620-231 Vector Analysis

Students may gain credit for only one of 620-231 and 620-233.

One of 620-113, 620-123 and 620-143.

This subject develops the manipulation of partial derivatives and vector differential operators. Students should develop the ability to obtain extrema of functions of several variables, calculate line, surface and volume integrals, and to work in curvilinear coordinates. This subject demonstrates the fundamental concepts of vector calculus and the relations between line, surface and volume integrals.

Functions of several variables topics include limits, continuity, differentiability, matrix version of chain rule, Jacobian, Taylor polynomials, and Lagrange multipliers. Vector calculus topics include vector fields, flow lines, curvature, torsion, gradient, divergence, curl and Laplacian. Integrals over paths and surfaces topics include line, surface and volume integrals; change of variables; applications including averages, moments of inertia, centre of mass, Green's theorem, Divergence theorem and Stokes' theorem; and curvilinear coordinates.

Up to 24 pages of written assignments, a 3-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.