A general multivariable calculus course based on the free OpenStax textbook. Volume 3 covers parametric/polar curves, vectors and 3D geometry, vector-valued functions, partial derivatives, and multiple integrals.
A review of parametric curves and polar coordinates carried over from Vol 2 Ch 7
Vectors in 2D and 3D, dot and cross products, lines and planes, quadric surfaces, and cylindrical/spherical coordinates
Curves in space, calculus of vector-valued functions, arc length, curvature, and motion in space
Functions of several variables, partial derivatives, the chain rule, directional derivatives and gradients, optimization, and Lagrange multipliers
Double and triple integrals over a variety of regions, polar/cylindrical/spherical coordinates, and change of variables