Level Surfaces of Multivariable Functions

A function of three variables gives one real number for each point in three-dimensional space. Each point is written with Cartesian coordinates, x, y, and z, and the function maps that ordered triple to a single value. These functions are often used to describe physical quantities that change across space.

A function of three variables assigns a single real number—a scalar value—to every point in three-dimensional space. These points are defined by their coordinates: x, y, and z.

A practical example is the electric potential surrounding a point charge. The potential at any spatial point depends on its distance from the c...