Linear Algebra and Applications
Duration
- One Semester or equivalent
Contact hours
- 60 hours face to face + Blended
On-campus unit delivery combines face-to-face and digital learning.
2023 teaching periods
| Hawthorn Higher Ed. Semester 1 |
Hawthorn Higher Ed. Semester 2 | |
|---|---|---|
Dates: Results: Last self enrolment: Census: Last withdraw without fail: |
Dates: Results: Last self enrolment: Census: Last withdraw without fail: |
Prerequisites
Assumed KnowledgeVCE Mathematical Methods or Equivalent
Aims and objectives
This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies
Unit Learning Outcomes (ULO)
Students who successfully complete this unit will be able to:
Students who successfully complete this unit will be able to:
2. 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).
3. 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).
4. Describe straight lines and planes in three dimensions and the relationships between them (K2, S1).
5. 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).
6. Use complex numbers to solve equations, describe graphically complex numbers in the Argand plane (K2).
Swinburne Engineering Competencies (A1-7, K1-6, S1-4): find out more about Engineering Skills and Competencies including the Engineers Australia Stage 1 Competencies.
Unit information in detail
- Teaching methods, assessment and content.
Teaching methods
Hawthorn
Type | Hours per week | Number of Weeks | Total |
Live Online Lecture | 4 | 12 | 48 |
| On Campus Tutorial | 1 | 12 | 12 |
| Unspecified Activities Independent Learning | 7.5 | 12 | 90 |
TOTAL | 150 hours |
Assessment
Types | Individual or Group task | Weighting | Assesses attainment of these ULOs |
Online Assignment | Individual | 15% | 1,2,3,4,5,6 |
| Examination | Individual | 55% | 1,2,3,4,5,6 |
| Test | Individual | 15% | 1,2,3,4 |
| Test | Individual | 15% | 4,5 |
Hurdle
As the minimum requirements of assessment to pass a unit and meet all Unit Learning Outcomes to a minimum standard, a student must achieve:
(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.
Reading materials
A list of reading materials and/or required texts will be made available in the Unit Outline.