Stokes' Theorem // Geometric Intuition & Statement // Vector Calculus

We're finally at one of the core theorems of vector calculus: Stokes' Theorem. We've seen the 2D version of this theorem before when we studied Green's Theorem which compared the circulation around a 2D curve to integrating the circulation density along the region. In contrast, Stokes Theorem is the three-dimensional generational to compare the circulation of a 3D curve in some vector field to the integral over the region of the curl of the vector field (note: the kth component of curl is what we used to call the circulation density). In this video we build up the geometric conceptual understanding of why the curl of a vector field would relate to the line integral along it's boundary, and then finally state the theorem.

0:00 The Geometric Picture
3:30 Recalling Green's Theorem
5:55 Stating Stokes' Theorem

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[mustafizurrahman]

Sir I had studied this topic in 1998 or 1999 but couldn't fathom anything. After 25 years, when I am 47 years old, I have been able to understand the intuition. Thank you awfully for enthralling explanation

[kieranvelasquez]

This is how every math lecture should be:
1.what this looks like/does
2.how to solve/do the problem
3.what this applies to

Awesome video made this theorem tie together everything from multi variable calculus so well!

[pankajjkumar]

Your geometric presentation is mind blowing.

[ahmeds]

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[tasninnewaz]

Geometric Intuition gives me geometric feeling.
Thank you Trefor!

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[Dr.MuhammadZubair-pz]

Dear Dr. mostly I am watching your lectures, in each lecture I realize that your geometrical representation of the problem is mind blowing and amazing.

[NumbToons]

3:20 Words of wisdom. 'Tendency to curl the surface' HOOOLY MOTHER OF ACCURATE DESCRIPTION.

[Chomusuke]

So lucky to get this in my first year itself...beautiful playlist sir!!

[judepazier]

I have begun watching your videos and this all is beginning to make so much sense! Vector calculus can get really abstract/difficult to picture but you made it clear and precise. Thank you for sharing!

[spiderkent]

I never really understand the idea behind the theory until I watch this video. Thank you very much.

[AnkurSingh-cvls]

that's what i was looking explanation and all these theorems amazed

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[wuyqrbt]

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And for me, when I'm Watching your videos, it's just look like I'm watching "Big Bang theory" or "Friends" series.
Thank you so much 💓

[transcendingvictor]

Amazing and enlightening video, it is like if the strange relations the Stoke's and Green's theorems describe now made sense. Thank you very much!!

[dodo-jsgw]

Thanks a lot ! It is much more intuitive now ! Hello from France :D

[raghuramabl]

Thanks a lot, you cleared my confusion regarding what exactly is going on when we apply curl on each point of the surface once again thank you 🙌👌🙏