Stokes' theorem intuition | Multivariable Calculus | Khan Academy

[@Ali2475]

In class this made me experience something which I would define as "brain death." You're my resuscitation, Sal.

[@IamFilter94]

I'm so Stoked my dudes

[@holycrapitsachicken]

Turn round for what?

[@agrajyadav2951]

@@holycrapitsachicken curl it man

[@devikabsree8087]

This is the most outstanding explanation of Stoke's theorem. So clearly explained. Thank you so much.

[@gabeham7532]

cap

[@lambda5949]

cap

[@panikostiritas5216]

Crazy how 3 hours of lectures amounted to me retaining 0 knowledge. Then 10 minutes of this and I understand it like crazy

[@Edgarisftw]

Just goes to show there is a difference between teaching and teaching. Many students, myself included, learn much more from these kinds of videos with a good visual compared to a fast talking teacher stressfuly cluttering on the board.

[@rowanyardley1781]

@@Edgarisftw also probably help that people have had that previous amount of teaching. This 'learning' essentially amounts to consolidating some misconceptions to most people

[@sudarshanseshadri5504]

Hours of reading the book and listening to prof lecture and this 10 mins was more effective than all that. And it’s not like Sal had the online video advantage - my prof also recorded and posted his lecture. Sal really has a gift.

[@kal5991]

30% of my exam for university 2 weeks ago was on stokes and greens theorem. Thank you so much for these videos :)

[@EldonSchoop]

When I took multivariable calculus, I never got an intuitive understanding of Stokes' Theorem. Now I do. Thanks, Sal. :)

[@coco_jae]

wow... finally, i understand the stoke's theorem.

[@bawol-official]

My final exam is in a week, I just got assigned homework for the sections on Vector Field, Green’s,Stokes, and Divergence theorem . Pray for me.

[@amandaferguson6901]

Wow I came here for Stoke's Theorem and I get an actual explanation of curl also

[@sbullock2976]

Wow. The simplicity of this explain blew my mind! Great video.

[@lordfieldsworth595]

Never have I understood this so well. Khan Academy strikes again

[@ParthPaTeL-wm3kt]

This is best video about stokes theorem in whole KZbin, Great, thanks dude

[@robromijnders]

Sal, you're a genius. Thank you!

[@battleangelgally7548]

Oh My Goodness! All those equations have suddenly started to make so much sense... Thanks a lot Sal!!!

[@elizabetheckenrod2203]

And now I can pass my final... Bless you, Khan Academy!

[@carmelpule8493]

I am now an old man and over 65 years ago I saw it all in this manner, The Curl is the amount of circulation behaviour around the smallest element dxdy. So if we total all the circulations on the elemental area, we find the circulation around the outer contour. This is no different from finding the total mass of a rod, If we know the mass per unit length then we integrate along the length to find the total mass. I believe that the following " activities have similar/related building blocks/ logic to produce the tacit differences. . 1. Cauchy Riemann relations 2. The Grad operator. 3. The curl operator. 4. the Divergence operator. 5 . Green's Curl theorems of circulation 6. Green's Divergent theorem of flux 7. Stoke's Curl theorem involving circulation 8. Divergence theorem involving divergences through volumes/surfaces, I always thought that students should see the close links there are in how these derivatives are combined to produce their " engineered" activity. dU/dx dU/dy dU/dz dV/dx dV/dy dV/dz dZ/dx dZ/dy dZ/dz and reduced to two dimensions dU/dx dU/dy dV/dx dV/dy .

[@sunset2.00]

Sal's voice is reassuring.

[@bijoythewimp2854]

My college didn't reach here. I am way ahead. I lost my faith in teachers long time ago. Sal and other youtube teachers are my only hope and I am contended to have them as my virtual teachers.

[@mmzzcc2]

I wish I could have seen this video when I was at the university! Thanks Sal!

[@Virtualexist]

I get so happy with him when the vector fields and path are in the same direction !!!

[@robertmatuschek913]

reasoning for dotting with N. …We do this because curl is a vector whose direction is orthogonal to the Counter clockwise rotation and the dot product calculates the amount of curl in S

[@MeshalWinehouse]

I’m on second year as a physicist 😮‍💨 can’t wait to graduate 😭😭 thanks for ur help.

[@larrymendel1]

the line integral of the vector field along C is the summation of all the curls on the surface

[@ananthakrishnank3208]

This helps. For math and engineering education, visual intuition is minimal one should get.

[@SourabhTiwari62]

Crystal clear..Thanks

[@अण्वायुवरीवर्त]

Okay then tell me why would u take 0 when field is Orthogonal to our line integral??? I may be late but it was crystal clear to u

[@अण्वायुवरीवर्त]

@Devang Trivedi Ikr, I was trying to tell him that this wasn't a crystal clear explanation, it was vague. Even sal mentioned it

[@shivamsharanlall672]

@@अण्वायुवरीवर्त but it is all clear. There is no vagueness....

[@अण्वायुवरीवर्त]

@@shivamsharanlall672 he just gave an example n I bet one example isn't enough

[@chemmaz]

@@अण्वायुवरीवर्त you don't have to understand stokes' theorem to answer your question. simply knowing what the dot product mathematically implies is enough.

[@chinkostik124]

Sal made me pretty stoked about Stokes' Theorem

[@wagsman9999]

Love the way Mr. Khan explains things.

[@thReipoints]

anybody else has an upcoming exam and is cramming the night before?

[@adhamsalama4336]

Yep.

[@Fiendnat138]

Wish me luck, test is on Thursday:>>!!!

[@Ydmaster]

@@Fiendnat138 hope you did well because I did really bad on my second midterm

[@22Tech]

yes but 6 years later

[@oneinabillion654]

My exam for calc3 in 2-3years. I'm studying this for field theory next semester. I dont know why the timetable is like that LOL

[@Prometeur]

Incredible explanation, Sal is a hero

[@cmprice11]

This video made it click. Thank you!

[@scp_at_iitb]

Love this explanation. Thanks

[@epezzulli1163]

Absolutely Great explanation.

[@KisekiTim]

Great video. Very intuitive and easy to understand for people entering the field.

[@shivamsharanlall672]

Now this is the physical explanation of a mathematical process.

[@DushyanthEdadasula]

Khan, your way of teaching is awesome!!😍😍😍

[@PartVIII]

thank you so much Sal. im really enjoying these vector calculus videos

[@tuanthanhtruong4075]

Wow This helped alot!!! Thanks!!!!

[@rafainfernal]

Best geometrical representation of this concept

[@messedup9544]

this really helps simplify the concept.THANK YOU

[@adityaprasad465]

In the fifth example, if the direction had switched an odd number of times, the curl might still be zero, but we would have gotten a positive result for the line integral. So this perspective is neat but has serious pedagogical limitations.

[@GOODBOY-vt1cf]

thank you so much

[@wooobooo1]

insane mouse control!! o.O

[@abhishekravindra4008]

CharlesWorth its one of those bamboo tablets lol

[@lidyasolomon5557]

@@abhishekravindra4008 screaming lol

[@craigcoates6247]

This man is a god

[@Citius1974]

Wonderful! I've been fascinated by Stokes' Theorem since reading about it in Maxwell's Treatise on E&M (Vol 1 Article 24)...This video is an excellent intuitive explanation!!

[@laurabeltran3746]

Thank you this was super clear!

[@sandracordoba6090]

Just brilliant!

[@meme_engineering4521]

You've got excellent knowledge and teaching skills👍👍👍

[@muhammadumar9753]

Thank you so much ❤️💕

[@yichizhang795]

Great explanation, thanks

[@funkymaniak]

Absolute gold

[@AS_tutor]

It seems like fun) Thank you!

[@bhaveshohal3390]

That was so great.....Thank You.....

[@jaswanthtalada.]

thank you

[@astherphoenix9648]

thanks, it's a good way to visualise

[@AsiaCrasie]

I've got a question: in that top right diagram, what if the vector field in the middle of the surface curled in the opposite way as those on the outside (aka spin clockwise on the inside of the surface and counter clockwise at/near the line integral)? Would the opposing curls eventually cancel out and give a 0 for the line integral? If not (which the theorem suggests), does this mean that, during the transition between curls, the net curl in between the two directions gives a net counterclockwise curl?

[@gurpritsingh2355]

Absolutely stunning video... Great explanation...

[@purpk86]

i LOVE your voice!

[@AjayPatel-te4kb]

Tq so much sir🙏

[@sanchayadari]

Awesome It made my day !

[@krkarthikeyan]

Fantastic is an understatement

[@odvutmanush3234]

Omg. Thanks a lot Sal.

[@GBabuu]

very well explained

[@jeffaschwarz]

Where are these videos? I get emails when new Khan videos are posted on youtube, but it is not in any playlist on the site.

[@abhi99ps]

Ya, I also realised that. They aren't on his site at all. I also found that some of his videos are on the channel "sal32458" instead.

[@moodaahmed7308]

amazing mate just amazing

[@tjfirhfjejUTH24]

great video thanks

[@ChristopherMarkusLacapra]

thanks

[@sukursukur3617]

Look through Aleph 0 explanation of this subject

[@RawdaAHafez]

That's amazing

[@suryaprakashsahu6142]

good explanation

[@সুমিতকর্মকার]

May I know which board or the background is used to write all those stuffs?

[@Podotoderoso]

Best Enchantress EU.

[@IHeartViHart]

HALP! I have no idea what's going on! Suppose I should actually watch the preceding videos, but it's more exciting like this. xD Knowing kills the suspense.

[@drtamiz]

Why do we dot it with the normal and not the tangential?

[@ztitan69]

thank you!!!

[@andrerossa8553]

great. tks

[@kuraignjenge4015]

yaaa this is helpful

[@Headrum]

Your voice sounds considerably more wise in this video.

[@foundede]

AUTODIDACTS RULE!

[@abhi99ps]

Which playlist is this in?

[@Macoranino]

thanks a lot

[@RougeSamurai77]

@Gavin Malus Well said.

[@hamzaabbasi8619]

Great !!

[@abhi99ps]

Its already 8 days since this video came about and its still not on the Khan Academy site. Also, this is not in the calculus playlist. Also, some of these videos are on a different channel instead (sal32458).

[@PlayMadness]

I knew some of those words!

[@macmos1]

I just finished cal II. I can't wait to learn cal III :)

[@rj-nj3uk]

what if the curl is in middle but on sides fields cancel the curve traversal to have net 0 integration of field throughtout the curve.

[@vinaychintu98]

superb

[@Jiwan01]

Hi, I'm good at Mirror's Edge :)

[@kamelalboaouh9595]

how come the "contour" is treated as a surface "boundary"??

[@nmakarowski]

i love it

[@anteil95]

Very good explanation, however there's one thing confusing me. Looking at the bottom right surface, if you follow the border, the vectors on the border cancel each other out. But what if there is still one set of vectors left within the surface, pointing to the right (like khan drew it)? What if these vectors didn't find any complementary ones to cancel out with? Adding all the vectors together would thus not equal zero, although adding the ones on the border would. There are several other examples which would contradict Stokes' theorem. Can somebody explain please?

[@benham118]

That's not quite the way it works because the vector field on the surface is continuous and so the vectors as seen in the diagrams wont actually cancel out in a discrete sense.

[@inteusproductions]

Munzu You look at each case separately, not to see if both of them satisfy it at the same time.

[@SadatHossain01]

King Salman Khan 👑👑

[@agrajyadav2951]

10:22 came outta nowhere

[@SneakyJeffZ]

is n just a normal vector or does it have to be a UNIT normal vector?

[@daviddavidson1090]

unit. That's why it has a hat and not an arrow.

[@KumarHemjeet]

The voice is of salman khan (founder of khan acaddemy).

[@NightbladeNotty]

when you are referring to the curl of F you mean the Gradient x(cross) F right?

[@andrewolejarz5293]

Yes

[@NightbladeNotty]

Gavin Malus ok?..

[@FitnessRegiment]

Gavin Malus Khan Academy ban this guy from your channel please!

[@FitnessRegiment]

are you actually stupid? I'm german

[@yichizhang795]

Gavin Malus You ignorant racist

[@TheMrFrontera]

Haha i found your comment to be hilarious! I know the slight familiarity. Like you were sitting in class but didnt know what the hell was going on

[@andreirocks1992]

Maaaath! Yes!

[@fabiana37]

I love you