Authorised by Academic Registrar, April 1996
Objectives The student is expected to understand techniques and applications of Laplace transforms and Fourier series, and to be able to employ a basic suite of methods for some of the numerical problems and approximations most commonly encountered in engineering and science, with an understanding of their relative advantages, likely accuracy and computational efficiencies.
Synopsis Topics include Laplace transforms (properties, applications including ordinary differential equations and linear systems generally; convolution, Heaviside and Dirac functions, inversion); Fourier series including harmonic analysis and convergence properties; floating point representation of numbers; propagation of errors; solution on non-linear equations in a single variable; interpolation; numerical solution of systems of linear equations by direct and indirect methods; least squares fitting; numerical integration including the Romberg algorithm for accelerated convergence; solution of ordinary differential equations in both initial value and boundary value problems; examination of computational efficiency; rates for convergence; error analysis; operation counts and computing time; introduction to suitable software packages for numerical approximations.
Assessment Assignments: 40% + Examination: 60%