Vectors and vector-valued functions, the dot and cross products, curves in space and the calculus of vector-valued functions. Multi-variable functions, limits, continuity, and differentiation. Partial ...

Cylindrical and spherical coordinates, double and triple integrals, line and surface integrals. Change of variables in multiple integrals; gradient, divergence, and ...

Differentiation of algebraic and trigonometric expressions can be used for calculating rates of change, stationary points and their nature, or the gradient and equation of a tangent to a curve.