620-171 Mathematics 1P

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

Special permission of the Director of First-year Studies (normally requiring a high level of achievement in VCE Specialist Mathematics 3/4, or in 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 important topics not previously studied at school, and giving a fresh perspective on familiar topics. The treatment in the pair of subjects 620-171, 620-172 is more advanced than that given in 620-181 and 620-182 and more topics are covered, so that the student passing 620-171 and 620-172 enters 200-level considerably ahead of students who have taken 620-181, 620-182.

Foundations: sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus: functions of one real variable (including limits and continuity), derivatives; curve sketching; maxima and minima, curvature; antiderivatives and the definite integral; trigonometric functions and their inverses, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Vectors and linear equations: vectors in three-dimensional space, dot and cross products, triple products, determinants; linear dependence; equations of lines and planes, geometrical applications; bases and coordinates, dimension; row reduction, rank, inverse, solution of linear equations, geometrical interpretation. 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.