Parametric equations, polar coordinates, and vector-valued functions

This course is a part of AP®︎ Calculus BC, a 12-course Topic series from Khan Academy.

We are used to working with functions whose output is a single variable, and whose graph is defined with Cartesian, i.e., (x,y) coordinates. But there can be other functions! For example, vector-valued functions can have two variables or more as outputs! Polar functions are graphed using polar coordinates, i.e., they take an angle as an input and output a radius! Learn about these functions and how we apply the concepts of the derivative and the integral on them.

This course contains 9 segments:

Defining and differentiating parametric equations

Second derivatives of parametric equations

Finding arc lengths of curves given by parametric equations

Defining and differentiating vector-valued functions

Solving motion problems using parametric and vector-valued functions

Defining polar coordinates and differentiating in polar form

Finding the area of a polar region or the area bounded by a single polar curve

Finding the area of the region bounded by two polar curves

Calculator-active practice