units

MTH1030

Faculty of Science

# Monash University Handbook 2011 Undergraduate - Unit

### 6 points, SCA Band 0 (NATIONAL PRIORITY), 0.125 EFTSL

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

 Level Undergraduate Faculty Faculty of Science Offered Clayton First semester 2011 (Day)Clayton Second semester 2011 (Day)Gippsland Second semester 2011 (Day)Gippsland Second semester 2011 (Off-campus) Coordinator(s) Semester One - Dr Leo Brewin; Semester Two - Dr Simon Teague (Clayton), Dr John Arkinstall (Gippsland)

#### 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)

MTH1035, MTH1085