# MTH1030 - Techniques for modelling - 2019

## 6 points, SCA Band 2, 0.125 EFTSL

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

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Coordinator(s)

Associate Professor Burkard Polster (Semester 1)
Dr Norman Do (Semester 2)

Unit guides

Offered

Clayton

• First semester 2019 (On-campus)
• Second semester 2019 (On-campus)

Prerequisites

MTH1020 or VCE Specialist Mathematics units 3 and 4 with a study score of at least 30

Prohibitions

ENG1005, ENG1091, MTH1035

## 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.

## Outcomes

On completion of this unit students will be able to:

1. Understand the basic concepts of linear algebra, recognise and manipulate elements of vector spaces;
2. Formulate and solve equations involving vectors and matrices, including for three-dimensional geometry;
3. Identify and evaluate improper integrals;
4. Solve simple first and second order differential equations, and formulate them for applications to physical systems;
5. Compute Taylor series expansions, with remainder, for functions of one variable;
6. Apply Taylor series and l'Hopital's rule to compute limits;
7. Understand and compute the convergence properties of infinite series;
8. Provide written reports that contain complete mathematical arguments.

## Assessment

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 2 hours and 10 minutes.

End of semester examination (2 hours): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for both the end-of-semester examination and continuous assessment components.