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.
@@Edgarisftw also probably help that people have had that previous amount of teaching. This 'learning' essentially amounts to consolidating some misconceptions to most people
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.
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 .
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
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.
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!!
@@अण्वायुवरीवर्त you don't have to understand stokes' theorem to answer your question. simply knowing what the dot product mathematically implies is enough.
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.
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?
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).
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?
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.
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.
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.
In class this made me experience something which I would define as "brain death."
You're my resuscitation, Sal.
This is the most outstanding explanation of Stoke's theorem. So clearly explained. Thank you so much.
cap
cap
I'm so Stoked my dudes
Turn round for what?
@@holycrapitsachicken curl it man
Crazy how 3 hours of lectures amounted to me retaining 0 knowledge. Then 10 minutes of this and I understand it like crazy
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.
@@Edgarisftw also probably help that people have had that previous amount of teaching. This 'learning' essentially amounts to consolidating some misconceptions to most people
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.
30% of my exam for university 2 weeks ago was on stokes and greens theorem. Thank you so much for these videos :)
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.
wow... finally, i understand the stoke's theorem.
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.
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
.
Wow I came here for Stoke's Theorem and I get an actual explanation of curl also
Sal, you're a genius. Thank you!
the line integral of the vector field along C is the summation of all the curls on the surface
Never have I understood this so well. Khan Academy strikes again
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
Oh My Goodness! All those equations have suddenly started to make so much sense...
Thanks a lot Sal!!!
And now I can pass my final... Bless you, Khan Academy!
This is best video about stokes theorem in whole UA-cam, Great, thanks dude
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.
I wish I could have seen this video when I was at the university! Thanks Sal!
Love the way Mr. Khan explains things.
I’m on second year as a physicist 😮💨 can’t wait to graduate 😭😭 thanks for ur help.
I get so happy with him when the vector fields and path are in the same direction !!!
This helps. For math and engineering education, visual intuition is minimal one should get.
this really helps simplify the concept.THANK YOU
Sal's voice is reassuring.
thank you so much
Great video. Very intuitive and easy to understand for people entering the field.
Absolutely Great explanation.
Wow This helped alot!!! Thanks!!!!
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!!
Crystal clear..Thanks
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
@Devang Trivedi Ikr, I was trying to tell him that this wasn't a crystal clear explanation, it was vague. Even sal mentioned it
@@अण्वायुवरीवर्त but it is all clear. There is no vagueness....
@@shivamsharanlall672 he just gave an example n I bet one example isn't enough
@@अण्वायुवरीवर्त you don't have to understand stokes' theorem to answer your question. simply knowing what the dot product mathematically implies is enough.
thank you so much Sal. im really enjoying these vector calculus videos
Incredible explanation, Sal is a hero
This video made it click. Thank you!
Khan, your way of teaching is awesome!!😍😍😍
Thank you this was super clear!
Sal made me pretty stoked about Stokes' Theorem
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.
Just brilliant!
thanks, it's a good way to visualise
thank you
You've got excellent knowledge and teaching skills👍👍👍
That was so great.....Thank You.....
thanks
It seems like fun) Thank you!
very well explained
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.
Absolutely stunning video... Great explanation...
Great explanation, thanks
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?
anybody else has an upcoming exam and is cramming the night before?
Yep.
Wish me luck, test is on Thursday:>>!!!
@@Fiendnat138 hope you did well because I did really bad on my second midterm
yes but 6 years later
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
This man is a god
Thank you so much ❤️💕
Best geometrical representation of this concept
insane mouse control!! o.O
CharlesWorth its one of those bamboo tablets lol
@@abhishekravindra4008 screaming lol
Omg. Thanks a lot Sal.
Look through Aleph 0 explanation of this subject
Absolute gold
great video thanks
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.
Tq so much sir🙏
That's amazing
Fantastic is an understatement
Now this is the physical explanation of a mathematical process.
good explanation
Awesome
It made my day !
great. tks
Why do we dot it with the normal and not the tangential?
i LOVE your voice!
May I know which board or the background is used
to write all those stuffs?
thank you!!!
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).
thanks a lot
@Gavin Malus
Well said.
superb
amazing mate just amazing
yaaa this is helpful
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.
Great !!
Which playlist is this in?
i love it
how come the "contour" is treated as a surface "boundary"??
I knew some of those words!
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?
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.
Munzu You look at each case separately, not to see if both of them satisfy it at the same time.
Maaaath! Yes!
I just finished cal II. I can't wait to learn cal III :)
when you are referring to the curl of F you mean the Gradient x(cross) F right?
Yes
Gavin Malus ok?..
Gavin Malus Khan Academy ban this guy from your channel please!
are you actually stupid? I'm german
Gavin Malus You ignorant racist
Your voice sounds considerably more wise in this video.
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.
is n just a normal vector or does it have to be a UNIT normal vector?
unit. That's why it has a hat and not an arrow.
Best Enchantress EU.
AUTODIDACTS RULE!
Hi, I'm good at Mirror's Edge :)
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
what does the multiplication with the normal vector mean?
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.
Me too.
The voice is of salman khan (founder of khan acaddemy).
I love you
King Salman Khan 👑👑