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

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

@Edgarisftw

4 жыл бұрын

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

Жыл бұрын

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

I'm so Stoked my dudes

@holycrapitsachicken

7 жыл бұрын

Turn round for what?

@agrajyadav2951

2 жыл бұрын

@@holycrapitsachicken curl it man

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

@gabeham7532

Жыл бұрын

cap

@lambda5949

Жыл бұрын

cap

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.

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.

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

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

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

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

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

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

Sal, you're a genius. Thank you!

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

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

Love the way Mr. Khan explains things.

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

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

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

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

Absolutely Great explanation.

this really helps simplify the concept.THANK YOU

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 .

Great explanation, thanks

Awesome It made my day !

This video made it click. Thank you!

Absolutely stunning video... Great explanation...

Sal made me pretty stoked about Stokes' Theorem

Absolute gold

Thank you this was super clear!

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

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

thanks, it's a good way to visualise

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

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

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

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

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.

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

thank you so much

It seems like fun) Thank you!

Incredible explanation, Sal is a hero

amazing mate just amazing

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

Just brilliant!

Best geometrical representation of this concept

Omg. Thanks a lot Sal.

thank you

Great !!

thanks

Thank you so much ❤️💕

Fantastic is an understatement

thank you!!!

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?

i LOVE your voice!

great video thanks

That's amazing

very well explained

Now this is the physical explanation of a mathematical process.

great. tks

This man is a god

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.

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!!

good explanation

Tq so much sir🙏

Intuitive!

yaaa this is helpful

i love it

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

@adhamsalama4336

4 жыл бұрын

Yep.

@Fiendnat138

4 жыл бұрын

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

@Ydmaster

4 жыл бұрын

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

@22Tech

4 жыл бұрын

yes but 6 years later

@oneinabillion654

4 жыл бұрын

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

Crystal clear..Thanks

@user-vi3pi9rf7w

5 жыл бұрын

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

@user-vi3pi9rf7w

4 жыл бұрын

@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

4 жыл бұрын

@@user-vi3pi9rf7w but it is all clear. There is no vagueness....

@user-vi3pi9rf7w

4 жыл бұрын

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

@chemmaz

3 жыл бұрын

@@user-vi3pi9rf7w you don't have to understand stokes' theorem to answer your question. simply knowing what the dot product mathematically implies is enough.

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.

I knew some of those words!

Sal's voice is reassuring.

insane mouse control!! o.O

@abhishekravindra4008

6 жыл бұрын

CharlesWorth its one of those bamboo tablets lol

@lidyasolomon5557

4 жыл бұрын

@@abhishekravindra4008 screaming lol

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.

Maaaath! Yes!

superb

Which playlist is this in?

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.

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

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

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

thanks a lot

@RougeSamurai77

7 жыл бұрын

@Gavin Malus Well said.

Look through Aleph 0 explanation of this subject

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.

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

Best Enchantress EU.

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).

Your voice sounds considerably more wise in this video.

I love you

Me too.

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

@daviddavidson1090

7 жыл бұрын

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

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

Woah

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

9 жыл бұрын

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

9 жыл бұрын

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

AUTODIDACTS RULE!

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

10:22 came outta nowhere

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

@andrewolejarz5293

9 жыл бұрын

Yes

@NightbladeNotty

9 жыл бұрын

Gavin Malus ok?..

@FitnessRegiment

9 жыл бұрын

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

@FitnessRegiment

9 жыл бұрын

are you actually stupid? I'm german

@yichizhang795

9 жыл бұрын

Gavin Malus You ignorant racist

what does the multiplication with the normal vector mean?

@carultch

Жыл бұрын

It's a dot product. The normal vector to an area is defined to point perpendicular to that area. When you take the dot product, you multiply corresponding components and add them up. Or in other words, you project one vector onto the other, and multiply the projection with the second vector.