.
Wow. My mind flew across mathematical lightyears! I think my calculus was really getting a little rusty. Thank you! I just got smarter just by watching this video. Instant subscription!
Hi Flammable Maths... I think we can do more simpler... because the Laplace transform of I(t) is just (pi/2)* (s - 1)/(s² - 1) which is (pi/2)*(1/(s+1)). Therefore, using the linearity of the inverse Laplace transform, we obtain that I(t)=(pi/2)*L^(-1) {1/(s+1)}(t) = (pi/2)*exp(-t). Since I=2*I(t=1) we have: I=2*(pi/2)*exp(-1)=pi/e and we're done. Have a nice week-end :)
I was thinking the same thing!! The above equations from FG implies s ^= +-1 and that he only needed to take the inverse LT of 1/(s+1) which reduces to 1/e^t. In addition, if you're going to use a Laplace Transform why not replace cos(x) as Re(e^(ix)) from Euler's formula?
With all honesty I wish you become a doctoral degree in mathematics and achieve a great contribution in this field. You deserve this. You are a natural teacher. Your content worth. It helps people get interested in this discipline. Besides, I think math is more than just a discipline.....
At @12.55 we could get a faster result by simplifying the expression in s to get ~ 1/(s+1), the IL of which is exp(-t) . This is such a great video. Good job.
thanks for showing how to do the inverse laplace transform! It really is like integrating, because you know the integral by knowing it's derivative. In this case, you know the inverse laplace transform because you know the laplace transform of the result. Pff haha.
for the pdf, you can just do a/(x^2 + 1) + b/(x^2 + s^2) bcz it's just product of linear equations in terms of x^2 so u made ur life a bit harder there
Dude, I'm really interested to domain this theme (the Laplace transform), could you tell, which should be the things I need to study to have good bases when I start to study this heavily?
What about the integral of sinx/(x^2+1) from 0 to infinity? Can it be expressed in terms of π, e or other known constants? I did a little search on the net and I found only numerical approximations to it, not an exact value. Also, trying the same approach as this video, it leads to ln(s)/(s^2-1) and I have no idea what is the inverse Laplace transformation of this one. Any idea if we can proceed from here or do we need a different approach for this one?
Hi :) if you want the exact value of the integral of sin(x)/(x^2+1) from 0 to +infinity you should use the Exponential integral function Ei and then the exact value is just (Ei(1)-e^2*Ei(-1))/2e where Ei is not an elementary function but a special one... and so no results can be obtained in terms of real numbers like pi, e or other known constants. I hope this helps you. Bye :)
10:50 i have a question. can u realy say that sqrt(s^2)=s? s is a complex number by definition of Laplace Transforms. I dont remember, but maybe it's related to Re (s)
Bro, I love to work with these videos when I understand them, and just watch in awe when I don't. What level of math or physics are laplace transforms taught? Max I've learned so far is Multivariable Differential Calculus and Physics C
At my university Laplace transforms are introduced in Differential Equations because of their phenomenal way to transform high order constant coefficient differential equations into algebraic problems (as long as initial conditions are known). Laplace and Fourier transforms are explored more in depth in higher level (graduate or senior level undergraduate) complex analysis classes.
You make great videos man, that really helps me learn new things. I am only the beginner, so could you please give me a clue my can't we change the order of integration so easily? Just tell what topic I need to read, no need to tell the whole story. Thx. BTW: best animation I've ever seen
I’ve really loved the fight, don’t get me wrong, but next time, please, be explicit with the measure tools. Or you can just use residue. Nice videos, boi.
Nice. I do think think you risk a hernia from all that heavy lifting. I thought you were just gonna make cos(x) into e^(jwx), recognize this as Fourier transform of Cauchy, set w=1, taste victory, and get drunk.
since you integrate both integrals from 0 to inf I think that is the main reason why order of integration doesn't matter. Correct me if I'm wrong, cheers!
In some cases swapped limits can 'coincidentally' match when we do not have uniform continuity, in the same way that the limits of two sequences can match without the sequences being inherently related.
That was one of the funniest things I've seen all week.
EDIT : Also, pi/e = 1, why didn't you write it like that?
pi/e = 1.15572734979
Bhuyakasha It’s an “engineering are bad at math” joke.
Fundamental theorem of engineering
By the fundamental theory of engineering, pi=3, e=2,and because we know that for large enough values of 2 2=3 we get pi=e which implies pi/e=1
Gauss, Riemann, Dirichlet, and Euler start a mathematics fight club where you beat people to death with integrals. The last man standing was papa flammy, and he wasn't even part of the club
Damn mah boi Hunter I miss you down there in the comment section! Are you doing well?
**Flawlessly uses Laplace transforms to solve integral** **forgets the s at the end of bois**
LOLLLLLL at 3:30 wtf. Hahhahah
Gotta love the Roblox effects
I couldn’t even understand it !!! X D
the new mortal kombat game looks pretty sick :D
It was hillarious!
Omg, my two favorite math senpais are converging in this parallelism of infinitely divergent software of youtube
14:18 Sure you can get that result from other integrals. For example, integral(pi/e · dx) defined from 0 to 1. I'm just being annoying ;P Great video! Really enjoyed it!
Or from the integral of exp(-x/pi) from pi to infinity :D :P
XD
Flammable Maths - Abusing the linearity of everything makes me happy🤣
“Pure mathematics is, in its way, the poetry of logical ideas.” ~Albert Einstein !!!
“And that’s why poetry is not used very often because it is completely unnecessary and complicated” - me
ALBERT GODSTEIN
@@buttapotato1233 beauty is hard to grasp
LOL you are so funny, loved the new challenger approaching joke!
I admire your mathematical ability SOOO much, keep doing what you're doing. :)
For engineers: Wolfram Mathematica gives the right answer instantly. When you're in a hurry, of course. If you have some time, try it with the residue theorem.
I'm beginning to think that papa flammy is a big fan of laplace transformations...
He's a physicist :v
That's because laplace transforms are fuc,king dope bruh.
Best 15 minutes of my life. Please keep doing this kinds of videos.
Are you doing this video at school,coleage ,btw ???
Your life must suck
So according to my engineering calculations, the result of this integral is obviously 1.
I would've combined 𝜋/2(s/(s²-1)-1/(s²-1)) into 𝜋/2((s-1)/(s²-1))=𝜋/2(1/(s+1))
Wow. My mind flew across mathematical lightyears! I think my calculus was really getting a little rusty. Thank you! I just got smarter just by watching this video. Instant subscription!
at the end of the video you wrote ( thank you
It's supposed to be a heart, turned sideways.
@@tomkerruish2982 r/wooosh
Great video! Very elegant solution.
This Integral could also be solved by residue theorem very elegant. With this approach you can almost read off the result from the definition ;)
Hi Flammable Maths... I think we can do more simpler... because the Laplace transform of I(t) is just (pi/2)* (s - 1)/(s² - 1) which is (pi/2)*(1/(s+1)). Therefore, using the linearity of the inverse Laplace transform, we obtain that I(t)=(pi/2)*L^(-1) {1/(s+1)}(t) = (pi/2)*exp(-t). Since I=2*I(t=1) we have: I=2*(pi/2)*exp(-1)=pi/e and we're done. Have a nice week-end :)
Mach weiter so, immer eine Freude ein neues Video von dir zu sehen.:)
God math was interesting but it's so much more interesting when memes are integrated within the teaching MMMMMMMMMMMMMMMM YUM
"memes are *integrated* "
Flammy always wins
Durch Zufall auf deinen Kanal gestoßen und innerhalb von paar Tagen alle Videos geguckt.
Bitte mach weiter so :^)
Aww, I first read about this back in....2001? This is one of the coolest integrals ever.
Im finishing my semester and all its going crazy, but 3:30 really made me laugh af. Thanks man!!!!!!!!
You know, you could have simplified the (s - 1)/(s² - 1) before doing the inverse Laplace transform. Might have been simpler...
Assuming s =/= 1
@@gamma_dablam - that's implicit
I was thinking the same thing!! The above equations from FG implies s ^= +-1 and that he only needed to take the inverse LT of 1/(s+1) which reduces to 1/e^t. In addition, if you're going to use a Laplace Transform why not replace cos(x) as Re(e^(ix)) from Euler's formula?
@@gamma_dablam This has already been assumed!
So it equals 1! That's so beautiful
pi/e? Isn't that just 1?
And sin(x) = x , it's trivial
Ah i see, an Engineer aswell
Tobias Görgen Yes i study chemical engineering and you?
I don't get it, why is it a joke that engineers are bad at math? XD
Civil Engineering
At 11:56, can't you simplify the expression to pi/2 * (1/(s+1)) and avoid all of the hyperbolic stuff
I was about to contour integrate. Considering f(z)....:3
@@kummer45 The contour integral is very literally two steps.
Hey man, nice vid! That is a really nice result.
With all honesty I wish you become a doctoral degree in mathematics and achieve a great contribution in this field. You deserve this. You are a natural teacher. Your content worth. It helps people get interested in this discipline.
Besides, I think math is more than just a discipline.....
At @12.55 we could get a faster result by simplifying the expression in s to get ~ 1/(s+1), the IL of which is exp(-t) .
This is such a great video. Good job.
Flammy: "Sooo now wee can plug every thing in"
Me: 😃
My favourite youtube channel ever
Flammable Maths i would be sooo happy if you could be my teacher
Beautiful
*Papa Bruce Lee* (min: 3:15)
Thank you so much dear Papa, great.
I learned and enjoyed.
Absolutely beautiful, elegant and surprising!
Thank you for showing wonderful Calculus technique!
You did it beautifully
3:00 bis 3:45 ist der beste Witz, dass ich in einem Mathevideo gesehen habe.
Sehr schön! Gratulierungen!
Amazing . Thank you
:)
12:40 "What are thooooooose" :)
thanks for showing how to do the inverse laplace transform! It really is like integrating, because you know the integral by knowing it's derivative. In this case, you know the inverse laplace transform because you know the laplace transform of the result. Pff haha.
Beautiful. Absolutely beautiful.
Thanks a lot! the way you explained is awesome
love this channel
THE SPICY MEMES MUH BOIIIIIIS!!!!!!!!!!
"That's hard to say .. Laplace Transformation." *Goes on saying it like 12 times quickly without batting an eye*
Thanks for this!
Amazing. I think this technique can be the key idea to previous videos.
for the pdf, you can just do a/(x^2 + 1) + b/(x^2 + s^2) bcz it's just product of linear equations in terms of x^2 so u made ur life a bit harder there
ur not a mathematician, you're a mathematician AND a comedian
Oh yeah? What about the integral from 0 to pi/e of 1?
4:20 Nice and fine? You mean cool and good
Kiritsu lmao
That was a good fight at 3:30. Keep it up.
I just imagine myself at the corner of the room, watching you kicking the air :^D
I love your videos it brings back happy memories from University
Sir you can do the partial fraction work easily by taking x^2=some variable u and can apply the same partial fraction as no x term is present
You can just use this: 1/(AB) = (1/(B-A))(1/A - 1/B) without solving (Ax+B)/(x^2+1) + (Cx+D)/(x^2+s^2) = 1/((x^2+s^2)(x^2+1))
Nais video, specially min 3:00
The general solution is pi/e^a (for cos(ax))
Hahaha, you showed that dominated convergence theorem who is boss!
Where do you bring these solutions from? You're amazing!
Awesome solution!
truly amazing!
That’s right, they are coming for you, but with giant butterfly nets!
I just used Leibnitz's method of integration.
Dude, I'm really interested to domain this theme (the Laplace transform), could you tell, which should be the things I need to study to have good bases when I start to study this heavily?
Cool. I've noticed one thing to simplify.
s/(s²-1) -1/(s²-1)=1/(s+1) =~> exp(-t)
That fight tho! :)
I appreciate the memes, my man. I'd be pleased if you salted my dish, bartender
0:20 whoooaaaah savage mathematian
What about the integral of sinx/(x^2+1) from 0 to infinity? Can it be expressed in terms of π, e or other known constants? I did a little search on the net and I found only numerical approximations to it, not an exact value. Also, trying the same approach as this video, it leads to ln(s)/(s^2-1) and I have no idea what is the inverse Laplace transformation of this one. Any idea if we can proceed from here or do we need a different approach for this one?
Thanks for the immediate response! Appreciated! I really wish you try it if you find the time. :)
Hi :) if you want the exact value of the integral of sin(x)/(x^2+1) from 0 to +infinity you should use the Exponential integral function Ei and then the exact value is just (Ei(1)-e^2*Ei(-1))/2e where Ei is not an elementary function but a special one... and so no results can be obtained in terms of real numbers like pi, e or other known constants. I hope this helps you. Bye :)
You make me miss mathematics courses!
new challenger approaching lol
cool bro
10:50 i have a question. can u realy say that sqrt(s^2)=s? s is a complex number by definition of Laplace Transforms. I dont remember, but maybe it's related to Re (s)
Do it with feyman technique :)
Laplace baked us a pi/e and it was delicious
Oh btw what do you do for a living aside from making YT videos?
Oh, same tbh but with Physics. Keep up mate
Do it again with residu theorem but in only 3 minutes
It is also possible by looking up Fourier transform table
The new smash bros looks amazing!
I love these types of videos
Bro, I love to work with these videos when I understand them, and just watch in awe when I don't. What level of math or physics are laplace transforms taught? Max I've learned so far is Multivariable Differential Calculus and Physics C
At my university Laplace transforms are introduced in Differential Equations because of their phenomenal way to transform high order constant coefficient differential equations into algebraic problems (as long as initial conditions are known). Laplace and Fourier transforms are explored more in depth in higher level (graduate or senior level undergraduate) complex analysis classes.
Very nice
12:00 you could have simplified that further, s/(s^2-1)*pi/2*(1-1/s)=pi/2*s(s-1)/(s(s^2-1))=pi/(2(s+1))
:^> You were on a pretty hard drugs after the 3rd minute, I admire you, Math God.
But is it rational?^^
Me neither :D
Were is Peyam when you need him? Doing something about the Chebyshev boi....
π is approximately 3
e is approximately 3
Therefore, π/e is approximately 1.
1 is rational
Therefore, π/e is rational.
Q.E.D.
;)
@@angelmendez-rivera351 Papa Euler would like to know your location
Such an amazing boi, isn't he? ☻
Hahahahahahahahahahahaha that was a pretty hard fight. ..😂
This is amazing. 😍
This is fucking amazing
Math-ninja-papaflammy is just awesome. Thou avoid some ChuckNorris-substitution if I can say ...
You make great videos man, that really helps me learn new things. I am only the beginner, so could you please give me a clue my can't we change the order of integration so easily? Just tell what topic I need to read, no need to tell the whole story. Thx.
BTW: best animation I've ever seen
Why don't you use lagrange interpolation to find the partial fraction decomposition quickly?
I’ve really loved the fight, don’t get me wrong, but next time, please, be explicit with the measure tools. Or you can just use residue. Nice videos, boi.
Nice. I do think think you risk a hernia from all that heavy lifting. I thought you were just gonna make cos(x) into e^(jwx), recognize this as Fourier transform of Cauchy, set w=1, taste victory, and get drunk.
Soooo coool😍
since you integrate both integrals from 0 to inf I think that is the main reason why order of integration doesn't matter. Correct me if I'm wrong, cheers!
Uniform continuity
+Harry Gross
well of course, without uniform continuity it wouldn't hold.
Not always true
how so?
In some cases swapped limits can 'coincidentally' match when we do not have uniform continuity, in the same way that the limits of two sequences can match without the sequences being inherently related.
Great video
Boy, you rock!