MTH1030 - Techniques for modelling

Leader(s): Semester One - Dr Leo Brewin; Semester Two - Dr Burkard Polster

Offered

Clayton First semester 2009 (Day)
Clayton Second semester 2009 (Day)

Synopsis

Solution of systems of linear equations using Gaussian elimination; introduction to vectors; methods of integration - substitutions and integration by parts; solution of first-order ordinary differential equations - separable, use of integrating factor; solution of second-order linear ordinary differential equations with constant coefficients and applications; Taylor series and series convergence; introduction to probability, discrete and continuous random variables; normal distribution; functions of several variables: partial derivatives, directional derivatives, maximum and minimum values.

Objectives

On completion of this unit, students will understand the key steps of the scientific method and how these are applied to modelling of simple physical phenomena; have developed skills in solving systems of linear equations; have developed skills in integral calculus; understand the concepts of probability, random variable and continuous probability distribution; have developed skills in using the normal distribution; have developed skills in solving the differential equations that arise from simple models of population growth and oscillations; be able to use vectors to represent lines and planes; be able to perform partial and directional derivatives of multivariable function; be able to prepare and write a scientific report which includes presentation of results from simple numerical models and the use of Excel to perform calculations; understand the use of Taylor series in approximating functions.

Assessment

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

Contact hours

Three 1-hour lectures and one 2-hour computer laboratory per week

Prerequisites

MTH1020 or VCE Specialist Mathematics units 3 and 4 (with an average grade of B or above in the written examination components)

Prohibitions

MAT1085 or MAT1812