| Semester 1, 2022 Springfield On-campus | |
| Units : | 1 |
| Faculty or Section : | Faculty of Health, Engineering and Sciences |
| School or Department : | School of Mathematics, Physics & Computing |
| Grading basis : | Graded |
| Course fee schedule : | /current-students/administration/fees/fee-schedules |
Staffing
Examiner:
Requisites
Pre-requisite: ENM1600 or Students must be enrolled in one of the following Programs: GCEN or METC or MENS or GDNS or MEPR or MSCN
Overview
This course follows ENM1600 Engineering Mathematics in developing the theory and competencies needed for a wide range of engineering applications. In particular, the concepts and techniques of complex numbers, differential equations, multivariable calculus and linear algebra are broadened. These mathematical techniques are explored in the context of engineering applications.
This course further integrates mathematical concepts to provide students with an introduction to the advanced skills required for engineering and surveying. Topics included are: Complex Numbers, Ordinary Differential Equations (ODEs), Series, Multivariable Calculus, and Linear Algebra. The introduction to Ordinary Differential Equations and Series topics include direction fields, Euler's method, first order separable ODEs, first order and second order linear ODEs with constant coefficients, Taylor and Fourier series. Multivariable Calculus includes representation of functions of several variables, surfaces and curves in space, partial differentiation, optimisation, directional derivatives, gradient, divergence and curl, line integrals of the 1-st and 2-nd kinds, iterated integrals, Green's theorem. The topic of Linear Algebra of ENM1600 Engineering Mathematics is extended to cover eigenvalues and eigenvectors, and symmetric and orthogonal matrices. Engineering applications are discussed in each topic.
Course learning outcomes
On completion of this course students will be able to:
- Critically examine and apply mathematical techniques and skills to solve problems essential to further study in engineering and surveying;
- Proficiently apply mathematical techniques to analyse and solve basic mathematical and authentic engineering and surveying problems relevant to this course.
- Effectively communicate mathematical concepts and arguments using appropriate notation;
- Use computational aids for graphing, matrix manipulation, concept development and problem solving in algebra and calculus within engineering and surveying contexts.
Topics
| Description | Weighting(%) | |
|---|---|---|
| 1. | Differential Equations and Series: direction fields - first order linear ODEs - Taylor series - Fourier series - Euler's method - second order linear ODEs with constant coefficients - engineering applications. | 35.00 |
| 2. | Multivariable Calculus: curves in space - surfaces in space - functions of several variables - partial differentiation - geometric interpretation of partial derivatives - maxima/minima problems - directional derivatives - vector fields - curl and divergence - line and work integrals - independence of path - engineering applications. | 35.00 |
| 3. | Linear Algebra: - eigenvalues and eigenvectors - symmetric and orthogonal matrices - engineering applications. | 15.00 |
| 4. | Complex number applications, Euler form and complex functions. | 15.00 |
Text and materials required to be purchased or accessed
(4th & 5th edn can also be used.)
(Available on course 精东传媒appDesk.)
Student workload expectations
To do well in this subject, students are expected to commit approximately 10 hours per week including class contact hours, independent study, and all assessment tasks. If you are undertaking additional activities, which may include placements and residential schools, the weekly workload hours may vary.
Assessment details
| Description | Group Assessment |
Weighting (%) | Course learning outcomes |
|---|---|---|---|
| Quiz | No | 10 | 1,3 |
| Problem Solving 1 | No | 30 | 1,3,4 |
| Problem Solving 2 | No | 30 | 1,2,3,4 |
| Problem Solving 3 | No | 30 | 1,2,3,4 |