620-141 Mathematics A

• Students enrolling in this subject are expected to have completed VCE Specialist Mathematics 3/4 (or an equivalent subject). Students who have completed VCE Mathematical Methods 3/4 but not VCE Specialist Mathematics 3/4 should discuss their suitability for undertaking this subject with the director of first-year studies.

• Students may only gain credit for one of [00]620-111, 620-121, 620-140, 620-141.

This subject introduces the manipulation of vectors, matrices, and systems of linear equations, the concepts of vector geometry, the properties of basic functions of calculus and basic work on complex numbers. Students should develop the ability to solve systems of linear equations, employ vector methods in geometrical problems, differentiate the basic functions of calculus and use differential calculus to solve extremal problems including problems involving functions of more than one variable. This subject develops the fundamental concepts in linear algebra, calculus and complex numbers necessary for further studies in mathematics.

Linear algebra, matrices and determinants, vector geometry 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; problems involving lines and planes; and scalar triple product. 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.

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.