620-143 Applied Mathematics

Note

Credit Points

Coordinator

Prerequisites

Normally, [99]620-141. Or any one of 620-111, 620-121, 620-180, 620-200 or 620-211; or concurrent enrolment in one of 620-180, 620-200, 620-211. Note: with subjects from 1998 (or earlier) as pre-requisites, students must have taken [98]620-121, or both of [98]620-141 and [98]620-142. Students with only [98]620-141 will need to take 620-180.

Semester

Contact

Subject Description

This subject introduces the terminology of ordinary differential equations; the principles of first and second order ordinary differential equations; linear systems of first and second order ordinary differential equations and their applications. Students completing the subject develop the ability to solve analytically first order ordinary differential equations (ODEs), second order linear ODEs, and systems of two or three linear first order ODEs using eigenvalue/eigenvector techniques; and to apply the above techniques to simple problems. The subject demonstrates the role of differential equations in applied mathematics.

Integration: antiderivatives and the definite integral; systematic integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Differential equations: first-order differential equations (separable, linear via integrating factor, homogeneous) and applications; second-order differential equations (reducible to first-order, linearly independent solutions), second-order linear differential equations (particular integrals, complementary functions) and applications; numerical solution of first-order equations. Systems of differential equations: Eigenvalues and eigenvectors; systems of first-order differential equations and applications; systems of second-order linear differential equations and applications.

Assessment

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