Monash University Handbook 2011 Undergraduate - Unit

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

Synopsis

Solution of systems of linear equations using Gaussian elimination; matrices, determinants, eigenvalues and eigenvectors; 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; the remainder term.

Objectives

On completion of this unit, students will:

1. understand the key steps of the scientific method and how these are applied to modelling of simple physical phenomena;
2. have developed skills in solving systems of linear equations;
3. have developed skills in integral calculus;
4. have developed skills in manipulating matrices and determinants;
5. have developed skills in finding eigenvalues and eigenvectors of a square matrix;
6. have developed skills in solving the differential equations that arise from simple models of population growth and oscillations;
7. be able to use vectors to represent lines and planes;
8. 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;
9. understand the use of Taylor series in approximating functions; and
10. be able to use the remainder term in Taylor series to estimate the error term in truncating a series.

Assessment

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

Chief examiner(s)

Dr Leo Brewin (First semester)
Dr Simon Teague (Second semester)

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

MTH1035, MTH1085