620-233 Vector Analysis (Advanced)

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

Students in the combined degree BE/BSc should note that credit exclusions exist between this subject and Engineering mathematics subjects. Refer to entries for 431-201 Engineering Analysis A and 431-202 Engineering Analysis B for details.

An H3 or better in 620-120 (UMEP Maths for High Achieving Students) or 620-121 together with an H3 or better in 620-123 or 620-113; or by invitation from the Head of Department.

This subject covers the material presented in 620-231 Vector Analysis plus additional material designed to provide deeper insight into interesting areas of vector analysis.

The 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, implicit and inverse function theorems, 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. Possible additional topics include differential geometry of surfaces.

Up to 36 pages of written assignments due during the semester (20%); a 3-hour written examination in the examination period (80%).