Stokes Theorem

In this video, I present Stokes' Theorem, which is a three-dimensional generalization of Green's theorem. It relates the line integral of a vector field over a curve to the surface integral of the curl of that vector field over the corresponding surface. After presenting an example, I explain why Green's theorem and Stokes' theorem are related.

[@skillogify]

Stokes' Theorem and the Divergence Theorem are such lifesavers in Electromagnetism

[@darshanbaishya30]

You are 100% right Tom

[@blackpenredpen]

Keep an eye on "12345" subscribers

[@dhunt6618]

I didn't see this in the comments yet, but I have to say I was really stoked about your vector analysis series (pun intended)! The one thing I would like to have seen you add would be mentioning more about the application side of things, i.e. how stokes theorem is used in E&M and other fields, but that because my first major was physics. Thanks again!

[@IsrraelSumano]

I admire your enthusiasm for teaching. I wish my professor was like you

[@emanuelmartinez3585]

What an incredible teacher! I hope to see more of your videos dr peyam!

[@junxionglu4079]

Local whirls add up to a global swirl. That's the enlightening moment for me. Thanks a lot!

[@sleepwalker1803]

You seem you really enjoy your subject. Thats is amazing. I wish I had a teacher like you. And thanks for making me understood Stoke's Theorem. I had a serious problem on visiualizing it in my mind.

[@angelkale7547]

Lol I just kept watching because of his positive energy! Keep up the great work 👍

[@AngeloHafner]

Você explica de forma espetacular. Parabéns.

[@lindsaywaterman2010]

Shouldn't the plane be drawn sloping towards the Y-axis since it cuts the Y-axis at 2. You seem to have the cylinder being cut, sloping toward the X-axis. Am I missing something?

[@drpeyam]

The plane slopes upwards, but other than that the picture is correct

[@thatdude_93]

Nice! I‘d love it if you’d make a series leading up to the proof of the general stokes theorem using differential forms etc. I don’t think there is a video on KZbin like that at the moment

[@drpeyam]

Sadly I don’t know anything about differential forms 😞

[@thatdude_93]

@@drpeyam Well then there's a reason to brush up on it :D

[@nouretaoufik]

@@drpeyam i sure u do but u re so humble

[@caiodesa9520]

Use Stokes' theorem to compute integral (y ^ 2dx + x ^ 2dy), where C is the outline of the part of the plane 2x + y + z = 4 that is in the first octant, counterclockwise.

[@jingwen1803]

Thank you Dr Peyam!! You put my mind at ease before final :)

[@bloe2603]

Hi sir, can i just ask, Can all the three theorems(greens,stokes and divergence) be used in the same question or only each theorem unique for a particular question?

[@abstractcafe2352]

A nice little review of Stokes Theorem. I wish I had a chance to use it in my Mech E courses, but I guess they reserve it for graduate courses in fluid/thermodynamics.

[@ricecabbage7546]

I’ll be able to pass math 2e this quarter because of your videos. Thank you!

[@drpeyam]

Thanks so much!!! And good luck 😄

[@alberteinstein7571]

Awesome! I would love to see a video about Calabi-Yau manifolds :D

[@DawgFL]

how do i know what the normal unit vector is? I've seen like 3 differnet formulas for it and I dont know when to use what.

[@kaokaoylan4510]

Hi Dr.Peyam, I am thinking that the normal vector should be instead of ???

[@drpeyam]

The normal vector is correct, remember that for the determinant you alternate + - +

[@kondojuma5489]

words are not seen well ....Mr... but it's good recture

Superb! Triloco mano. Thanks!

[@anshumanyadav24816]

Can you explain me please , " that S ( Surface ) coordinates (1,0,0 ) and (0,1,1 ) { I mean how they come } ???

[@ricardomanjarrez3392]

Now im ready for vector calculus

[@borg972]

What do you mean Stokes is for 3 or higher? how do you calculate the curl for more than 3 dimensions?

[@drpeyam]

There’s a generalization with differential forms :)

[@jameswilson8270]

Nice video. And released as promised. (+1)

[@shiina_mahiru_9067]

Yeah, ready for vector calculus next quarter

[@finweman]

Doesn't the normal vector need to be of unit length? If so, you're off by a factor of root(2).

[@drpeyam]

It doesn’t, actually, it depends if you’re integrating over S (in which case you need a unit vector) or integrate over D (in which case you don’t)

[@finweman]

@@drpeyam You learn something new every day.

[@rizkyagungshahputra215]

so the ∂Q/∂x-∂P/∂y comes from the curl(F) but F is in 2D?

[@drpeyam]

Yeah, more or less!

[@maheralwajih3151]

Thanks!

[@drpeyam]

Thanks so much for the super thanks, I really appreciate it 😍

[@maheralwajih3151]

@@drpeyam My pleasure, your videos helped me a lot in my assignment and research, keep doing these teaching videos, they help a lot of students.

[@padetass1442]

First

[@harikishan5690]

till after the finals,unfortunately😂😂

[@adeelali8417]

I'm one video short of completing my goal... SIGH