高斯積分, 積分 e^(-x^2) 中文版, Gaussian integral, integral of e^(-x^2)

[@grogcito]

3:52 for a brief moment I thought I could understand chinese

[@tptangeek814]

Grogcito It's funny when you notice he speak English doing math formulas ;)

[@adls04]

Grogcito XD

[@Ivan_1791]

Grogcito True. xD

[@eddiecurrent7721]

just like 14:14

[@JohnSilvavlogs]

It is just beautiful how math is such an transcendental language. I don't understand a thing in Chinese, but it though I was fluent while waching your video. Congratulations mate!

[@juanquiroa7062]

I just love how you clearly have fun with this channel and mathematics in general, it's great!

[@blackpenredpen]

Juan Quiroa thank you!

[@Invalid571]

I don't understand your language but I did understand what you were doing. Great solution.

[@PLSGuitar]

I understood approximately 0% of this.

[@red_paradise]

I didn't even manage to understand that much.

[@arnavanand8037]

_Cuz you dumb_

[@-Quasar-]

*𝒩 𝑜 𝒯 𝒽 𝑒 𝓎 𝒥 𝓊 𝓈 𝓉 𝒟 𝑜 𝓃 ‘ 𝓉 𝒰 𝓃 𝒹 𝑒 𝓇 𝓈 𝓉 𝒶 𝓃 𝒹 𝐼 𝓉*

[@MrCigarro50]

This integral is very important in statistics. But watching it in Chinese looks far more interesting. Thank you very much.

[@blackpenredpen]

1:33am. Good night people!

[@estebancanizales3303]

blackpenredpen thank you for all your videos

[@blackpenredpen]

Esteban Canizales thank you!!!

[@samuelminea5520]

blackpenredpen hello, blacpenredpen, you are assistant professor at university or highschool professor? Thx.

[@hgaclark9031]

blackpenredpen Hi I'm an a level student and did a question recently where I had to differentiate (1/(sin2x-cos2x)^2+2sin2xcos2x) but ended up getting zero! Could you help me? I feel I used all the rules correct but should it be zero? Thank youu

[@abranbsingh1024]

couldn't u produce the same in english?

[@jackhavenar4526]

He's only doing this because a guy told him to "learn how to speak English." Pro-revenge. :)

[@s94285]

雖然微積分還沒教到這，不過原來您也是台灣人 之前看的影片真是讓我獲益良多

[@blackpenredpen]

謝謝收看喔!!!

[@blackpenredpen]

柯廷諭 ：）

[@learnit2369]

@@blackpenredpen 我仍然不喜欢说中文，但我仍然喜欢这个视频。sorry if google translate did any mistake in translating.

[@doktorklaus300]

The mathematical language being clearly written and represented, it does not matter the language to explain; everything remains completely understandable. Once again many thanks Blackpenredpen.

[@TNThung]

英文聽久了 聽中文好不習慣😂 不過依舊教的很好👍👍👍

[@tom13king]

I keep hearing 'finite value'. What could that possibly mean in English?

[@blackpenredpen]

tom13king finite value. Lol

[@applealvin9167]

He said “finite value” in English in this video😂

[@andyshen553]

以一個完全沒學過極座標轉換的學生，我覺得你已經解釋的非常好了～ 用很「卡通般」的方式教學的很好👍👍👍

[@ZackSussmanMusic]

我在学习中文我也觉得你的video很帮助。谢谢 ：）

[@tim5279]

加油我在學習英文哈哈

[@JoeSneeky]

The moment when you realize that you skipped math class too often.

[@Koisheep]

In Spanish this is even more funny because "it all sounds Greek to me" translates as "me suena a chino" ("it all sounds Chinese to me")

[@企鵝-c3g]

哇！！謝謝你 我在這題想好久一直不懂為什麼換成y之後也等於Ｉ 非常感謝你！！！

[@General12th]

I don't understand a word of Chinese, yet I understood what you were doing, and I could do it myself and show others. Isn't math amazing!!!

[@matthewminsberg5754]

How do you say "isn't it" in Chinese?

[@鍾承恩-i6y]

Ian Chu Te In this case, 不是嗎 是不是 好不好 對不對 etc. are correct

[@鍾承恩-i6y]

Ian Chu Te Chinese is a causal language. I think it's much harder than Chinese. Even though I am Chinese(Taiwanese).

[@鍾承恩-i6y]

Ian Chu Te 你是中國人喔 我也是中國人 但我來自台灣這個地方 對了澄清一下 中華民國才是有爭議的國家 台灣只是個島

[@theonetheycallbo]

i use 真的嗎

[@kaoutarru4619]

Dui ma

[@joonah7316]

Im studying chinese. This actually was a really good exercise for me to try to understand

[@彭淳枻]

很清楚簡潔又有趣

[@blackpenredpen]

謝謝~!

[@stevesun11001]

双重積分 = e^-(x^2+y^2) 曲面下的體積 = e^(-r^2) 繞 z 軸旋轉 2pi = Integral e^(-r^2) 2pi r dr

[@John.Kaiser]

Todo me quedo claro, la explicación en chino lo hizo más fácil de entender.

[@WeijerChi]

第一次看到你在這個頻道說中文的影片XD

[@NishanthMoolam]

great video, but whats with the death star mic? ?

[@TCLTCLee]

老師您好： 請問影片一開始提到 e^{-x}積分收斂而且比e^{-x^2}小～ 可是， e^{-x}不是會跑到inf當x趨近-inf嗎？ 還是老師說的是e^{-｜x｜}，有加絕對值? 可是如果加絕對值，在0

[@劉韋伯-g8l]

您是台灣人嗎？一直有在看你的影片到偶然間看到這部三年前的影片，現在才知道你會說中文，拜見高手！

[@kevincaotong]

从今天的视频又看到了这个，真有趣！看到这个视频真想学习数学的中文词汇，好教一教我的哥哥 😂。请问，您有没有去过中国或台湾学习过数学？您的中文超级好！我中文讲得好，但是数学词一个也不知道！

[@吳旻徽]

我看了這個頻道的其他這麼多部英文微積分 才發現原來他會講中文 這感覺也太酷

[@PeachWorkingout]

thanks for your explanation into great detail~ 講解的很詳細！

[@arandompersononyoutube3739]

Is there English version of Gaussian integral from blackpenredpen

[@flornotlikeyou]

This is a beautiful demostration !!!

[@blackpenredpen]

Thanks!

[@まつまつ-x1f]

超級清楚的解釋!! 感激不盡

[@grant19960615]

讓我猜，您來自新加坡？你的影片真的很棒，我超喜歡。

[@blackpenredpen]

邱子軒 偶是呆丸狼啦！

[@grant19960615]

oh wow! pleasure!

[@blackpenredpen]

= )

[@MLnyamada]

Other video linked in description was unavailable, so I clicked the other one and now I'm here, having a calculus class in mandarim is not that different from standard calculus, I can't still understand what the teachers says, but at least I understand what's written

[@kazdono8646]

听曹老师讲中文很神奇的感觉

[@hsinchen4403]

太感謝了！講的超~清楚！

[@李疾風]

我第一次看到這個頻道就覺得老師有點像台灣人 現在偶然看到這部 還真的是XD

[@applealvin9167]

跟我一樣XD

[@KimuraSetsuna]

老師.....我....我!!!!!!!!!!!!haiz....I love your video....I enjoy this way of learning more then reading the textbook now....

[@birupakhyaroychowdhury974]

We can also use the Jacobian....

[@doxo9597]

Usually in his videos i don’t understand anything. This time i understood less than nothing.

[@昇翰-l7o]

Awesome instruction

[@马思园]

very clear solution! Very Beautiful!

[@woilymom]

很棒， 讲的很好，终于厘清了。

[@DaanSnqn]

I'm guessing 'pingfang'is the Chinese word for 'squared'.

[@yinchenxu5249]

No, It means ping-pong (kiddingXD)

[@DaanSnqn]

许崟琛 He must really like ping pong then since he says it a lot 😅

[@鍾承恩-i6y]

1234Daan4321 yes "平方" means "square"

[@DaanSnqn]

同志們想想社會廢死的都是廢物 Nice thank you 😄 I'm actually learning random Chinese words from a mathematics video

[@adls04]

Tell me how to pronounce those lines in romanji not everyone has a chinese keyboard

[@hrd_cld_drn]

Ohhhhhh… I don't know you can speak Chinese!!! 我之前都看你拉式轉換的影片自學誒 感謝你～

[@seroujghazarian6343]

What proves it is +sqrt(pi) and not -sqrt (pi)?

[@obinator9065]

Well, just look at the graph of e^-x^2, e cannot become a negative value(excluding complex nums), so the area is positive.

[@soup6941]

好淺顯易懂 很讚

[@xing_831]

听习惯你的英文影片，突然看到中文版会吓到，不过声音很好听😀

[@abc15500]

講得很好,感謝!

[@靳歙-q9w]

10:52若它的上下界是X~1怎辦

[@kibayuuto6634]

Yes you did everything right and I understood everything

[@Mau365PP]

Where's the english version?

[@bluebloo5574]

上到大學才知道數學的美。

[@blackpenredpen]

我以前也是啊!

[@呂永志]

曹老師好！請問您如何決定哪幾題是用中文講解，我倒是覺得可以不用那麼多中文版。

[@blackpenredpen]

呂永志 欸..就是看感覺欸 哈哈

[@anitachen-fq3eo]

超棒的謝謝

[@黃柏洋-o8c]

what the answer isn't +sqr(pi) or -sqr(pi) ?

[@oKrybia]

A curva da função fica acima do eixo x. Logo, o resultado da integral deve ser positivo.

[@weiboliu6095]

e^-x 在 -inf 到 inf上的积分不是有限的呀 宝贝儿？

[@王明-c4q]

非美漂亮的证明

[@Kmrabhinav569]

Hello there, why did you take a function in 'y'? I didn't understand

[@vaughanwilliamson173]

Whilst not being certain of where you didn't understand, could I venture to offer some comments. Firstly, taking the integral with the variable y shows that the result is the same, that is, the "I". Even if the variable to be squared in the exponent was "mickey mouse" and the integral involved d(mickey mouse), you would still have a result of "I". Call the variable whatever you like, but you will still get the same result - "I". Secondly and I think most importantly, it allowed the development of two "I"'s on a cartesian plane to allow for an eventual result. So the function with variable "x" is drawn at a 90 degree angle to the function with variable "y". When integrating each alone, they will give the same answer - "I". But multiplying the two integrals so we have "I"^2, which allows a way to the solution via essentially a rectangular to polar conversion. After the multiplication, and a quick manipulation of the powers of e, the exponent to be integrated was x^2 + y^2 . Of course we now have the double integral with respect to dx and dy. Recognizing that dx X dy = d(Area), and that the (x,y) point drawn can be expressed as a vector of magnitude r at an angle of theta anticlockwise from the 3 o'clock position, by a change of variables, the integral can be expressed in terms of r and theta where dr X d(theta) also gave a d(Area). So, by Pythagoras's Theorem, r^2 = x^2 + y^2. The two infinitesimals, dx and dy in the rectangular coord system change to r X dr X d(theta) in the polar coord system. With the change of variable, also came the change in the limits of integration, so the limits of r became 0 to infinity and limits of theta became 0 to 2 X pi. And after this, a solution for "I"^2 was determined and so a solution to "I". The above is my understanding of the process of solution and the need for the variable "y" and am open to correction. I have no ability with language other than English, however, as with some others, I also feel that I was able to follow our lecturer's arguments. Well done again blackpenredpen.

[@Avivalious]

讲的很可爱啊 赞

[@not_vinkami]

你的頻道好像幾乎沒有聽得懂你說話的人XD

[@p1997528]

聽得懂得來報到了

[@waifumk2384]

笑死 我一開始也是從他的英文影片認識他的

[@applealvin9167]

一開始還以為是華僑之類的😂

[@ritamdutta5860]

I dont know, chinese.. can anyone please help me?.. how did we get that line at 4:41

[@abranbsingh1024]

this video not being in english really broke my heart! lol

[@Koisheep]

The only question left is. Is this pinyin or a regional language? (I must have said it wrong but I'm a stem mayor I know like -inf about linguistics sorry)

[@humanppplus4306]

Konhat Lee Sakurai first, lemme correct a mistake of u pinyin is the equivelent of phonetic symbols in english so its not a language/dialect now getting back what he said, is mandarin 普通话 (standard chinese) but with some taiwan accent

[@obinator9065]

Pinyin is chinese writing system in latin

[@jishnugangadharan9677]

Started learning Chinese ✌✌

[@jinhuiliao1137]

Can we substitute dx with d(rcostheta) and dy with d(rsintheta)?

[@prydin]

I was waiting for an "isn't it" in the middle of all that Chinese... :)

[@Hacker118]

是中文,但你的普通話比較差 It is Chinese~ but your Putonghua is so broken

[@blackpenredpen]

不是broken, 是少用普通話教數學

[@Hacker118]

@@blackpenredpen 我的英文真的 broken 了

[@eneapane5831]

And I absolutely agree.

[@muneebahmed1848]

Beautiful language

[@s89072830]

It's so helpful ~

[@xdemao]

曹老师 太帅了

[@土撥鼠-r4g]

厲害

[@akinakinlolu2519]

Blackpenredpen speaking in Chinese HEEEEEEEEEEEEEYYYYYYYYYYYY. So cool. I understand it but I am a bit selfish redo the video in English PLEASEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!

[@DarkMage2k]

The dark days of bprp that history can't uncover easily

[@2688jojo]

想聽曹老師講解jacobian

[@靳歙-q9w]

supreme 好野人

[@AutroYou]

I somehow understood it without even understanding what you were saying lol

[@imanolmanzanares5000]

i only understood "okay" but nice video bro!!

[@調皮管家機器人]

請收下我的膝蓋 豪有料

[@KeNsHoRt47]

when the whiteboard starts speaking chinese

[@РоманИост]

それは可愛い!　P.S. 僕は日本人

[@lanhoiw]

請問積分(x^2)*e^(-x^2)求解?謝謝

[@estebansanches4236]

i cant speak english good but i understand the language of mathematics.

[@haohaolee9474]

牛逼 老師你哪裡人啊

[@applealvin9167]

From Taiwan

[@AnuragKumar-io2sb]

I understand ok😊

[@joseromero-ns6cj]

13:23 finally able to understand something :p

[@吳睿玹-h9m]

你好，請問影片內容中老師將x^2+y^2=r^2是甚麼意思呢?

[@Superman37891]

I just saw a video on this on another channel like 2.5 hours ago

[@austinyen1943]

太強了

[@ankushsingh4614]

What language is this?

[@rafaeldearaujo12]

A language between canadian and cucumber

[@paulraj7573]

answer seems different from that of english version.

[@ccg8803]

I'm only able to say... yesh, nonono. Yesh

[@jinzhanghsu4253]

哈哈為什麼中文講起來有點可愛的感覺……

[@林和陞-d9s]

還是聽英文的比較習慣哈哈!

[@AthamAldecua]

Hahaha I can still understand quite a bit of mandarin!

[@-AMdImranAli]

Can you make the video in English

[@ananyapathak8701]

The language common in you and me is *math*

[@andresxj1]

What happened to the english version?

[@blackpenredpen]

Peyam will upload that on his channel

[@kimchikoalaa714]

Mmmmm, sounds way better

[@靳歙-q9w]

13:39這行怎來