Stokes Theorem

The most important theorem about vector fields, Stokes' theorem, which relates the surface integral of the curl with the line integral over the boundary. Here orientation matters, which I'll explain as well.
Old Stokes Theorem Video • Stokes Theorem
Vector Calculus Playlist: • Vector Calculus
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[@erikdurfey5576]

I was so Stoked for this! Oddly I couldn’t help hearing Nacho Libre’s song “I am I am” with lyrics “Peyam Peyam” and tried to come up with the rest of the song. It’s in digressions like these that I at least try and salvage a mnemonic for the maths content I had originally come to watch. Dr Peyam you rock!

[@pablobarrio2712]

As a spanish native speaker when you say sentences in spanish like "claro que sí" it shocks me at first, but i like it, so keep doing it!

[@pandabearguy1]

Stokes theorem is realmy the fundamental theorem of calculus. Differentiable forms, manifolds and exterior dervatives generalizes the the FTC biurifuly.

[@drewpat9535]

Clear!!!! As usual! Greetings from Italy!!! You're our math's lighthouse!!!!

[@garyhuntress6871]

Once again, you've helped me understand something that I never really understood when I first learned it!

[@arvindsrinivasan424]

My waifu of theorems is the generalized stokes theorem. This specific case for curl field particularly beautiful and useful in E&M/Maxwells Equations

[@shivaudaiyar2556]

Thanks for such a great content with love from India

[@mehnishpatel9976]

Sir your work is really helpful for us Thank you so much

[@mehnishpatel9976]

Love from India

[@ThePhysicsMathsWizard]

Nicely illustrated, good job !

[@gardenmenuuu]

Sir your contents are amazing. I am so fascinated by these online contents from mr.peyam,blackpenredpen,3 blue 1 brown, mathologer, mind your decisions and so on.I would be more than happy if you could share the names of sites(webpages) that provide contents like these on maths!

[@رضاشریعت]

Electrodynamics secret weapon

[@azhakabad4229]

Stoke theorem leads to Navier-stokes problem in fluid mechanics by just explaining further.

[@TeoTheZethronOne]

You are genius. Thanks for this video!

[@ehess1492]

Surface integrals is where I hopped off the calculus train.

[@FlippityFloppittyFlom]

You guys got onto the calculus train?

[@AlfonsoNeilJimenezCasallas]

This topic remembers me calculus III at the university, nostalgia!

[@lambdamax]

I'm watching this video 100 times until I can reproduce this.

[@wqesdc8339]

hello, why in c the y and x was accepted as cosx and sinx, can u explain please ?

[@himanshuuu6361]

Helpful; love from india❤

[@jimmy_colombia]

Hola ✖️➕➖➗s soy estudiante universitario y ando en la onda matemática. Hay 4 saberes dentro del saber holistico matemático que se tienen que dominar en conjunto de lo contrario no nos formanos como buenos profesionales. 1: El saber CÓMO se hacen las cosas en matemática. También conocido como el saber PROCEDIMENTAL manual o ALGORITMO. 2: El saber el PORQUÉ de cada cosa que se hace en matemática. 3: El saber PARA QUÉ se hace lo que se hace en matemática, es decir en que se puede aplicar o posibles futuros usos el hacer matemático. 4: Este es un nuevo saber en el mundo actual computarizado. El saber ALGORITMICO COMPUTACIÓNAL es decir como llevar lo que se hace en el saber procedimental y manual a operaciones u órdenes matemáticas por computador, en otras palabras saber manejar paquetes matemáticos como Maxima, Maple, Mathematica, Xcas Dentro de estos paquetes están los paquetes númericos como MatLab, Numérico-Símbolico como los mencionados anteriormente, también conocidos como CAS o Computer Algebra System o en español también conocido como SAC o Sistema de Algebra Computaciónal Por favor puedes ahondar y exponer en un nuevo video sobre el tema de los saberes holisticos en matemática y crear un nueva serie exponiendo el 4to saber, es decir iniciar una serie de vídeos en algún paquete matemático. Yo recomiendo Máxima por que es gratuito Gracias totales 👍

[@naturemeets]

Thanks!.C00L video.

[@RalphDratman]

Does the boundary C have to lie in a plane for the theorem to work?

[@drpeyam]

No, not necessarily

[@guill3978]

What is the surfice area of the region of the surfice of the cone x^2+y^2=z that is delimitatrd by the cylinder (y-3)^2+x^2=1?

[@souhilaoughlis5832]

Can you help me sir with this question? Let f(x)=(m+1)x² +2mx +m-2 Q:what are the values of m that makes x1 and x2 two solution for f(x)=0 one of them is negative and the other is positive and x1≠x2

[@clubstepdj]

One postive and one negative Let the solutions be r1 and r2 From here, the product (r1r2) must be negative (negative times positive) The product of sum is (constant)/(leading coef.) = (m - 2)/(m + 1) Like i said earlier, this quantity must be negative, or the other way to say it, less than 0 (m - 2)/(m + 1) < 0 Solve this by graphing or by number line, you'll get -1 < m < 2 That's the first condition, the next condition: r1 ≠ r2 means that there's 2 solutions, which means b² - 4ac > 0 (2m)² - 4(m+1)(m-2) > 0 4m² - 4(m² - m - 2) > 0 4m² - 4m² + 4m + 8 > 0 4m + 8 > 0 4m > -8 m > -2 Next, we combine the two solutions (-1 < m < 2) and (m > -2), again, using number line or logic, you'll get -1 < m < 2 as the final answer

[@souhilaoughlis5832]

@@clubstepdj thank you very much! :D

[@umerfarooq4831]

Well taught btw I always walk left

[@vigneshshaik3988]

Instead if we find the curl of F it is zero.😂😂

[@dr_rich_r]

I got . Although by a consequence of Stokes' theorem, we could integrate this over any surface with the same boundary, for example the unit disk in the xy-plane. Then the unit normal is , and curlF dot n is 0, so its surface integral would be 0.