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 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 complex numbers. Students should develop the ability to solve systems of linear equations, employ vector methods in geometrical problems, sketch and manipulate hyperbolic functions 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, and 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, and applications to solving systems 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. Calculus topics include intuitive idea of limits, continuity and differentiability of functions of one variable; 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 of complex exponentials and applications.

Up to 36 pages of written assignments during the semester (10%); a 45-minute written test held mid semester (0% or 10%); a 3-hour written examination in the examination period (80% or 90%). The relative weighting of the examination and mid-semester test will be chosen so as to maximise the student's final mark.