Authorised by Academic Registrar, April 1996
Objectives The general objective of this subject is for students to consolidate and expand knowledge and skills in algebra and geometry, study advanced differential calculus including ordinary differential equations and functions of several variables and investigate applications (particularly for use in other engineering and science subjects), and establish groundwork for further developments.
Synopsis Understand matrix algebra and its uses, especially in solving linear equations; calculate vector products and use vectors in the study of three dimensional geometry, especially of planes and straight lines; calculate partial derivatives, differentials, gradient vectors and directional derivatives of functions of several variables; use the calculus of functions of several variables to calculate approximations and construct tangent planes and normal lines to a surface; find local extreme values and saddle points for functions of several variables, in particular using Lagrange multipliers for constrained problems; calculate arc lengths of curves and line integrals and understand the notion of a conservative vector field and associated potential functions; develop skills to solve first order differential equations and second order linear differential equations with constant coefficients.
Assessment Examinations (2 hours): 85% + Assignments: 15%