Differential equations
BS BN BT DT BC BP BDT
Dr Alistair Carr
6 points * First semester * 4 hours per week * Gippsland/Distance (odd-numbered years only) * Prerequisites: GAS1612, GAS2612, GAS2622, GAS2621 (and subject GAS2623 is desirable)
This subject aims to treat several advanced methods for solving ordinary and partial differential equations with physical applications, and the use of numerical approximations where appropriate. Topics include review of techniques for solving ordinary differential equations; the power series method and Frobenius solutions; Bessel functions and Legendre polynomials; Sturm-Liouville theory - separation of variables and the use of integral transforms for linear partial differential equations in two or more independent variables; Green's functions for ordinary differential equations; use of the phase plane and analysis of critical points for linear and non-linear systems; introduction to numerical methods for partial differential equations. On-campus students are offered lectures and tutorials, supplemented by assignments and study uides. Some assignment work is corrected but does not count directly towards assessment grades. One of the assessment assignments is a long essay on a technical, historical or `applications' topic.
Assessment
Two assessment assignments: 40% * Examination: 60%
Prescribed texts
O'Neil P Advanced engineering mathematics 3rd edn, Wadsworth, 1991
Recommended texts
Borrelli R L and Coleman C S Differential equations - a modeling approach Prentice-Hall, 1987
Haberman R Elementary applied partial differential equations Prentice-Hall, 1983
Huntley I D and Johnson R M Linear and non-linear differential equations Ellis Horwood, 1983
James G and others Advanced modern engineering mathematics Addison-Wesley, 1993
Kreyszig E Advanced engineering mathematics 7th edn, Wiley, 1993