620-123 Applied Mathematics (Advanced)

Note

Credit Points

HECS Band

Coordinator

Prerequisites

One of 620-111, 620-120 (MUPHAS Mathematics), 620-121 or [99]620-141 with a grade of H1.

Semester

Contact

Subject Description

This subject introduces the classification and principles governing the solution of the basic first and second order differential equations. Students completing the subject develop the ability to classify and solve with accuracy and confidence the basic differential equations of first and second order and to translate that understanding into mathematical formulation of physical problems. This subject demonstrates the power of differential equation modelling in advancing an understanding of complex physical processes from a wide variety of real world phenomena.

Integration: systematic integration; approximate integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution in cartesian and polar co-ordinates. Differential equations: first-order differential equations (linear via integrating factors, separable and homogeneous) and applications; second order differential equations (reducible to first order, linearly independent solutions), second order linear differential equations with constant coefficients, particular integrals and complementary functions and applications. Systems of differential equations: systems of linear differential equations with constant coefficients, applications of matrix methods, stability; equilibrium and stability of conservative systems, small oscillations; first-order autonomous nonlinear systems and the phase plane.

Assessment

Up to 24 pages of written assignments, class tests totalling not more than 1.5 hours and a 3-hour end-of-semester written examination.