This is awesome! I remember some years ago seeing a formula that generalized "xth derivatives" for all real number x (negative x would mean integration), and I remeber that it was some crazy integral formula that I gad difficulty understanding where it came from... could you do a video on that? Also, I love the Gamma and the Zeta function, could you do some videos going deepl into them and proving some of their properties? Thanks a lot for the channel
Wait it's actually a real method? I've written this comment as a joke
День тому+1
@@marble17 Yes, sort of. When solving separable differential equations, it's possible to "separate" the dx from the dy and let each be used as separate integration variables. It's a little bit of abuse of notation, but it works because of the chain rule, and it's very commonly done when solving this type of equation.
At university fifty years ago, now I am wondering how many lecturers really understood what they had to teach. It must be good for the lecturers today to discover these videos and learn how to slow the pace to match the capabilities fo their students..? ...maybe the tutors also learn well in the tutorials they give. Love to all mathematics students and lecturers. 🎎🎀📝✅
definitely a much more intuitive way of explaining this than a lot of people have given. this has made me curious though, what if i took the derivative to the power of i of an expression? i suppose it would need to equal the dx/dy of the original expression when multipled with itself
Quite coincidental to think that I have started a few days back to go in depth on fractional calculus and you guys uploaded a video about it. I’m doing physics (not maths) and my intent is to find an approach for coordinate transformation under fractional calculus. It seems quite simple at first glance but there are several issues arising when trying to compute a “half-jacobian” as there exists asymmetry. Maybe one day I’ll find a solution
For a moment I wasted way more time than I intended when I started this video by reading up the wikipedia page of double factorials, but doing that helped me to notice that (2m)!! and (2m-1)!! fit nicely into the formulas of expressing double factorials with just factorials, for even and odd numbers: (2m)!! == (2^m)*m! (2m-1)!! == (2m)!/ (2^m)*m! What I get is: ( 2^2m)*((m!)^2) / ( (2m)! * sqrt(pi) ) Which is not just unreadable, but also likely wrong.
It does exist, for all negatives numbers except for negative integers. I.e. the Gamma function exists everywhere except for Gamma(z) where z is an integer and z
Any recomendations about where to learn diffrential equations with fractional derivatives. I would prefer books as I can read faster than I can watch a video
2:29 ah, i see. How do i do that? Sounds like finding a first order derivative for second order derivative. 4:024:226:48 So the gamma function is the generalized factorial Definitely a little complicated concept, I'd need to practice it. Thank you for sharing. How is this useful? The graph, ok, getting a middle function.
I think prev 2ish vids were familiar topics, so I just went thru them without paying attention. now it's back to pausing often and trying to stay awake in a different way
English nitpick around 11:36 : "They have both merits and demerits" should be something like "They both have pros and cons." (This position of "both" refers to the two formulas and is more natural.) Unfortunately, the English word "demerit" does not mean the same as Japanese 「デメリット」(and this usage of "merit" is a little unnatural). Great video though!
So, what might the formal definition of a half derivative be? I kinda get the generalization for natural numbers in exponential functions, but what about the half derivative of cos(θ)? And, what are the practical applications of the half derivative (given the derivative is slope and the second is curvature)?
Great video once again! This is really easy to pause and keep up with, and the subtitles help a lot. If there wasn’t any animegirls I would be very nervous about that gamma function and how it looks when opened. I did pause at 9:50 to think how on earth can we simplify fraction that has m terms, but I missed the option of doing something m times. That feels almost like cheating. topic request: geometric functions in differentials and integration. Why do they work like that? I never really understood them. To stay true to your format you’d likely have to pick some more complex idea that requires going through the more basic aspects first.
If we can have a half derivative, can we have a negative derivative? Can we have a complex derivative? What's the derivative of the Lambert W function between the values of 1 and e^1/e or between the values of e^-e and 1?
Does it work in the général case ? For sin, cos, exponential functions ? I guess you could use their taylor expansion. Are there functions you can’t half derivate ?
Thinking about the inverse operation, integration, we are left with a "constant of integration", and we have multiple constants of integration for repeated integration, so in fractional calculation, what are the implications for performing a 1/2 integration? What would it mean to have half of a constant of integration?
Constant of integration exists because when you integrate it is impossible to know how high you should start the function, if that makes sense. There is no exact C value if the integral is indefinite, so therefore it's better to think of C not as an actual number but any number ever. (1/2) * C of a certain C value would still be a C value, so therefore I don't think an answer would have 1/2 * C. Not sure though idk
I'm surprised you only did 1/2 derivatives when it isn't much extra effort to generalize fractional derivative. You can even use complex numbers and get the z-th derivation.
Substitute x=1/2 into the integrand, then apply the u=√t (or t=u²) substitution. Simplifying the expression transforms it into the Gaussian Integral, which converges to √π.
@@arthurgames9610 yeah I know. :p You can find plenty of videos explaining how to evaluate the Gaussian Integral, it's too complicated to explain in just a comment.
Похоже, все уже поняли: чтобы стать хорошим агрономом, кулинаром и спортсменом (ну или газовиком, в случае с госпожой Сикокку), нужно хорошо знать математику!☝👀
Just wait until the developers add a quarter-derivative in the next update.
That's just another real number. Boring. How about we do a complex order derivative. The (a+ib)th derivative.
Next update would be i-th derivative. That is, half integration.
Why not find the (Dual Number 0+1e)th derivative? half-joking.
@@soulevans7334 or a + ib)th factorial maybe?
You can already take that from yhis video already. Just replace n with 1/4 instead of 1/2 in the formula
Half derivative is either deriv or ative. Problem solved!
Bruh
Or derve or ivati
*mind blown*
Babe wake up Zundamon's theorem just uploaded
These two anime girls have taught me more complicated shit than my maths teacher.
WAKE UP NEW ZUNDAMON THEOREM VIDEO DROPPED 🗣🗣🗣🗣🗣🗣
thank you once again for the banger zundamon's theorem en! i feel smarter already 🗣🗣🗣
Zundamon @1:28: "I allow it." 😻
Learning real math with 'kawaii' aesthetics is inexplicably adorable!
wtf I love the fractional calculus now
cant wait for discussion about grup theory
absolute GEM
This is awesome! I remember some years ago seeing a formula that generalized "xth derivatives" for all real number x (negative x would mean integration), and I remeber that it was some crazy integral formula that I gad difficulty understanding where it came from... could you do a video on that?
Also, I love the Gamma and the Zeta function, could you do some videos going deepl into them and proving some of their properties? Thanks a lot for the channel
I know it is time to sleep, but Zundamon takes precedence!
Morphocular made a video on this, it's really interesting
IF ZUNDAMON'S THEOREM LOVES MY POST I WILL DO ONE PUSHUP THEN READ THE ENTIRE OLD TESTAMENT 🗣🔥🔥🔥🔥🔥
brb
@@_papa_john What chapter are you on now ?
hey zundamon, metan, can you take suggestions for videos if we have any math stuff we can't understand? I'm sure we'd all love that!
4:36 no way my intuition was right
Lul
Great video as always 👍
Zundamon is bacc
Finally found a good math teacher! Love from 🇧🇹
Me multiplying the d/dx with dx so that i only left out d
Actually that can be a valid thing to do in some cases (separable differential equations), but then you'd have to integrate both sides afterwards.
Wait it's actually a real method? I've written this comment as a joke
@@marble17 Yes, sort of. When solving separable differential equations, it's possible to "separate" the dx from the dy and let each be used as separate integration variables. It's a little bit of abuse of notation, but it works because of the chain rule, and it's very commonly done when solving this type of equation.
Damn, thanks for the new lesson I've learned :)
8:33
when the figures are already smaller then whiteboard started scrolling*
.
Whoa, there's a lot happening here..💀
finally you made a video on fractional derivatives
At university fifty years ago, now I am wondering how many lecturers really understood what they had to teach. It must be good for the lecturers today to discover these videos and learn how to slow the pace to match the capabilities fo their students..? ...maybe the tutors also learn well in the tutorials they give.
Love to all mathematics students and lecturers. 🎎🎀📝✅
I’m in university and somehow I’m learning math above my pay grade 💀
I would never had thought I'd learn maths through a video with anime-like characters. Not complaining tho!
언제나 흥미로운 주제네요. 영상 잘 시청했습니다. ㅎㅎ
일본어 채널도 잘 보고 있어요
tysm to my degree in engineering for making me able to understand Zundamon videos!
Very beauty that Derivatives meets Factorials
definitely a much more intuitive way of explaining this than a lot of people have given. this has made me curious though, what if i took the derivative to the power of i of an expression? i suppose it would need to equal the dx/dy of the original expression when multipled with itself
another quality zundamons theorem upload
The gamma function yields values in terms of the square root of pi for fractions with a denominator of 2 and odd numerator.
There was a video by Morphocular that defined derivatives for all rational numbers!
New Zundamon's Theorem vid dropped, let's gooooo
welp gonna put off sleeping for 12 minutes
A half-derivative is just a spiritual successor. Problem solved.
Quite coincidental to think that I have started a few days back to go in depth on fractional calculus and you guys uploaded a video about it. I’m doing physics (not maths) and my intent is to find an approach for coordinate transformation under fractional calculus. It seems quite simple at first glance but there are several issues arising when trying to compute a “half-jacobian” as there exists asymmetry. Maybe one day I’ll find a solution
Another banger has been dropped
I'm 10% sure I saw comment in a prev video saying to make music less loud
but it's too late. I can't unhear it
I love this I'm exactly the target audience for this lol
New Zundamon LETS GOOOOO
For a moment I wasted way more time than I intended when I started this video by reading up the wikipedia page of double factorials, but doing that helped me to notice that (2m)!! and (2m-1)!! fit nicely into the formulas of expressing double factorials with just factorials, for even and odd numbers:
(2m)!! == (2^m)*m!
(2m-1)!! == (2m)!/ (2^m)*m!
What I get is:
( 2^2m)*((m!)^2) / ( (2m)! * sqrt(pi) )
Which is not just unreadable, but also likely wrong.
Now extend factorials for negative numbers
Won't that just mean integration??
@al-ahsanabhro1070 nah it means finding dx/d
It does exist, for all negatives numbers except for negative integers. I.e. the Gamma function exists everywhere except for Gamma(z) where z is an integer and z
i could learn anything if only zundamon was teaching
Any recomendations about where to learn diffrential equations with fractional derivatives. I would prefer books as I can read faster than I can watch a video
2:29 ah, i see. How do i do that? Sounds like finding a first order derivative for second order derivative.
4:02 4:22 6:48 So the gamma function is the generalized factorial
Definitely a little complicated concept, I'd need to practice it.
Thank you for sharing. How is this useful?
The graph, ok, getting a middle function.
zundamon is back with this one 🔥🔥
Interesting to see x^2, its halfe derivative and 2x do not all intersect in a single point for x> 0. There are only pairwise intersections.
ガンマ関数含む特殊関数の親玉的存在である「合流型超幾何微分方程式」を取り扱って欲しい。
I think prev 2ish vids were familiar topics, so I just went thru them without paying attention. now it's back to pausing often and trying to stay awake in a different way
constantly writing notes to self. 1:54 so "dx" isn't d*x cuz that'd be silly
Now prove this for trig functions
@@化學柒頭 Just write the trig function as a power series and apply this rule to each term
This is a great video! I can’t immediately think of where this might be used. Where can it possibly be useful?
The most adorable teachers are back with a new class ♥♥♥
English nitpick around 11:36 : "They have both merits and demerits" should be something like "They both have pros and cons." (This position of "both" refers to the two formulas and is more natural.) Unfortunately, the English word "demerit" does not mean the same as Japanese 「デメリット」(and this usage of "merit" is a little unnatural).
Great video though!
This was fun to watch! 😊 Are there any practical uses of the half derivative? 🤔
LET'S GO √DIFFERENTIATE 🗣️🗣️🗣️🔥🔥🔥
So, what might the formal definition of a half derivative be? I kinda get the generalization for natural numbers in exponential functions, but what about the half derivative of cos(θ)? And, what are the practical applications of the half derivative (given the derivative is slope and the second is curvature)?
well now i finally know what the gamma function is XD
Great video once again! This is really easy to pause and keep up with, and the subtitles help a lot.
If there wasn’t any animegirls I would be very nervous about that gamma function and how it looks when opened.
I did pause at 9:50 to think how on earth can we simplify fraction that has m terms, but I missed the option of doing something m times. That feels almost like cheating.
topic request: geometric functions in differentials and integration. Why do they work like that? I never really understood them. To stay true to your format you’d likely have to pick some more complex idea that requires going through the more basic aspects first.
amazing video as always
I loved this video, thanks, very interesting
Ok lets be real. How many people are actually watching this because of the math 😂
Half-Deterative? Impressing. Now try Half-Fuction.
If we can have a half derivative, can we have a negative derivative? Can we have a complex derivative? What's the derivative of the Lambert W function between the values of 1 and e^1/e or between the values of e^-e and 1?
Thanks mayonese karaage man
ok now half derivative of e^x please
It's possible talk about the π-th derivative?
Didn't they already make a video like this
Does it work in the général case ? For sin, cos, exponential functions ? I guess you could use their taylor expansion. Are there functions you can’t half derivate ?
The Gamma Function /-_-/
I rember searching what (2m)!!/(2m-1)!! is equal to and I did got sqrt(pi)*gama(n+1)/gama(n+1/2)
So the half derivative of sinx would be -sinx and the half derivative of cosx would be -cosx?
Awesome video
I love this stuff
i wonder if 1/3 derivatives exist
Their extension literally works for any "real number"-derivative
WE STAN
Thinking about the inverse operation, integration, we are left with a "constant of integration", and we have multiple constants of integration for repeated integration, so in fractional calculation, what are the implications for performing a 1/2 integration? What would it mean to have half of a constant of integration?
Constant of integration exists because when you integrate it is impossible to know how high you should start the function, if that makes sense. There is no exact C value if the integral is indefinite, so therefore it's better to think of C not as an actual number but any number ever. (1/2) * C of a certain C value would still be a C value, so therefore I don't think an answer would have 1/2 * C. Not sure though idk
Why not just square it all and get (d/dx) x^2a ?
What about minus-derivative? Is it just integration?
Day 2 of requesting that Zundamon and Metan kiss
can you cover prime number theorems?
Saw this in japaneese too!
when they drop the xth derivative with respect to x🗣🗣
Now what about irrational derivatives?
I'm surprised you only did 1/2 derivatives when it isn't much extra effort to generalize fractional derivative. You can even use complex numbers and get the z-th derivation.
Zundamon wants to know exactly where pi came from!
Substitute x=1/2 into the integrand, then apply the u=√t (or t=u²) substitution.
Simplifying the expression transforms it into the Gaussian Integral, which converges to √π.
@@witchhazel415This is the easy part bro. It becomes tricky when it comes actaully calculate the Gaussian Integral.
@@arthurgames9610 yeah I know. :p
You can find plenty of videos explaining how to evaluate the Gaussian Integral, it's too complicated to explain in just a comment.
I remenbern I watched this vids in japanese. Familiar with the concept I felt like if I already spoke the language
ig at 10:12 it shud just be 2, not 2 raised to m in the multiplication
There are m factors that each need to be multiplied by 2, so the 2 raised to m multiplication is correct.
@brblowgames9251 oh ok tysm
Dude... That's what I call an advanced math. And it's pretty depressing to realize that cute anime girls understand it but you don't😦
Come on bro, if u really want you can learn anything ;)
why did youtube recommend me two anime girls discussing random math problems?
What can half-derivatives be used for?
Похоже, все уже поняли: чтобы стать хорошим агрономом, кулинаром и спортсменом (ну или газовиком, в случае с госпожой Сикокку), нужно хорошо знать математику!☝👀
I like your videos
Im telling you its terance tao. Also whats a derivative anyway i got lost once you started squaring them
Pi jumpscare
Well that was interesting.
How nice
Well, you confused right?
In ODE there is (y')^1/2 and y^(0.5)
You are confusing!
Many people use d^0.5/d^(0.5)x
Instead of (d/dx)^0.5 😂
d/dx f(x) = f'(x)
√d/dx f(x) = √f'(x)
🤑🤑🤑
Zundamon!!!
how did we get that expression at 8:31 ua-cam.com/video/SzNO8q0rlPc/v-deo.html please explain
They are applying the same "formula" twice on the same expression
@@AshifKhan-sn6jx oh hm, guess i needa watch the video again