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!
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!
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)
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.
Dr. Peyam, I already love math but you make it even better. Thanks for all the excellent content.
3:01 , No I am not a recreational vehicle
Was 0:36 a skyrim referance?
Dr. Peyam elite gamer confirmed ???
Yep, and hehehe, no, I just like the meme! I did use to play video games though, lots of SNES and N64 🙂
I really hope physics students are watching you as well. I would have loved this (and your other) videos when I took E&M!
Nice. Gonna learn this on Wednesday. As always thank you Dr. Peyam
I will say, once again, your channel deserves more popularity :)
:)
Te recomendaria que acercaras más la cámara hacia la pizarra ✌
Thanks man, you're great!
Cool! :)
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!
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)
Thanks!
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.
All I hear is:
Are you cross RV?
You sign V.
درود بر شما
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?
By convention, S is oriented outwards or upwards
Flux? that sounds suspiciously like physics..
Indeed
First! :)
Oreo is on the screen
Where?
@@drpeyam On the bottom right corner as the link for the subscribe button. Cool!
Oh! Hahahaha, true!
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