# MTH1030 - Techniques for modelling

## 6 points, SCA Band 2, 0.125 EFTSL

#### Offered

Clayton First semester 2007 (Day)

Clayton Second semester 2007 (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