Mathematics 3B | Units of study... | Swinburne University of Technology

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. 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).

Courses with unit

This unit must be taken for disciplines in:

Robotics & Mechatronics Engineering,
Telecommunications Engineering,
Electrical and Electronic Engineering,
Biomedical Engineering
Science

and

Mathematics majors/minors/co-majors

Unit information in detail

- Teaching methods, assessment, general skills outcomes and content.

Teaching methods

*Scheduled face to face: Lectures (48 hours), Tutorials (12 hours)
*Scheduled synchronous online Learning events n/a
Non-scheduled online learning events and activities n/a

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 - 60%	1, 2, 3, 4, 5, 6

Minimum Requirements to pass this unit will be made available in the full Unit Outline available to students when unit is offered.

General skills outcomes

During this unit students will receive feedback on the following key generic skills:
• Analysis Skills
• Problem Solving Skills
• Ability to work independently

Swinburne Engineering Competencies for this Unit of Study
This Unit of Study will contribute to you attaining the following Swinburne Engineering Competencies:
• 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

• 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.

Reading materials

There is no textbook for this unit. However, students are expected to access

Mathematics 3B Study Guide, available through Blackboard (posted under Learning Material).

Texas Instruments 30XB MultiView Calculator is the only calculator that may be permitted to be used in this unit.

Reading and Reference Materials

The Library has a large collection of resource materials. Listed below are some references that will provide valuable supplementary information to this unit.

E. Kreyszig, Advanced Engineering Mathematics, 10^th edition, Wiley, 2011.
G. James et al., Advanced Modern Engineering Mathematics, 4^th edition, Prentice Hall, 2010.

K.A. Stroud, Advanced Engineering Mathematics, 4^th edition, Macmillan Press, 2003.

Duration

Contact hours

Prerequisites

Aims and objectives