Linear Algebra and Applications
Duration
- One Semester or equivalent
Contact hours
- 60 hours
On-campus unit delivery combines face-to-face and digital learning.
2022 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
Offered from 2017
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).
Courses with unit
Bachelor of Engineering (Honours) [Discontinued]Unit information in detail
- Teaching methods, assessment, general skills outcomes and content.
Teaching methods
Assessment
|
Types | Individual or Group task |
Weighting | Assesses attainment of these ULOs |
| Online Assignments | Individual | 15% | 1, 2, 3, 4, 5, 6 |
| Class Test 1 | Individual | 15% | 1, 2, 3 and (part of) 4 |
| Class Test 2 | Individual | 15% | 4,5 |
| Examination | Individual | 55% | 1, 2, 3, 4, 5, 6 |
General skills outcomes
During this unit students will receive feedback on the following key generic skills:
- K2 Maths and IT as Tools: Proficiently uses relevant mathematics and computer science and information science concepts as tools.
- S1 Engineering Methods: Applies engineering methods in practical applications.
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.
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Study resources
- Text books, recommended reading and references.
Text books
Recommended reading
The Library has a large collection of resource materials, both texts and current journals. Listed below are some references that will provide valuable supplementary information to this unit.
Croft, A., Davison,R., Hargreaves,M. and Flint,J. Engineering Mathematics: A Modern Foundation for Electronic, Electrical, and Systems Engineers , Fourth Edition, Addison-Wesley, 2013 (available in the library; can be ordered from the bookshop; covers most of 1st and 2nd years; contains many electrical and electronic engineering applications).
Fitzgerald, G. & Peckham, I., Mathematical Methods for Engineers and Scientists, Prentice Hall, 1996 (available in the library).
Stroud, K.A., Engineering Mathematics, Macmillan, London, 6th edn., 2007 (available in the library; can be ordered from the bookshop; contains lots of solved problems.
References
Texas Instruments 30XB MultiView Calculator. Note that this is the only calculator permitted to be used in some of the assessments in this unit and these assessments will be set on the assumption that students have such a calculator.