Integral transforms
Not offered in 1997
Dr Alistair Carr
3 points * First semester * 2 hours per week * Gippsland/Distance * Prerequisites: GAS1611 (and subject GAS2612 is desirable) * Prohibition: MAT3910
Objectives The objectives of this subject are for students to understand 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 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 Fourier transforms - including applications to ordinary and partial differential equations; Fourier cosine and sine transforms; Mellin and other integral transforms; the Z-transform and some of its applications. For on-campus students, lectures and tutorials are held, supplemented by study guides and five non-assessable assignments.
Assessment Gippsland - Class tests: 40% * Distance - assessment assignments: 40% * Examination: 60%
Prescribed texts
O'Neil P Advanced engineering mathematics 4th edn, Wadsworth, 1995
Recommended reading
James G and others Advanced modern engineering mathematics Addison-Wesley, 1993
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