Matrices, Vector Calculus and Complex Analysis
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
AND ONE OF
MTH10013 Linear Algebra and Applications
OR
MTH10003 Engineering Mathematics 2P *
OR
MTH10007 Engineering Mathematics 2 *
01-June-2025
02-November-2025
Learning outcomes
Students who successfully complete this unit will be able to:
- Calculate the eigenvalues and eigenvectors of 2x2 and 3x3 matrices (K2, S1)
- Interpret the quadratic form and find its canonical form (K2, S1)
- Use the Cayley-Hamilton theorem to simplify matrix powers (K2, S1)
- Apply Vector Calculus to analyse and model processes that arise in scientific and engineering applications (K2, S1)
- Apply Green’s theorem, Ostrogradsky-Gauss’ divergence theorem and Stokes’ theorem (K2, S1)
- Perform operations with complex numbers, understand and use the concepts of analyticity and function singularities in computing contour integrals (K2, S1)
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 |
| Online Learning activities | 1.00 | 12 weeks | 12 |
| Unspecified Activities Independent Learning | 6.50 | 12 weeks | 78 |
| TOTAL | 150 |
Sarawak
| 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 |
| Online Learning activities | 1.00 | 12 weeks | 12 |
| Unspecified Activities Independent Learning | 6.50 | 12 weeks | 78 |
| TOTAL | 150 |
Assessment
| Type | Task | Weighting | ULO's |
|---|---|---|---|
| Examination | Individual | 50 - 55% | 1,2,3,4,5,6 |
| Online Quizzes | Individual | 5% | 1,2,3,4,5,6 |
| Test | Individual | 20 - 25% | 1,2,3 |
| Test | Individual | 20 - 25% | 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
- Matrix Analysis: eigenvalue problems, reduction to canonical form, matrix operations, science and engineering applications
- Vector Calculus: derivatives of a scalar and vector-valued functions; differential vector operators; line, surface and volume integrals; Green’s, Ostrogradsky-Gauss’ and Stokes’ theorems with applications
- Functions of a complex variable: review of complex numbers, analytical functions, differentiation of function of a complex variable, complex series, singularities, zeros and residues, contour integration, science and engineering applications
Study resources
Reading materials
A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.