620-121 Mathematics A (Advanced)

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 solution of systems of linear equations by row operations, row echelon form and reduced row echelon form; matrices, rank of a matrix, inverses, applications to solving sytems 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, differentiability. Single and multivariable differential calculus topics include treatment of polynomial, rational, trigonometric, exponential, logarithmic, and hyperbolic functions and their inverses; implicit differentiation; applications to graph sketching; level curves, partial derivatives, chain rules for partial derivatives, 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; and fundamental theorem of calculus, Liebniz's theorem, improper integrals.

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