Three-dimensional geometry and vectors, vector-valued functions and motion in space, partial derivatives, and multiple integrals
An introduction to three-dimensional coordinate systems, vectors, the dot and cross products, lines and planes in space, and quadric surfaces
An introduction to vector-valued functions and their calculus, including derivatives and integrals of r(t), tangent lines for space curves, arc length, curvature, normal and binormal vectors, and the tangential and normal components of acceleration
An introduction to multivariable functions and their partial derivatives, including limits and continuity, the chain rule, directional derivatives and gradient vectors, tangent planes, local and absolute extrema, and Lagrange multipliers
An introduction to multiple integrals: double integrals over rectangles and over general regions, areas and volumes by double integration, double integrals in polar form, triple integrals in rectangular, cylindrical, and spherical coordinates, and substitutions (change of variables) in multiple integrals