Mathematics 3B
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
and one of:
or
or
Anti-requisite (Similar in content)
and
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:
1. Calculate the eigenvalues and eigenvectors of 2x2 and 3x3 matrices (K2, S1).
2. Interpret the quadratic form and find its canonical form (K2, S1).
3. Use the Cayley-Hamilton theorem to simplify matrix powers (K2, S1).
4. Apply Vector Calculus to analyse and model processes that arise in scientific and engineering applications (K2, S1).
5. Apply Green’s theorem, Ostrogradsky-Gauss’ divergence theorem and Stokes’ theorem (K2, S1).
6. Perform operations with complex numbers, understand and use the concepts of analyticity and function singularities in computing contour integrals (K2, S1).
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 |
On Campus Lecture | 4 | 12 | 48 |
| On Campus Class | 1 | 12 | 12 |
| Online Learning Activities | 7.5 | 12 | 90 |
TOTAL | 150 hours |
Assessment
| Types | Individual or Group task | Weighting | Assesses attainment of these ULOs |
| Test 1 | Individual | 20-25% | 1,2,3 |
| Test 2 | Individual | 20-25% | 4,5 |
| Examination | Individual | 50-55% | 1,2,3,4,5,6 |
| Online Quizzes | Individual | 5% | 1,2,3,4,5,6 |
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
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.
• 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.
Reading materials
A list of reading materials and/or required texts will be made available in the Unit Outline.