620-121 Mathematics A (Advanced)

Students may only gain credit for one of 620-121, 620-140 and 620-141.

A high level of achievement in VCE Specialist Mathematics 3/4, or equivalent, or special permission of the Director of First Year Studies.

This subject prepares students for later studies in mathematics and statistics, or other disciplines in which mathematical concepts of calculus and linear algebra are needed, introducing important topics not previously studied at school, and giving a fresh perspective on familiar topics.

Linear algebra topics include the solution of systems of linear equations by row operations, row echelon form and reduced row echelon form; matrices, rank of a matrix, inverses and applications to solving systems of linear equations; determinants and applications; vectors in two and three dimensions; dot and cross products; triple products; and problems involving lines and planes. Foundations of analysis topics include number systems, methods of proof, mathematical induction; functions, sequences, limits, continuity and differentiability. Calculus topics include hyperbolic functions and their inverses; implicit differentiation; applications to graph sketching; level curves, partial derivatives, chain rules for partial derivatives and directional derivative; tangent planes; and extrema for functions of several variables. Complex numbers topics include Cartesian and polar form, De Moivre's theorem, powers, roots of equations and complex exponential; conversions between powers and multiple angles; and derivatives and integrals of complex exponentials and applications. Riemann integration topics include the integral as the limit of a sum; the fundamental theorem of calculus, Leibniz's theorem; and improper integrals.

A 45-minute written test held mid semester (0% or 15%); a 3-hour written examination in the examination period (85% or 100%). The relative weighting of the examination and mid-semester test will be chosen so as to maximise the student's final mark.