Multivariable calculus, class #37: More on Stokes' Theorem

Mathematician spotlight: The LGBTQ+ mathematician

We reveal the themes behind the choices of mathematicians who were spotlighted. We do an example of using Stokes' Theorem to replace a vector surface integral with a vector line integral over the boundary. We show that, for a surface in the xy-plane, Stokes' Theorem reduces to Green's Theorem (which we already studied). We do an example of Stokes' Theorem where we replace a vector line integral over a closed curve, with a surface having that curve as its boundary. We then discuss the "surface independence" property of curl vector fields, and use it to compute an integral that seems completely impossible.

[georgesadler]

Professor Diana Davis, thank you for a well organized and exceptional video/lecture on Stokes Theorem in Multivariable Calculus. Although, I took, Calculus Three many years ago, I am still learning more about Stokes Theorem and its impact on Mathematics. I also encountered this theorem in Engineering Electromagnetics and Engineering Physics One and I did not understand this powerful theorem. I took Engineering Physics One at the old Catonsville Community College in Baltimore County, MD in the late 1980's and Electromagnetics at the University of Maryland, College Park in the early 1990's.

[abdallahamouda]

you are really a fantastic teacher and a pretty nice person. I really loved it when you said if you what to change the world be that change really cute