Surface integral of a vector field

In this video, I calculate the integral of a vector field F over a surface S. The intuitive idea is that you're summing up the values of F over the surface. Enjoy!

[@XanderGouws]

Was 0:36 a skyrim referance? Dr. Peyam elite gamer confirmed ???

[@drpeyam]

Yep, and hehehe, no, I just like the meme! I did use to play video games though, lots of SNES and N64 🙂

[@BRORIGIN]

3:01 , No I am not a recreational vehicle

[@lightspd714]

Dr. Peyam, I already love math but you make it even better. Thanks for all the excellent content.

[@dhunt6618]

I really hope physics students are watching you as well. I would have loved this (and your other) videos when I took E&M!

[@andres.robles6]

Te recomendaria que acercaras más la cámara hacia la pizarra ✌

[@khanster]

Nice. Gonna learn this on Wednesday. As always thank you Dr. Peyam

[@jameswilson8270]

I will say, once again, your channel deserves more popularity :)

[@drpeyam]

:)

[@matiasocciel4697]

Thanks man, you're great!

[@georgecooper7389]

Cool! :)

[@eddiefloyd8950]

Fantastic video Dr.Peyam! I was wondering if you could do me a favor and recommend me some books so that I can self study Calculus 3 (Multivariable Calculus), Linear Algebra, and Differential Equations? Thanks!

[@drpeyam]

Calc 3: Div, Grad, Curl, and also the book by Adams Linear Algebra: The book by Lay and the book by Friedberg Diff Eqns: The book by Smale (for ODEs), the book by Evans (for PDEs)

[@eddiefloyd8950]

Thanks!

[@Galileosays]

Archimedes would have enjoyed it. But why is it pi^2/16 ? In the same way 3Blue1Brown questions " Why is the area of a sphere 4piR^2". In other words, how would Archimedes have solved the surface integral of the vector field with geometry? Archimedes invented the hydraulic screw (helicoid) and proved that the volume ratio of sphere to cylinder is 2:3. It seems here that the integral of the helicoid vector is the result of a projection on the xy-floor (z=0), which has area pi/4, times the projection on the z-axis which has length pi/2, times the factor 1/2 because we are looking only upward.

[@XanderGouws]

Don't you also need to tell us which way the surface is oriented? So that our normal vector is facing in the right direction?

[@drpeyam]

By convention, S is oriented outwards or upwards

[@RiaziMohandesi]

درود بر شما

[@8dolev]

All I hear is: Are you cross RV? You sign V.

[@Hobbit183]

First! :)

[@borg972]

Flux? that sounds suspiciously like physics..

[@HilbertXVI]

Indeed

[@funkycude57]

Peeeeyyyaaaaaammmm

[@rudolfgyorkei9558]

Oreo is on the screen

[@drpeyam]

Where?

[@rudolfgyorkei9558]

@@drpeyam On the bottom right corner as the link for the subscribe button. Cool!

[@drpeyam]

Oh! Hahahaha, true!