Curl 1 | Partial derivatives, gradient, divergence, curl | Multivariable Calculus | Khan Academy

[@djjdjd470]

This guy is a polymath! He knows everything a student can need . We are fortunate to have him rendering his services free on youtube and also there are no adds! He is truly magnificent

[@TempvsMortis]

Holy crap, before these videos, curl, divergence, and the dot product were just abstract ideas thrown at me in class. I just had to memorize the formulas. Now, they all make perfect sense to me! I couldn't ask for more.

[@kameelamareen]

Man I just don't know how to thank you enough for making me feel that mathematics are extremely logical and very beautiful to comprehend, cheers man and merry christmas

[@fahimahmedbhuiyan2252]

Man I just don't know how to thank you for making me feel that mathematics are extremely logical and beautiful to comprehend.

[@maxdavidsoncox1]

he loves the word intuition

[@RougeSamurai77]

I N T U IT I O N N T U I T I O N

[@tarunramkanuri3581]

M Cox , really man, he uses that word a lot...

[@ethanlevine1935]

if no one has told you yet: you can only perform a dot product between two vectors. Technically, del is not a vector; rather, it is shorthand for an operation (the gradient). However, it is extremely useful to use it as if it were a vector in order to simplify other operations (i.e. div and curl) and that is why we use it there, even though it is "abusing" the notation

[@zachgianikos9543]

And suddenly an entire semester of aerodynamics makes sense.

[@PasanJayaweeraYashoda]

electromagnetism for me

[@jacobschmitt7033]

calc III over here

[@theworldofall287]

engineering maths l 🙋🙋

[@matrixkernel]

Excellent choice of example. I studied the curl in college failed to gain much intuition for it. The right hand rule always seemed kind of ad hoc to me.

[@shabirkabiri]

thank you, you give us intuition that explains all the fundamentals and roots of the concepts.

[@bhaveshsingh511]

all three videoes on curl were superb..your eg under consideration simplifies the topics by great deal, Sir

[@harishli2020]

I wud say its the best explanation on divergence and etc by anyone till now for me... great, please post more videos on fluid mechanics and heat transfer...

[@suddhasattasaha4793]

Amazing content! Excellent lecture on this topic 👍

[@harishli2020]

I wud say its the best explanation on divergence and etc by anyone till now for me... Great, please post more videos on fluid mechanics and heat transfer......

[@Blossoms777]

Thank you so much. You are the answer to so many of my prayers.

[@vaibhavbijapur6037]

"Rate of change in given direction" - this absolute gem, saves a sem!!!!! 😂

[@sparshsarode5470]

thanks a ton... was struggling with the meaning behind divergence... understood completely from previous videos

[@LYNDONisHERE1]

Khan Academy has been my life line against all the professors in this bloody country who are afflicted but acute 'tenure-itis'.... Thank you for your generous and free knowledge !

[@TheSarcasticEngineer]

I love you, Sal =) I was struggling with the wording of my lecturer's notes but you've set that straight.

[@AbhishekNigam]

+ThatDanoBloke Same here, I found it hard to understand the book.

[@Imagine359]

Thank you so much! I can't express how helpful this is.

[@ocayaro]

Good explanation of the physical significance of curl.

[@sarinajm3792]

im not religious but ...God bless you❤😍

[@RyanJensenEE]

such a good explanation. The mathematical definition makes SO much sense now with this intuitive understanding.

[@bbbwind]

Great, Very clear explanation, Thanks a lot

[@ivyzheng8681]

nice explanation ！finally understand the curl.

[@batrarohit1]

Thanks to you, I started laughing out loud in the library when he went on his twig spree.

[@nathanaelsnyder372]

LITERALLY A LIFESAVER

[@thwackspongbelm]

Thanks, Sal. Really helping with understanding these Vector Calculus topics intuitively. How come Del (dot) F(x,y,z) is an abuse of notation?

[@shivampapat7332]

Thank you so mvh sir....helped a lot.✌

[@pikachu_guitar]

God of Teaching

[@solapowsj25]

Dot products and cross products. First steps in engineering electromagnetics.

[@ajaykumarpasupuleti4094]

I think he is same guy from 3Blue1Brown. Any how thank you so much.

[@kaustubhpaturi4801]

I too thought the same thing boi!

[@zakaofficial9226]

Good job! ❤

[@thwackspongbelm]

Ahhh, of course... thank you very much Ethan. And thanks again to Sal.

[@amjedalsadig2647]

Thank you for your hard work to make learning easy for us , I went to your channal but i couldn't find this playlist, i really need to watch this videos can you help me please and sorry for the trouble

[@Nisikto]

Very Clear!

[@donitasz]

Bravo. I really wish you were my teacher.

[@bilawalali3929]

Thank you sir.

[@sprSprEye]

Sal likes the words intuition and twig!

[@d-devlis4055]

thaaaannnk youuu

[@mithunb2717]

I just understood curl in one shot. Thanks. I am trying to download this video, unfortunately half - the best part is corrupt. Any help...

[@mithunb2717]

Mithun BNow I can see, there is no problem.. thanks though :)

[@arunesh3301]

Many Thanks!

[@malithyapa]

this is amazing!

[@bananian]

I can tell from the ugly handrawn graph in the thumbnail that we're back with Khan. 😎

[@simranjeetdhanjal609]

rotation is happening in the xy plane?

[@lhmissio]

OH MY GOD THANKS

[@unotrenpentados]

Gracias.

[@HAWXLEADER]

it is called a rotor too.... like rot(v)

[@oprabin]

oh man! it just saved me from losing the entire semester.

[@jameyatesmauriat6116]

Thank you for explanation but I didn't really find it that clear

[@narongrit3061]

I saw many people pleasure about how beatiful of calculus is but for me It never get in any single of my nerve T_T any recomandation ?

[@trollfootballgeneration8645]

What level maths is this?because I'm in 9th grade and I totally understand this..

[@tuni496]

Intuitive academy

[@randomvideosbyarandomguy2709]

Only college students can relate...

[@ashwinsoni4568]

Legends are watching this in 2023

[@Falcrist]

Newtonian pooh sticks.

[@sunnyRajkarnikar]

i don't understand why every time he uses the del operator, he calls it an "abusive notation". can anyone tell me why that's so. i really hope someone tell me why.

[@iancurtis123]

He says 'abuse of notation'. Using the dot/cross product notation just helps you to remember the formula, but you aren't actually calculating a dot product when you find e.g. div F, you're not projecting del onto F. You're operating on the elements of F 'in the same way' as you would take the dot product of two vectors. So you're abusing (wrongly using) the notation to make things easier. The del operator itself isn't an abuse of notation, but the way grad, div and curl are written with del are abuses of notation.

[@zeffery101]

first thought needs more jpeg, but then realized its from 2008

[@blamemygender1]

@PaulClou no, as if garrison know shit, we'd need mr hat

[@erikhicks6184]

Only 68 comments?

[@nextblain]

damm now i cant concentrate i am just counting >(

[@chaitanyavarma1747]

'lemme draw my twig...'

[@kschwab14]

so much twig in this video

[@simplecrs13]

Are you God?