MAT3026

Differential equations

Not offered in 1998

Dr Alistair Carr

8 points
* Two 2-hour lectures and one 2-hour tutorial per week
* First semester
* Gippsland/Distance (odd-numbered years only)
* Prerequisites: MAT1085 or GAS1615, MAT2030 or GAS2612, MAT2047 or GAS2621, MAT2077 or GAS2622
* Prohibitions: MAA3021, MAA3072, MAT3022, MAT3031, GAS3621

Objectives Ability to formulate practical problems as systems of ordinary or partial differential equations. Facility with the use of the various techniques for the solution of differential equations, including Bessel functions and Legendre polynomials, Green's function techniques, separation of variables, use of Laplace and Fourier transforms numerical approximation algorithms. Understanding of qualitative behaviour of solutions of systems of ordinary differential equations near equilibrium.

Synopsis This subject treats several advanced methods for solving ordinary and partial differential equations with physical applications, and the use of numerical approximations where appropriate. Topics include basic stability theory for linear systems with phase plane analysis for critical points, Green's functions, the Frobenius method, Bessel functions and Legendre polynomials, and Sturm-Liouville theory, standard partial differential equations with applications, Dirichlet and Neumann boundary problems, numerical methods for boundary value problems in two variables.

Assessment Examination (3 hours): 70%
* Assessment assignments: 30%

Prescribed texts

O'Neil P Advanced engineering mathematics 4th edn, Wadsworth 1995

Recommended texts

Kreyszig E Advanced engineering mathematics 7th edn, Wiley 1993