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.
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
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.
@@kappasphere 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
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!!
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.
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
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!
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!
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!
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。
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.
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
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!
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
なんていうか何でも複素空間に押し込めてしまえっていう
「雑さ」を感じる瞬間はあるんだけどね
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
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
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
This channel is such a gem!!! Combining anime and maths so smoothly and cutely, can't wait to see it grow!
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.
@@kappasphere 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.
いつも通り数学の面白さが爆発してる
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。
I can barely comprehend why this is so interesting thank you!
Math + anime girls
Winning combo
三角関数の非整数階微分の話、面白いし納得感ある
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……
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
When the shift of trig functions is mentioned, things suddenly get more clear. Thanks for another interesting and informative video!
Unimaginable that even using the basic integral and differential definition,we can understand the whole process.
次は微分作用素回微分作用素を作用させるか
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.
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
どこに行ってもリーマンが出てくる現代数学…
this video was surprisingly good. like it is better than other videos on this topic on youtube.
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!!
3:35一様収束する関数でのみ定義されるのかそうでない関数でも定義されるのか…
I didn't understand a single word but I liked it
Thanks for this innovative format, _domo arigato gozaimasu!_
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.
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.
雖然不懂日文,但還好有英文字幕,很棒的影片👍
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。。。
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.
Me when university math: 😴 🥱
Me when Zundamon math: 😮😯😲🤯
That sine result at the end is one of the coolest things I've seen in a long time!!!
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
From Canada with love 💕 this is great I immediately subscribed
Very good video. I feel my brain expanding
Finally got the kind of content I tried to optimize my youtube recommendation for!
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
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。
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
this is actually so well put together, ty!
Thank you very much for this video !!
1/2回微分が出たと思ったらすぐ拡張するな
Good work ! Can't wait for new videos of this type 😁
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!
Anime girls explaining calculus? Listening rn
we're poor af to pay attention to class so this is the alternative we need 😂
これは最高です。大好きですwww
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!
That was fascinating!
I love using the two characters to teach using the Socratic method. I wish it was used more often.
Hi ! From French ! -- > Cette vidéo est sympa , vraiment atypique mais sympa .
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
my mind was blown multiple times wow. awesome vid
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!
the purple one is quite brilliant
拡張は楽しいねえ
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( . .)"
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
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.
How is it that I’m doing a math PhD and have never seen this? Incredible
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!
Merci d'expliquer cela, votre chaîne est incroyable !
位相が90°単位じゃなくて半端にずれるのなるほどなー
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。
数学と日本語の勉強、二つの僕の好きな物 草
Very nice !
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?
I think i got lost somewhere at the complex extension part
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。
Japanese vtuber math videos? did not expect that
Zundamon soltando la matemática prohibida, que buen video.
UA-cam reccomends me this, and i watch it. What had my life come to.
Espero con esto animarme aprender más matemáticas.😊
This is awesome
that repeated integration would have been easier to follow using induction, just saying 😅
btw I love zundamon 😭😭😭😭
I like this a lot. 👍
Is this voicevox? Always impressive voices
i'm not sure how i got here, but i like math so i welcome these videos with open arms ^^
So i have to read subtitles while trying to understand this complicated math...fine
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
The girl on the right is really cute nano da
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
何この魔法
I listen only for their voices and do not care about what they have to say at all...
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?
3Blue1Brown's been real quiet after this dropped...
i don't mind the anime girls. i do with we got graphs or something tho and neat visuals like a 3b1b video
My eyes are bleeding. Integration is a right inverse of derivative, but it's far from being unique.
この分水階微分の公式の下限は関数fの零点や刻限が零になるcを選んで計算すればいいです。だから多項関数はc=0、指数関数はc→-∞なんです