MTH1030

Techniques for modelling ( 6 points, SCA Band 2, 0.125 EFTSL)

Undergraduate

(SCI)

Leader: Dr Anthony Lun

Offered:
Clayton First semester 2006 (Day)
Clayton Second semester 2006 (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; Taylor series and series convergence; introduction to discrete and continuous random variables; 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 'scientifc method' and how it can be 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 random variable and continuous probability distribution; have developed skills in solving the differental 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 use spreadsheets to perform calculations and present results from simple numerical models; understand the use of Taylor series in approximating functions; have developed skills in the use of computer algebra software as an aid for modelling; and be able to prepare and write a scientific report.

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