Month: March 2022

In this lecture we continue our discussion of smooth surfaces, introducing some key concepts like the Gauss map and the area vector. We’ll also sketch out how to finally talk about differential forms on curved surfaces, rather than in flat \(\mathbb{R}^n\).

• Video
• Slides

This lecture takes a first look at smooth surfaces. There’s of course way more to know about surfaces than we can pack into a single lecture (and we’ll see plenty more later on), but this lecture will cover two very important perspectives: the extrinsic description of a surface via a local parameterization, which tells us where points sit in space, and the intrinsic description of a surface via coordinate charts, which lets us work with a surface without worrying how it’s embedded in space.

• Video
• Slides