Undergraduate - UnitMTH1020 - Analysis of change

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered, or view unit timetables.

Synopsis

Properties of real and complex numbers; algebraic functions and common transcendental functions; modelling change using elementary functions; limits and continuity; rate of change, derivatives, local and global extrema; sums and integrals, anti-derivatives, calculus applications: optimisation, area and volume, introduction to differential equations; Vectors in two- and three- dimensional space.

Outcomes

On completion of this unit students should have a firm grasp of the properties of real and complex numbers and the analytical properties of elementary functions, be competent in using the basic techniques in differential and integral calculus to investigate the behaviour of functions which are used to model change in real-life situations and demonstrate basic knowledge of vectors in two- and three-dimensional space. In particular, they will have acquired knowledge of: the properties of real and complex numbers; the concepts of limit, continuity, differentiable and integrable functions; the basic analytic properties of simple algebraic functions and common transcendental functions; the concepts of local and global extrema; the inter- relationship between differentiation and integration; will have developed skills in: working out the functional behaviour by means of neat sketch-graphs; determining basic properties and behaviour of functions by analytic, numerical and graphical means; giving geometric interpretation of and the limiting processes involved in taking the derivative and the integral of a function; using differentiation and integration techniques in applied contexts; vectors and two and three-dimensional space; communicating and interpreting mathematical results; using computer algebra software to analyse change of real-life problems; and will have developed and/or strengthened the ability to present mathematical arguments in writing.

Assessment

Examination (3 hours): 60%
Assignments and tests: 40%
Students must pass the examination to be awarded a pass grade.

Chief examiner(s)

Associate Professor Cristina Varsavsky

Contact hours

Three 1-hour lectures and one 2-hour support class per week

Prerequisites

MTH1010 or VCE Mathematical Methods units 3 and 4 (with an average grade of C or above in the written examination components)

Prohibitions

MTH1055. Please note that students who have already completed MTH1030 or MTH1035 cannot enrol in MTH1020.