We'll talk about some common objects (points, curves and surfaces) and the spaces ($\mathbb{R}$, $\mathbb{R}^2$, and $\mathbb{R}^3$) they live in. Our goal is to figure out how many equations are required to describe the different objects in the different spaces. Also, we'll talk about how to measure distances between points in the various spaces.

In the last four weeks of the semester we'll integrate over various curves and surfaces in $\mathbb{R}^3$; you'll see this material over and over.

In the last four weeks of the semester we'll integrate over various curves and surfaces in $\mathbb{R}^3$; you'll see this material over and over.