Authorised by Academic Registrar, April 1996
Objectives The objectives of this subject are for students to understand applications of the Heaviside step function and Dirac delta function, particularly in using the Laplace transform; develop understanding of the properties of the Laplace transform and skill in applying that transform, particularly to solving linear differential equations; be able to determine the Fourier series for a periodic function, and use its convergence properties; be familiar with the Fourier transform (and related transforms) and applications to elementary linear differential equations; understand the basic properties of the (discrete) Z-transform, and its applications to solving linear difference equations and summing certain infinite series.
Synopsis This subject introduces several integral transforms with some of their applications, and also Fourier series and the discrete Z-transform. Topics include separation of variables for partial differential equations; Laplace transforms - properties, and applications to ordinary and partial differential equations and to certain integral equations; the Dirac and Heaviside functions; Fourier series, including half-range expansions and convergence properties; Fourier transforms - properties, and applications to ordinary and partial differential equations; Fourier cosine and sine transforms; Mellin and other integral transforms; the Z-transform and its use for solving linear difference equations and for summing infinite series. For on-campus students, lectures and tutorials are held, supplemented by study guides and five assignments. The latter are corrected but the work does not count directly towards assessment grades.
Assessment Gippsland - Class tests: 40% + Distance - assessment assignments: 40% + Examination: 60%