MATH 2015U – Calculus III

This course develops multivariable differential and integral calculus and vector calculus. Topics include: Cylinders and quadric surfaces; multivariate functions (scalar fields, limits, continuity, partial derivatives, chain rule); directional derivatives and gradients; curves and surfaces in Euclidean space; Taylor’s theorem in several variables; linear and quadratic approximations; multivariate optimization; iterated integrals over rectangular domains in 2 and 3 dimensions; spherical and cylindrical polar coordinate transformations; general coordinate transformations; iterated integrals over non-rectangular domains; vector fields; vector differential operators (gradient, divergence, curl); parametric curves and arc length; parametric surfaces and surface area; line integrals and surface integrals; Green’s theorem; Gauss’ theorem; Stokes’ theorem.
Credit hours: 3
Lecture hours: 3
Tutorial hours: 1
Prerequisite(s): MATH 1020U and (MATH 1850U or MATH 2050U)
Credit restriction(s): MATH 2810U, MATH 2010U, MATH 2020U