Multivariable calculus, class #36: Stokes' Theorem

Mathematician spotlight: Edgar Duéñez

We do an example of integrating a vector field (electric field) over a cone, to find the electric flux. We explain Stokes' Theorem, and do several examples of how to "compatibly orient" a surface and its boundary curve. We do an example of applying Stokes' Theorem over a spherical cap, changing the given vector surface integral into a vector line integral over its circular boundary.

[georgesadler]

Professor Davis, thank you for an excellent conclusion to Surface Integrals and a solid introduction to Stokes Theorem in Multivariable Calculus. From studying and analyzing this information, I found this topic difficult to follow in Calculus Three.

[MohammadrezaParsa-kp]

I think the orientation of the last surface is wrongly determined !!

[CarlosDominguez-yric]

Hi, I have a question. In the example of the minute 44:23 I wonder if the Stokes’ theorem still holds if I were using a cone that is not a smooth surface at the origin x=0, y=0, z=0. Why that Theorem would still hold in that case? Thank you.

[aemrek.]

why don't you just use the right hand rule