620-181 Mathematics 1R

Note

This subject is not available to students enrolled in any Bachelor of Science course. Combined Science/Engineering students are required to take Science Mathematics.

Credit Points

Coordinator

Prerequisites

VCE Specialist Mathematics 3/4, or an equivalent secondary school program.

Semester

Contact

Subject Description

This subject prepares students for later studies in engineering and other disciplines in which mathematical concepts are needed, introducing both important topics not previously studied at school, and giving a fresh perspective on familiar topics. The treatment in the pair of subjects 620-181, 620-182 is less advanced than that given in 620-171 and 620-172 and fewer topics are covered, so that students passing 620-181 and 620-182 enter 200-level significantly behind students who have taken 620-171, 620-172.

Vectors and matrices: Vectors in three-dimensional space, dot and cross products, triple products, determinants; equations of lines and planes, geometrical applications; matrices, row operations, inverses; solution of linear equations, row-reduction, rank. Calculus: functions of one real variable, derivatives; curve sketching; maxima and minima, curvature; antiderivatives and the definite integral; trigonometric functions and their inverses; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Differential equations: gradient fields, first-order differential equations (linear via integrating factors, separable and homogeneous); linear differential equations with constant coefficients, particular integrals and complementary functions; applications to damped oscillators and resonance.

Assessment

Up to 35 pages of written assignments, four hours of end-of-semester written examination (one hour of which will be a written examination on differential equations) and class tests totalling not more than 1.5 hours.