Course Description

This is the second course in the calculus sequence. Building on the foundations of single-variable calculus (MATH 101) and linear algebra (MATH 120), MATH 102 extends the ideas of differentiation and integration into higher dimensions. The course begins with vectors, lines, planes, and quadric surfaces, then moves to vector-valued functions, arc length, and curvature. The core of the course develops multivariable differential calculus, partial derivatives, gradients, directional derivatives, tangent planes, linear approximations, and optimization via Lagrange multipliers, followed by multivariable integral calculus: double and triple integrals in Cartesian, polar, cylindrical, and spherical coordinates, with change-of-variables techniques. The course culminates with vector calculus: line integrals, surface integrals, and the three great theorems of Green, Stokes, and the Divergence Theorem that unify the subject.