Leader: T Lun
Clayton First semester 2006 (Day)
Malaysia First semester 2006 (Day)
Clayton Second semester 2006 (Day)
Malaysia Second semester 2006 (Day)
Synopsis: Multivariable calculus: double and triple integrals, parametric representation of lines and curves in three dimensional space, use of Cartesian, cylindrical and spherical coordinates, surface and volume integrals, the operations of the gradient, divergence and curl. Ordinary Differential Equations: solve systems of linear differential equations and the 2nd order Sturm-Liouville type problems. Partial differential equations: the technique of separation of variables and the application of this technique to the wave equation, the heat equation and Laplaces equation.
Objectives: On completing this unit, students will be able to represent curves parametrically solve line integrals on these curves; solve double and triple integrals in Cartesian, cylindrical and spherical coordinates; represent surfaces parametrically and solve flux integrals across these surfaces; perform the operations of the gradient, divergence and curl, use these operations in the solution of surface and volume integrals through the Divergence theorem and Stokes theorem; solve systems of simple ordinary differential equations; establish the eigenvalues of these systems; identify and solve 2nd order linear Sturm Liouville differential equations; represent a periodic function with a Fourier series and identify even and odd series expansions; solve elementary partial differential equations through the method of separation of variables; apply this technique to the wave equation, the heat equation and Laplaces equation; classify 2nd order linear partial differential equations as elliptic, parabolic or hyperbolic.
Assessment: Assignments and test: 30% + Examination (3 hours): 70%
Contact Hours: Three hours of lectures, one two-hour practice class and seven hours of private study per week