What is a Surface Integral?

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!

[a_llama]

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

[rnov]

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.

[fireemblem]

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

[OuroborosVengeance]

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

[ShivanshTrisal]

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

[alexsaldana]

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 👌🏾🔥

[SimsHacks]

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

[Galileopi]

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

[thedoublehelix]

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

[alejandrobarrantes]

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

[Firoo_]

What is the SI unit for surface integral
dose?

[gerardsagliocca]

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

[guill]

Are you interested in primality testing for very large numbers?

[jamesbentonticer]

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

[gerardsagliocca]

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

[emmepombar]

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.