The Main Idea: Level Sets

What are Functions?

Basic definitions: domain, range, and derivative.

Level Sets of Single-Variable Functions

The geometric relationship between level sets and zeros (or roots) of functions.

Level Sets of Multivariable Functions

The geometry of level sets and an introduction to singularities.

Why are Level Sets Important?

Example of level sets in our daily lives.

Level Surfaces

Implicit surfaces are the level sets of a function of three variables.

Level Curves in Higher Dimensions

Implicitly-defined curves in space are just the intersection of surfaces in space.