### Overview

This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies.

### Requisites

Teaching periods
Location
Start and end dates
Last self-enrolment date
Census date
Last withdraw without fail date
Results released date

### Learning outcomes

Students who successfully complete this unit will be able to:

• Perform simple operations involving determinants, the rank of a matrix and its null space (K2)
• Perform operations with vectors and have a working understanding of vector spaces. Use vectors to calculate scalar and vector products, determine linear (in)dependence of vectors (K2, S1)
• Use the methods of Gaussian elimination, Cramer’s rule and inverse matrices to solve systems of linear equations and apply them to relevant examples (K2, S1)
• Describe straight lines and planes in three dimensions and the relationships between them (K2, S1)
• Use curvilinear coordinates, linear transformations and conversions with parametric forms to solve simple problems. Determine the curvature and radius of curvature for a curve, angular velocity and torque (K2, S1)
• Use complex numbers to solve equations, describe graphically complex numbers in the Argand plane (K2)

### Teaching methods

#### Hawthorn

Type Hours per week Number of weeks Total (number of hours)
Live Online
Lecture
2.00 12 weeks 24
On-campus
Class
2.00 12 weeks 24
On-campus
Class
2.00 12 weeks 24
Online
Directed Online Learning and Independent Learning
1.00 12 weeks 12
Unspecified Activities
Independent Learning
5.50 12 weeks 66
TOTAL150

### Assessment

Type Task Weighting ULO's
ExaminationIndividual 40 - 50% 1,2,3,4,5,6
Online AssignmentIndividual 20 - 30% 1,2,3,4,5,6
TestIndividual 10 - 20% 1,2,3,4
Tutorial ExercisesIndividual 10 - 20% 1,2,3,4,5,6

#### Hurdle

As the minimum requirements of assessment to pass a unit and meet all ULOs to a minimum standard, an undergraduate student must have achieved:

(i) an aggregate mark of 50% or more, and(ii) at least 40% in the final exam.Students who do not successfully achieve hurdle requirement (ii) will receive a maximum of 45% as the total mark for the unit.

### Content

• Matrices. Matrix algebra operations, determinants, rank, nullity, basis, linear independence
• Vectors. Direction, magnitude, vector spaces, sub-spaces spanning and bases, scalar product and vector product
• Systems of linear equations. Elementary row operations, augmented matrix, row-echelon form, Gaussian elimination, Cramerâ€™s rule, inversion
• Elements of linear geometry & differential geometry. Equation of straight lines and planes, intersection & distance between points, lines and planes. curvilinear coordinates, curvature, velocity and acceleration
• Linear transformations. Matrix of linear transformations, rotations, inversions and projections
• Complex numbers and their properties. Imaginary numbers, Argand plane in Cartesian and polar forms, roots of complex numbers, complex exponential form and applications

### Study resources

#### Reading materials

A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.