1.
Review: Draw yourself a picture demonstrating what the expression \(\|\vec{r}_u\times\vec{r}_v\|\) represents.
Section 5.2 Surface Area Formula for Parametric Surfaces
Give a parametrically defined surface, what is its surface area? In this video I walk through the derivation of the surface area formula. In many ways it is completely analogous to what we have previously done with arclength, except in the higher dimensional case we exploit the cross product for being able to find the area of our little patches.
Learning Objectives:
- State the Surface Area formula for parametric surfaces
- Explain geometrically what the cross product in the formula represents
