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 and determinants, eigenvalues and eigenvectors; introduction to vectors; parametric curves; 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; Sequences and series, Taylor series and series convergence, the reminder term.

Objectives

On completion of this unit, students will:

1. understand the key steps of scientific method and how these are applied to modelling of simple physical phenomena;
2. have developed skills in solving systems of linear equations;
3. understand the theory of solving a system of n linear equations with m unknowns;
4. have developed skills in the manipulation of matrices and determinants;
5. have developed skills in finding eigenvalues and eigenfunctions of square matrices;
6. have further developed skills in integral calculus;
7. have developed skills in solving the differential equations that arise from simple models of population growth and oscillations;
8. have developed skills in solving the differential equations that arise from simple models of population growth and oscillations;
9. understand the process of setting up differential equations to model a simple physical process;
10. be able to use vectors to represent lines and planes;
11. be able to develop vectorial quantities in Rn;
12. be able to parameterise curves and planes in R3;
13. understand the use of Taylor series in approximating functions and to estimate errors in truncating a series;
14. be able to apply rigorous mathematical reasoning to problem solving;
15. be able to develop simple mathematical proofs; and
16. be able to prepare and write scientific report which includes presentation of results from numerical and theoretical models and effective use of appropriate mathematical software in problem solving.

Assessment

Continuous assessments: 40%
Final Examination: 60%

Chief examiner(s)

Dr Leo Brewin

Contact hours

Three 1-hour lectures plus one 2-hour tutorial/computer laboratory per week.

Prerequisites

VCE Specialist Mathematics with an ATAR/ENTER score of 95 or above; a VCE study score of 35 or above in Specialist Mathematics; a High Distinction in MTH1020; or by approval of the Head of School of Mathematical Sciences. In order to enrol in this unit students will need to apply via the Faculty of Science office.

Prohibitions

MTH1030, MTH1085