Multivariable Calculus | Two Stoke's theorem examples.

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  • Опубликовано: 29 янв 2025

Комментарии • 15

  • @danielvolinski8319
    @danielvolinski8319 3 года назад +5

    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
    @nicolem.1028 4 года назад +5

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

  • @malawigw
    @malawigw 4 года назад +1

    Im am so stoked for another stokes theorem video!

  • @benjaminbrat3922
    @benjaminbrat3922 4 года назад +7

    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
      @davidescobar7726 4 года назад +2

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

    • @benjaminbrat3922
      @benjaminbrat3922 4 года назад +2

      @@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

  • @Mircor55
    @Mircor55 4 года назад +1

    Excellent video!

  • @rodrigolopez3874
    @rodrigolopez3874 4 года назад +1

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

  • @filipbaciak4514
    @filipbaciak4514 4 года назад +1

    Great videos, you're doing a great job.

  • @stewartcopeland4950
    @stewartcopeland4950 4 года назад +1

    @ 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
      @malawigw 4 года назад +1

      yeah unless you specify y = z

  • @giovannimariotte4993
    @giovannimariotte4993 4 года назад +2

    There is a mistake in the curl

  • @miguelcerna7406
    @miguelcerna7406 4 года назад +1

    Zero both times??

  • @joshlazor6208
    @joshlazor6208 4 года назад +1

    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

    • @PhaedkrK
      @PhaedkrK 4 года назад +1

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