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

Prerequisites
MTH10013 Linear Algebra and Applications

Rule

Admission into a Bachelor of Engineering (Honours), Bachelor of Aviation or Bachelor of Science, and all related Professional and double degrees.
OR
MTH00005 Applied Engineering Mathematics
OR
MTH00007 Preliminary Mathematics

Teaching Periods
Location
Start and end dates
Last self-enrolment date
Census date
Last withdraw without fail date
Results released date
Semester 1
Location
Hawthorn
Start and end dates
26-February-2024
26-May-2024
Last self-enrolment date
10-March-2024
Census date
31-March-2024
Last withdraw without fail date
12-April-2024
Results released date
02-July-2024
Semester 2
Location
Hawthorn
Start and end dates
29-July-2024
27-October-2024
Last self-enrolment date
11-August-2024
Census date
31-August-2024
Last withdraw without fail date
13-September-2024
Results released date
03-December-2024

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 vector (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)
On-campus
Lecture
4.00 12 weeks 48
On-campus
Class
1.00 12 weeks 12
Unspecified Activities
Independent Learning
7.50 12 weeks 90
TOTAL150

Assessment

Type Task Weighting ULO's
ExaminationIndividual 55% 1,2,3,4,5,6 
Online AssignmentIndividual 15% 1,2,3,4,5,6 
TestIndividual 15% 1,2,3,4 
TestIndividual 15% 4,5 

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: basic matrix algebra, multiplication of matrices, special matrices, determinants, inversion, Cramer's rule, rank, null space, basis, linear independence
  • Vectors: direction and magnitude, vector spaces, sub-spaces spanning and bases, linear dependence / independence, length of a vector and the scalar product, area of a parallelogram and the vector product. Examples and applications to simple models
  • Elements of linear geometry: equation of a line, equation of a plane, intersection between lines and planes, distance from a point to a plane, distance from a point to a line, distance between two lines
  • Systems of linear equations: elementary row operations, augmented matrix, row echelon form, Gaussian elimination, Cramer’s rule, inversion method, solution in the parametric form. Examples and applications to relevant models
  • Elements of differential geometry: curvilinear coordinates, curves and their properties, curvature, velocity and acceleration
  • Linear transformations: system of linear equations in the matric form, matrix of linear transformations, examples: rotations, inversions and projections. Applications to fundamental examples.
  • Complex numbers and their properties: imaginary numbers, complex conjugates, Argand plane in Cartesian and polar forms, de Moivre’s theorem, 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.