[Eng Sub] √(-1)-th Derivative | Fractional Calculus
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- Опубліковано 6 вер 2024
- Half Derivative: • 【半微分】微分の世界との間に存在するらしい「...
[Correction] At 7:50, it was necessary to multiply by -1 during the integration with respect to t. This does not affect the overall explanation. Sorry for the confusion.
In a previous video on half derivatives, we explored the introductory world of fractional calculus. In response to a request, this time we will delve into imaginary-order derivatives and explore the world of fractional calculus in more depth.
In addition, we use the terms 'non-integer order' and 'fractional order' interchangeably. In fractional calculus, not only rational order but also real and complex orders are considered, but conventionally, the term 'fractional' is used.
[References]
arxiv.org/pdf/...
www.mathpages....
[BGM]
ほのぼのワルツ【リコーダー】(commons.nicovi...)
[Materials]
VOICEVOX:ずんだもん
VOICEVOX:四国めたん
立ち絵(坂本アヒル様)
効果音ラボ
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#math
#differential
#differentiation
![[Eng Sub] What is e to the Power of d/dx? | Shift Operator](http://i.ytimg.com/vi/INTKzi0qXpY/mqdefault.jpg)
![[Eng Sub] What is e to the Power of d/dx? | Shift Operator](/img/tr.png)
![[Eng Sub] Formal Derivative: Differentiating Something That Diverges to Infinity](http://i.ytimg.com/vi/SGllxZ3WNkA/mqdefault.jpg)
we need anime girls in en math videos this is revolutionary
Yo, Azali. I never expected to see you here, holy moly.
AZALI?!
hi azali
it is
And I thought getting recommended a Japanese calculus video was weird enough
I can't believe a 14 minute video of two anime girls talking about math in Japanese changed my whole worldview about Calculus. I feel like I've witnessed the true form of the derivative now. Thank you so much.
Learn math and Japanese at the same time,
What a great service!
That way I can *really* not understand whats going on 😂
I guess this is what I get for mainly watching STEM videos and Japanese learning videos lmao...guess the algorithm decided to combine the two
Think this got recommended to me by my math and anime interest
Math VTubers, what a time to be alive.
if there can be java tutorials on pornhub, i see no issue here...
Thank you for including english subtitles!
定義が複数種類あるとはいえ、従来の性質を満たしつつ上位互換として定義したものは、補間する様子が美しい…
三角関数のα階微分で位相がずれるの、めっちゃおもしろい！
I love that insight at the end, it reminds me of the exponentiaion of i
i^0 = 1, equivalent to sin
i^1 = i, equivalent to cos due to being a 90 degree shift
i^2 = -1
i^3= -i
and so on...
AND
i^a/b = rotation of (a/2b)pi, a perfect way to rotate a rational fraction of 360
It is because
i = e^(iπ/2)
and therefore, from exponent rules:
i^x = e^(i x π/2)
If you know Euler's formula, it is a very simple calculation, but it was fun to see i^x going in a circle when trying it out on the calculator for the first time.
@@kappascopezz5122 I'd argue it's the opposite relation. Pretend you don't know Euler's Number/Napier Constant: e, for a moment. In a R2 grid (and arguably, through intuition in the R number line by itself) the (-1) Multiplication is a 180 degree rotation, right? Then in R2 with i as the unit in one of the axis (or as one of the basis vector), the definition that multiplying by i twice (i^2 = -1) yields a 180 degree rotation implies that multiplying by i is a 90 degree rotation. Likewise i^3 will be a 270 degree rotation i^3/2 will be a 135 degree rotation, etc. AND i^x= a rotation around the unit circle
First time I realized that exponentiation of i is a rotation was so mind-blowing.
複素空間への拡張ってこうして見ると恐ろしく強力なツールだよね
そのままでは統合できない数理的な次元を複素空間での角運動量１つで統合できてしまう
This channel is such a gem!!! Combining anime and maths so smoothly and cutely, can't wait to see it grow!
Anime girls explaining calculus? Listening rn
we're poor af to pay attention to class so this is the alternative we need 😂
I never thought of explaining maths as a dialogue between two characters, but this is really well executed.
Well, the famous video about turning a sphere inside out is done like that
I love your teaching style! I had barely understood fractional differentiation prior to watching this video, but you presented it in an intuitive way. The modeling of extended sin differentiation as phase shifting at the end was also really fascinating, I never made that connection until now
複素数に虚数単位iをかけると複素数平面上でその座標が90°ずれるように、三角関数のα階微分が位相の変化を表すのが興味深い……
日本語をよくわかりませんですから、サブタイトルをありがとう。このビデオは本当によく作りました。
In Japanese, subtitle is "字幕（じまく, zimaku）"
@@richard-gj8fs Thank you
三角関数の非整数回微分の話はなるほどなと思いました。いつも面白い動画をありがとうございます。
Math + anime girls
Winning combo
いつも通り数学の面白さが爆発してる
I can barely comprehend why this is so interesting thank you!
When the shift of trig functions is mentioned, things suddenly get more clear. Thanks for another interesting and informative video!
1/2回微分が出たと思ったらすぐ拡張するな
韓国の高校生ですが、とても興味深いです. 本で読むよりはるかに良いようです。しかも可愛いキャラクターもいっぱい！満足です. 文法が合っているかわかりませんが、良い映像ありがとうございます。
三角関数の非整数階微分の話、面白いし納得感ある
次は微分作用素回微分作用素を作用させるか
I didn't understand a single word but I liked it
this video was surprisingly good. like it is better than other videos on this topic on youtube.
日本語も微積分も良く分からないのに、なぜか今見ている。。。
類似のコメントはありますが、次は行列（テンソル）階微分を聞きたいです。
雖然不懂日文，但還好有英文字幕，很棒的影片👍
解析やってるとコーシー君を色んなところでお目にかかれる
Cauchy and Euler. When i see differential equations i see Laplace, Fourier and Lagrange for Extrema and Extremals.
こういう「それっぽい拡張を作ろう」は数学研究の大事な手法のひとつ
三角関数のα階微分が位相変化に留まるの, 微分演算子をかけることを考えたらとても自然でしっくりくる.
どこに行ってもリーマンが出てくる現代数学…
Me when university math: 😴 🥱
Me when Zundamon math: 😮😯😲🤯
フーリエ級数にしてから考えればイメージ湧きやすいよって事ですね
I don't speak Japanese but from what I see at the beginning they are talking about the integral derivative of riemman liouvulle..
理系ずんだもんかっこかわいい
I loved the part with the trigonometric functions where you explain that our world of calculus was just part of a much larger world. Beautiful
最後に出て来た別の定義式だと、複素フーリエ級数展開できる関数は全部行けるってことか。αが実数の範囲だと工学的な意味がイメージ出来ていいな。
その定義の場合αに複素数が入ってくると、回転と拡大縮小が入れ替わるのかな。回転と拡大を入れ替える事に何の意味があるのかは想像つかないけど、どういうものかだけはイメージしやすくて嫌いじゃない
i really didn't expect to see such a specific subject which i'm interested in way too much and which i also can't find the works/interests of the other people on,on a video explained by anime girls.
this is something else.
Finally got the kind of content I tried to optimize my youtube recommendation for!
Such a niche video, combing both higher level math discussion and anime girls talking about it. I’m glad to see it! The two characters having dialogue actually helps a lot, a lot of math videos are just, “here’s a math concept” without much flair, but this opens the door to potential confusions or surprises that are worth mentioning. For example, I’m sure it’s more clear to some that numbers like 1-i are partially real and partially imaginary (literally having a “real” part with 1 and an “imaginary” part with i) but I considered it as *just* an imaginary number before, since that’s how I’ve needed to work with it in the past through my college classes. Hearing these two talk about it really helped me with comprehending it better. A lot of this video is far above my current level of understanding, but I am happy to still get a lot from it!!
これは、凄い！！高校時代に、三角関数の加法定理はあるなら、三角関数の乗法定理は無いのかいろいろ計算したことがありましたが、Sin(ｘ＋Πα/2）から、何やらヒントになりそう！X=0を代入したらダメかな？
We need more! Today was my Calculus II exam in my university and This anime girl had thaught me "Cauchy's integral formula", so I got a nice score!
Thanks for this innovative format, _domo arigato gozaimasu!_
I had seen the idea of continuously varying the order of the derivative to smoothly change from one function to another. The video I saw showed a polynomial varying between x^3, x^2, and x as the degree of differentiation was changed through non-integer values. That felt a little arbitrary to me but explaining it with sines like at 13:10 made it so obvious
THAT WAS SOOOOOOOO AAAMAAAZIIIIING! I had to stop every 10 seconds and get my MIND BLOWN! It is now a puddle of white goo, but it was worth it. I have to show this to a math teacher!
大好きなずんだもんと先取り学習しちゃおうと思ったけど先取りすぎて何やってるのか分からなかったw
Very good video. I feel my brain expanding
I thought it was a VTuber skit, but it's a real deal maths channel... Thank you so much!! My fears for college decrease with every resource I find.
In other day we got only fans teacher who teaching math. Now we get anime vtuber who also teaching math. Let them cook. 🔥🔥
拡張は楽しいねえ
位相が90°単位じゃなくて半端にずれるのなるほどなー
that repeated integration would have been easier to follow using induction, just saying 😅
btw I love zundamon 😭😭😭😭
It's been a hot minute since I last took Calculus and differential Calculus was too much of a last minute whiplash after barely getting integrals down for me to do much other than barely pass, but I would have loved this at the time. Even without the plus of two cute girls explaining it in 日本語, it's gentle enough to me to learn on the side without the pressure of having to pass.ありがとう！
i'm not sure how i got here, but i like math so i welcome these videos with open arms ^^
Thank you very much for this video !!
Unimaginable that even using the basic integral and differential definition,we can understand the whole process.
this is actually so well put together, ty!
I know Zundanmon is famous for delivering interesting trivia, but never will I expect in my life her delivering advanced math, so this is a pleasant surprise!
That sine result at the end is one of the coolest things I've seen in a long time!!!
数学と日本語の勉強、二つの僕の好きな物 草
ちょとした応用
L=lim (ⅹ→0)
D=d/dx
D1=(1/D)^s xのs階セキブン(s>1の非整数 これは、UP主様の『1/2階微分』で私がコメ欄でコメントさせてもらっています。)
D2=D^m m=0,1,2,3......
P=exp(x)/(1+exp(x))
リーマンゼータをζ(z)
η(z)=(1-2^(1-z))*ζ(z)
とすると,
η(s-m)=L*D1*D2*P
が成立します。
個人的には、LDP=自民党
による、解析接続と名付けています。
連投をお許し下さい。(蛇足です。)
上記が成立する背景(発端)は、
① log(1+u)をマクローリン展開する。
② u→exp(x)をブチ込む。
③ Aha!
です。
③をxでビブンするとPになる。
もしくは、
Pは初項=exp(x),公比= -exp(x),
として,無限等比数列の和の公式
に代入する。(Eulerの方法)です。
ここまでくるともはや複素正則関数以外は相手してないって感じがする。
I think i got lost somewhere at the complex extension part
That was fascinating!
これは最高です。大好きですｗｗｗ
ive never thought of proofing the derivative of trigonometric functions using euler's formula, truly fascinating
well it's an extension because as far as I know you can't derive Euler's formula without being able to differentiate sine and cosine.
Hi ! From French ! -- > Cette vidéo est sympa , vraiment atypique mais sympa .
This might actually help me for my college entrance exam
Not about the imaginery differentiation and stuff but being able to express multiple integration into one integration actually might be used to reduce time thx!
my brain has expanded by 5%.
Zundamon soltando la matemática prohibida, que buen video.
I love using the two characters to teach using the Socratic method. I wish it was used more often.
How is it that I’m doing a math PhD and have never seen this? Incredible
the purple one is quite brilliant
neuron activation
Man, this UA-cam's algorithm is getting better. Some nice recommendations lately, though I know just a handiful of japonese words (listening them only), there is an english sub to my aid. Thanks, whoever created this and YT.
Great video. Very informative. Grettings from ITA brasillllllll. Is the purple one single?
Good work ! Can't wait for new videos of this type 😁
3Blue1Brown's been real quiet after this dropped...
what an amazing video
i didnt understand a single word, but i could keep up with the ideas you presented
this was a new experience
loved it
I don't know why I have seen this but I enjoyed it
初見です! ずんだもん数学すごい分かりやすかったのでチャンネル登録させていただきます( . .)"
From Canada with love 💕 this is great I immediately subscribed
UA-cam reccomends me this, and i watch it. What had my life come to.
積が反交換関係で結ばれてるとき、
積分の順序が交換されたなら、
積分は反交換関係になりますか？
my mind was blown multiple times wow. awesome vid
Where did I land?
Brother I am in the same situation 😂
微分積分学のずんだもんビデオ、絶対にないわけないだろじゃん！
Ah, sehr interessante Präsentation. Bei uns wird Mathematik im Regelfall von unterqualifizierten Pädagogen (Schulmathematik), oder von unterbezahlten, oft älteren Herren (Universitätsmathematik) unterrichtet; da ist diese fernöstliche Kunst eine mir willkommene Abwechslung!
Beste Grüße aus Deutschland
Imagine you're playing a random jpn rpg videogame and you get stuck in this😂😂
Ютуб рекомендации, блин, куда вы меня завели... Аниме тянки под кафную музыку обсуждают математику. Мммм... Не останавливайтесь, мне нравится
1. Can we generalize this for e.g. nonstandard analysis or vector calculus?
2. Are there any comprehensive resources for solving ODEs involving fractional derivatives?
gamma function: domain expansion, imaginary numbers
Merci d'expliquer cela, votre chaîne est incroyable !
So i have to read subtitles while trying to understand this complicated math...fine
Those girls are the smartest 4th graders whom I've ever seen!!
you never answered that one brazilian guy as to whether the purple one is single
Japanese vtuber math videos? did not expect that
i’m guided here from a game discord (exponential idle, which has a part that explores fractional integration), and I can’t say I’m disappointed. made me understand more (though not sure if it helps, since I don’t have a good foundation. guess I have to watch your other videos
anime girls really do make many things better