Multivariable Calculus

One extra input changes the picture: z = f(x, y) assigns a height to every point of the plane, and the graph becomes a surface. These three lessons read that surface the way a surveyor does — as a flat map of level curves — then measure its slope one direction at a time, and finally assemble those slopes into the gradient, the arrow that points uphill. This material runs past the AP AB/BC syllabus, but every tool in it is the single-variable derivative, used twice.