Multivariable Calculus | Two Stoke's theorem examples.

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[@danielvolinski8319]

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.

[@nicolem.1028]

It's been a while since I've studied calculus, so thank you for your videos! They make for excellent review

[@benjaminbrat3922]

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]

@Benjamin Brat Hi. What knowledge must I have to understand this? I would really appreciate if you could guide.Thanks budy.

[@benjaminbrat3922]

@@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

[@malawigw]

Im am so stoked for another stokes theorem video!

[@MIRCOR55]

Excellent video!

[@filipbaciak4514]

Great videos, you're doing a great job.

[@giovannimariotte4993]

There is a mistake in the curl

[@stewartcopeland4950]

@ 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?

[@malawigw]

yeah unless you specify y = z

[@rodrigolopez3874]

What do you have to integrate in the line integral to obtain the area of the surface?

[@miguelcerna7406]

Zero both times??

[@joshlazor6208]

Hey Michael Penn, how did you get (1, 0, 0) and (0, 1, 1) as your two vectors in the determinant matrix? @ kzbin.info/www/bejne/ZoqopH6GgJWVm5o

[@PhaedkrK]

since S = , S_x = and S_y = ... just take partials w/ respect to x and y to find S_x and S_y