Always great to watch your videos! I particularly like your Abstract Algebra series. On this video though, looking at it naively I was pretty convinced that the field F was the gradient of the potential f(x,y,z)=x^2*y^2*z-z^2 and that therefore, curl of F is 0. Did I miss something? It doesn't change much, though.
@@davidescobar7726 That's standard calculus stuff. I particularly like Early Transcendentals Calculus by Stewart, pretty pictures, but Adams and Essex cover some stuff more in-depth
First example: curl(F) = 0 so there is no need to calculate the surface integral. Also x^2 + (1/2)(y^2 + z^2) = 1 is a surface, not a curve.
It's been a while since I've studied calculus, so thank you for your videos! They make for excellent review
Im am so stoked for another stokes theorem video!
Always great to watch your videos!
I particularly like your Abstract Algebra series.
On this video though, looking at it naively I was pretty convinced that the field F was the gradient of the potential f(x,y,z)=x^2*y^2*z-z^2 and that therefore, curl of F is 0. Did I miss something? It doesn't change much, though.
@Benjamin Brat Hi. What knowledge must I have to understand this? I would really appreciate if you could guide.Thanks budy.
@@davidescobar7726 That's standard calculus stuff. I particularly like Early Transcendentals Calculus by Stewart, pretty pictures, but Adams and Essex cover some stuff more in-depth
Excellent video!
What do you have to integrate in the line integral to obtain the area of the surface?
Great videos, you're doing a great job.
@ 2:18
x^2 + 0.5(y^2 + z^2 ) = 1 : Is it not rather the equation of an ellipsoid, instead of our curve which is an ellipse in the plane y = z?
yeah unless you specify y = z
There is a mistake in the curl
Zero both times??
Hey Michael Penn, how did you get (1, 0, 0) and (0, 1, 1) as your two vectors in the determinant matrix? @ ruclips.net/video/0YEsKPK0be8/видео.html
since S = , S_x = and S_y = ... just take partials w/ respect to x and y to find S_x and S_y