Linear Algebra and Applications
Duration
- One Semesteror equivalent
Contact hours
- 84
On-campus unit delivery combines face-to-face and digital learning.
2024 teaching periods
| Hawthorn Higher Ed. Semester 1 |
||
|---|---|---|
Dates: Results: Last self enrolment: Census: Last withdraw without fail: |
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:
1. Perform simple operations involving determinants, the rank of a matrix and its null space (K2).
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).
Unit Learning Outcomes (ULO)
Students who successfully complete this unit will be able to:
1. Perform simple operations involving determinants, the rank of a matrix and its null space (K2).
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).
Courses with unit
Associate Degree of EngineeringUnit information in detail
- Teaching methods, assessment, general skills outcomes and content.
Teaching methods
Hawthorn
Type | Hours per week | Number of Weeks | Total |
Live Online Lecture |
2 |
12 |
24 |
On Campus Class | 2 | 12 | 24 |
On Campus Class | 2 | 12 | 24 |
Online Directed Online Learning and Independent Learning | 1 | 12 | 12 |
Unspecified Activities Independent Learning | 5.5 | 12 | 66 |
TOTAL | 150 hours |
Assessment
| Types | Individual or Group task | Weighting | Assesses attainment of these ULOs |
| Online Assignments | Individual | 20-30% | 1, 2, 3, 4, 5, 6 |
| Tutorial | Individual | 10-20% | 1, 2, 3, 4, 5, 6 |
| Test | Individual | 10-20% | 1, 2, 3 and (part of 4) |
| Examination | Individual | 40-50% | 1, 2, 3, 4, 5, 6 |
(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 44% as the total mark for the unit and will not be eligible for a conceded pass.
General skills outcomes
During this unit students will receive feedback on the following key generic skills:
• Teamwork skills
• Analysis skills
• Problem solving skills
• Communication skills
• Ability to tackle unfamiliar problems
• Ability to work independently
• Teamwork skills
• Analysis skills
• Problem solving skills
• Communication skills
• Ability to tackle unfamiliar problems
• Ability to work independently
Content
• 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, Cramer’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
- Text books, recommended reading and references.
Text books
Recommended reading
References
A list of reading materials and/or required texts will be made available in the Unit Outline.