Authorised by Academic Registrar, April 1996
Objectives On completion of this subject the student is expected to demonstrate an understanding of the basic computational techniques of calculus, including those involving partial differentiation of functions of two variables; understand sufficient of the conceptual basis of calculus to be able to apply it to derive formulations of scientific and engineering problems; demonstrate facility in computations involving row-reduction algorithms for solution of linear systems, and eigenvalues and eigenvectors of a small square matrix; demonstrate an understanding of the structure of the solution set of a linear system and of the interpretation and uses of eigenvalues and eigenvectors.
Synopsis Topics covered include the following. Calculus: complex numbers; hyperbolic functions and their inverses; extension of systematic indefinite integration beyond GAS1613; extension of differential equations including homogenous and linear ODEs; convergence of series; Taylor's theorem; partial differentiation and local extrema of functions of two variables. Linear algebra: linear systems of equations and row-reduction algorithms; linear dependence of vectors and subspaces of Euclidean n-space; eigenvaluesand eigenvectors; diagonalisation of matrices; applications to mechanical and electrical systems.
Assessment Class tests and assignments: 40% + Examination (3 hours): 60%