units

MTH1035

Faculty of Science

18 September 2017
23 October 2019

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## 6 points, SCA Band 0 (NATIONAL PRIORITY), 0.125 EFTSLRefer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.
## SynopsisSolution 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: - understand the key steps of scientific method and how these are applied to modelling of simple physical phenomena;
- have developed skills in solving systems of linear equations;
- understand the theory of solving a system of n linear equations with m unknowns;
- have developed skills in the manipulation of matrices and determinants;
- have developed skills in finding eigenvalues and eigenfunctions of square matrices;
- have further developed skills in integral calculus;
- have developed skills in solving the differential equations that arise from simple models of population growth and oscillations;
- have developed skills in solving the differential equations that arise from simple models of population growth and oscillations;
- understand the process of setting up differential equations to model a simple physical process;
- be able to use vectors to represent lines and planes;
- be able to develop vectorial quantities in Rn;
- be able to parameterise curves and planes in R3;
- understand the use of Taylor series in approximating functions and to estimate errors in truncating a series;
- be able to apply rigorous mathematical reasoning to problem solving;
- be able to develop simple mathematical proofs; and
- 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% ## Chief examiner(s)## Contact hoursThree 1-hour lectures plus one 2-hour tutorial/computer laboratory per week. ## PrerequisitesVCE 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. ## ProhibitionsMTH1030, MTH1085 |