Multivariable calculus, class #34: scalar surface integrals

Mathematician spotlight: Henry Segerman

We briefly discuss 3D printing, and show a short clip about stereographic projection. We do an example using the parameterized "waterdrop surface" (DD's favorite surface), parameterized by r and theta. First we look at the r-curves and the theta-curves on the surface. We use the tangent vectors in the r- and theta-directions to find a normal vector to the surface, and we use it to find the equation for a tangent plane. Then we discuss how to find the surface area of a parameterized surface, using an infinitesimal parallelogram, and a method analogous to the Jacobian expansion factor. We find the surface area of a cone, first using basic geometry and then using the surface area method that we just derived. We give the equation for scalar surface integrals, and do an example where the "surface" is the xy-plane, and then compute it using a standard double integral in polar coordinates and then with parameterized surfaces, and see that everything comes out exactly the same.

[BRIJESHKUMAR-jnlm]

Mam the way you introduced and explained the surface integral was so so amazing . Mam I am really fond of your method of making students understand things rather than just cramming them up. You make mathematics so interesting .

[georgesadler]

Professor Davis, thank you for another awesome video/lecture on scalar surface integral in Multivariable Calculus. This is a tremendous amount of material for students to comprehend in one lecture. I will rewatch this video for more analysis on this topic.

[Gamma_Digamma]

4:08 the same risks of in person classes during the COVID 19 era

[puneetkumar]

Thank you so much for this video . I really love it for the first ever time. But I need help in understanding the matrix . At a higher conceptual level and I need to look at the use of it . I want to study the dynamics at master level.❤️👌👌👌🙏👍