Engineering mathematics
BI BM BN BR BEC
Dr Alistair Carr
3 points * Full-year subject * 1.5 hours per week * Gippsland/Distance * Prerequisites: GAS1611, GAS1612 and a computer programming subject
This subject is designed to introduce techniques and applications of Laplace transforms and Fourier series, and to introduce suitable methods for the numerical problems and approximations most commonly encountered in engineering and science, and to examine their relative advantages, their likely accuracy, and their computational efficiencies. 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 of 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. On-campus students are offered lectures (one hour per week in first semester, two hours per week in second semester) supplemented by study guides and assignment work, and an optional weekly tutorial. For distance dducation students there are study guides and sssignment work, and compulsory participation in a residential school.
Assessment
Assignments: 40% * Examination: 60%
Prescribed texts
Atkinson E Elementary numerical analysis 2nd edn, Wiley, 1989
O'Neil P Advanced engineering mathematics 3rd edn, Wadsworth, 1991
Recommended reading
Burden R L and Faires J D Numerical analysis 4th edn, PWS-Kent, 1989
James G and others Advanced modern engineering mathematics Addison-Wesley, 1993
Plybon B F An introduction to applied numerical analysis PWS-Kent, 1992