What is a Surface Integral?

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Surface Integral
In this video, I give an example of how to calculate a surface integral, which is a way of calculating the integral under a function, but over a surface. The key to this is to parametrize the surface and turn this integral into an ordinary double integral. Lots of beautiful calculus theorems (like Stokes and Gauss-Green) use this important concept. Enjoy!
Parametrize a surface: • Parametric surfaces
Another Surface Integral Example: • Surface integral of a ...
Surface Integral of a Vector Field: • Surface integral of a ...
Check out my Vector Calculus Playlist: • Line integral of a fun...
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Опубликовано:

21 окт 2020

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Комментарии : 48

@r1nov8 3 месяца назад

would like to take a minute to say that your such a good tutor doc, soft spoken and detailed explanations. Hope you do more of these types of videos.

@drpeyam 3 месяца назад

Thank you so much!!!

@a_llama 3 года назад

The recent surfaces video of yours made me look into differential geometry, thanks for the motivation haha

@fireemblem2770 3 года назад

I have not looked at surface integrals in way too long. THANK YOU DR. PEYAM!!!

@OuroborosVengeance 3 года назад

So clear! I love how i learn so easily with your videos, they are perfect

@alexsaldana6916 3 года назад

You just opened my eyes to another way to see and calculate the Surface Integral, thank you so much, keep doing videos like that, and if you could explain some difficult exercise would be great 👌🏾🔥

@ShivanshTrisal 3 года назад

Why fear, Dr Peyam is there!! I was just starting this, thanks for wonderful explanation Dr Peyam!!

@Galileo2pi 3 года назад

You are great pal, one of the best. Hi from Spain

@Ben-sx5xb 2 года назад

Thank you for the great example!

@jamesmonteroso824 3 года назад

finallly Dr. Peyam.....

@SimsHacks Год назад

We don't calculate the length of the cross product. We calculate sqrt[det(D^T D)], where D is the derivative of the parametrisation. Looks like equivalent

@IceBelly 2 года назад

Thank you

@thedoublehelix5661 3 года назад

Ahh I missed this video for some reason loll. Btw I like to think of the surface intgral like the mass of a really thin sheet thats molded to fit some mold where f is the density. It doesn't really make much sense bc the sheet would have to be "infinitely thin" but I guess you could think about the limit of the masses of a bunch of finite sheets as the thickness goes to 0 or something like that

@Firoo_ 3 года назад

What is the SI unit for surface integral dose?

@user-ps1dm4fc4l 3 года назад

ايلافيوه اب دكتور بيان (:

@jamesbentonticer4706 3 года назад

I shall be the envy of my friends when they find out I crossed two vectors!

@palantea1367 3 года назад

I'm your fan Dr peyam! c:

@drpeyam 3 года назад

Thank you!!!

@gerardsagliocca6292 Год назад

Can r be a function of 3 variables ??

@gerardsagliocca6292 Год назад

Why is r a function of 2 variables u and v ??

@moeidmehri2153 3 года назад

master :))

@drpeyam 3 года назад

Doctor ;)

@alejandrobarrantes8657 3 года назад

here is a problem mr peyam. Find a linear operator such that: O(y¨)=O(y) for all functions with second derivative, and the other restriction is O(y^2)=(O(y))^2???????

@a_llama 3 года назад

Maybe differentiate both sides of Oy^2 = (Oy)^2?

@alejandrobarrantes8657 3 года назад

@@a_llama mmm I already tried that and I couldnt get anything...try something else

@drpeyam 3 года назад

What is O?

@GiacomoAakbr 3 года назад

@@drpeyam O as an Operator (linear in this case)

@drpeyam 3 года назад

Any operator?

@subhadipsarkar7692 3 года назад

❤️

@guill3978 3 года назад

Are you interested in primality testing for very large numbers?

@drpeyam 3 года назад

Not really, I don’t like number theory

@a_llama 3 года назад

@@drpeyam :o finite fields are the future!

@drpeyam 3 года назад

Nah, real numbers it is for me

@gerardsagliocca6292 Год назад

You got to tell the viewer WHY you do some of the steps !

@drpeyam Год назад

@emmepombar3328 3 года назад

This was too much, "then you do magic here, that I don't explain". Why is dS just the length of the cross product? Why do I replace y with the parametrization? At least for me, this video doesn't answer the question "What is a Surface Integral". Sorry, normaly I really like your videos, but on this I think I am missing too much knowledge on this topic.

@drpeyam 3 года назад

You should check out my playlist, it covers the basics. Also, I give some intuition at the end of this video

@emmepombar3328 3 года назад

@@drpeyam i will do. Thank you.