620-231 Vector Analysis

Note

Credit Points

HECS Band

Coordinator

Prerequisites

Either one of 620-113, 620-123, 620-143; or one of [98]620-122, [98]620-142 and one of [98]620-130, [98]620-132.

Semester

Contact

Subject Description

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, 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, Stokes' theorem; curvilinear coordinates.

Assessment

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.