What is Stokes theorem? - Formula and examples

Where Green's theorem is a two-dimensional theorem that relates a line integral to the region it surrounds, Stokes theorem is a three-dimensional version relating a line integral to the surface it surrounds. For that reason, Green's theorem is actually a special case of Stokes Theorem.

Again, Stokes theorem is a relationship between a line integral and a surface integral. Before you use Stokes theorem, you need to make sure that you're dealing with a surface S that's an oriented smooth surface, and you need to make sure that the curve C that bounds S is a simple, closed smooth boundary curve with positive orientation.

Since Stokes theorem can be evaluated both ways, we'll look at two examples. In one example, we'll be given information about the line integral and we'll need to evaluate the surface integral. In the other example, we'll be given information about the surface integral and we'll need to evaluate the line integral.

0:00 // About Stokes theorem
2:41 // Example 1
10:46 // Example 2

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

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[sabdf]

Finding videos for math this advanced that is this high quality and well explained is very rare. You and Prof Leonard have saved my calc grades 1-3! Thank you so much! Engineers everywhere bow down to you

[leslypaz]

I've spent the last two hours watching KHAN videos and looking up other videos/pdf on Stokes Theorem. I somehow came across your video, and I completely understand it now. You teaching method is superb and at good pace, and you just saved my life because my test is tomorrow.

[grum]

I've been trying to learn Stokes Theorem through Khan Academy, and your video is so much more comprehensible then their entire collection of videos on the subject. Thanks so much!

[omarbrokeit]

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[picknikbasket]

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[neemo]

i miss the old days when i thought triple integrals were a lot

[aojiao]

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[tb]

I was in tears over Stokes Theorem...I didn't understand what was going on at all. Twenty minutes with you and I'm out of the dark. I can't tell you how grateful I am.

[IMadeOfClay]

Hi Krista. Love your channel. Super happy that you have done a more advanced video. Would love to see more :)

[pipturbine]

Not gonna lie but this lady has advanced me from my year1-3 engineering degree, thanks Krista

[Anmolorb]

Final is in 5 hours lmao thanks for saving me =D

This is the best video i've ever watched about stokes' theorem. Lots of thanks.

[Ai]

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[muwongeevanspaul]

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[josecarlosribeiro]

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[Sstratos]

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[Ai]

Loved the way you presented this concept, thanks a LOT

[victorpaesplinio]

Thank you for the clearest explanations! In the second example I solved for the other side (line integral) and it matched! I think that now I can nail my last calc 3 exam for the semester

[mohammeda]

Honestly the cool thing about Stokes theorem is your explanation, thanks a lot.

[andyfox]

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