Authorised by Academic Registrar, April 1996
Objectives The objectives of this subject are to enable students to determine the gradient and the directional derivative of a scalar field; determine the surface integral of a scalar function over a given surface; determine the potential of a conservative force field; determine the divergence, and curl of a vector field; apply Stokes' theorem to find the flux of a vector field across a surface; use Gauss's theorem to find the divergence of a vector field; find grad, div and curl in Cartesian, as well as Non-Cartesian (curvilinear) coordinate systems; prove simple identities involving grad, div and curl using cartesian tensors (index notation); use the properties of vector fields to describe fluid flow, electric and magnetic fields, energy flux, electric current densities, gravitational fields, heat transfer, conservative vector fields, solid mechanics, concentration of chemical species, etc.
Synopsis This subject aims to develop the basic results and methods in the differential and integral calculus of vector functions through physical applications, and to introduce Cartesian tensors; vector functions of a single variable and their derivatives; integrals of vector functions along curves and over surfaces; vectors in three dimensions; gradient of a scalar field and divergence and curl of a vector field; orthogonal curvilinear coordinates; Stokes,' Gauss's, and Green's theorems; applications to electromagnetism; tensor algebra, four-vectors in special relativity. The subject is taught by lectures and tutorials. Study guides present the basic material, with illustrations and notes on further reading. Some assignment work provides exercises which are corrected but do not count directly towards assessment grades.
Assessment Two assessment assignments: 40% + Examination: 60%