ENGSCI 711 : Advanced Mathematical Modelling
Engineering
2025 Semester One (1253) (15 POINTS)
Course Prescription
Course Overview
A selection of modules on mathematical modelling methods in engineering, and mathematical techniques for solving the emergent Differential Equations. These include the use of methods to gain a quantitative understanding of the behaviour of the system described by these equations, as well as Asymptotic Methods to obtain approximate solutions in situations where the system can evolve on different time\length scales, and\or exhibit regions of rapid change. Special focus will be given to self-organisation phenomena in complex systems.
Capabilities Developed in this Course
| Capability 2: | Sustainability |
| Capability 3: | Knowledge and Practice |
| Capability 4: | Critical Thinking |
| Capability 5: | Solution Seeking |
| Capability 6: | Communication |
Learning Outcomes
- Apply asymptotic analysis to obtain approximate solutions to certain partial differential equations that describe physical and mechanical problems. (Capability 3.1, 3.2, 4.1, 4.2 and 5.1)
- Understand the motivation for qualitative analysis of differential equations. (Capability 2.1, 3.1, 3.2, 4.1 and 4.2)
- Evaluate the phase space and its key qualitative features of interest. (Capability 3.1, 3.2, 4.1 and 4.2)
- Analyse the stability of fixed points in the phase plane. (Capability 3.1, 3.2, 4.1 and 4.2)
- Understand the bifurcation analysis of simple one- and two-dimensional systems of differential equations. (Capability 3.1, 3.2, 4.1, 4.2 and 6.1)
- Apply model reduction techniques based on centre manifold theory. (Capability 3.1, 3.2, 4.1 and 4.2)
- Understand how centre manifold theory connects bifurcation theory and stability analysis. (Capability 3.1, 3.2, 4.1 and 4.2)
- Create experience with applying theory and techniques to the analysis of engineering, biological and chemical systems. (Capability 3.1, 3.2 and 5.1)
- Apply stability analysis to reaction-diffusion systems. (Capability 3.1, 3.2 and 4.2)
Assessments
| Assessment Type | Percentage | Classification |
|---|---|---|
| Assignments | 30% | Individual Coursework |
| Final Exam | 50% | Individual Examination |
| Test | 20% | Individual Test |
| 3 types | 100% |
| Assessment Type | Learning Outcome Addressed | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ||
| Assignments | ||||||||||
| Final Exam | ||||||||||
| Test | ||||||||||
- Students must sit the exam to pass the course. Otherwise, a DNS (did not sit) result will be returned.
- A passing mark is 50% or higher, according to University policy.
- Assignments are penalised at 4% of the total mark for each hour.
Workload Expectations
This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.
For each week in this course, you can expect up to 2 hours of lectures, a 1 hour tutorial, 2 hours of reading and thinking about the content and 5 hours of work on assignments and/or test preparation.
Delivery Mode
Campus Experience
Attendance is expected at scheduled activities including labs/tutorials.
Lectures will be available as recordings.
The course will not include live online events.
Attendance on campus is required for tests.
The activities for the course are scheduled as a standard weekly timetable.
Learning Resources
Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).
Please remember that the recording of any class on a personal device requires the permission of the instructor.
Health & Safety
Students must ensure they are familiar with their Health and Safety responsibilities, as described in the university's Health and Safety policy.
Student Feedback
At the end of every semester students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback and respond with summaries and actions.
Your feedback helps teachers to improve the course and its delivery for future students.
Class Representatives in each class can take feedback to the department and faculty staff-student consultative committees.
Based on the 2024 SET evaluation, lecturers will continue to provide plenty of examples and practice problems and strive to improve the consistency of nomenclature.
Academic Integrity
The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework, tests and examinations as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. A student's assessed work may be reviewed against electronic source material using computerised detection mechanisms. Upon reasonable request, students may be required to provide an electronic version of their work for computerised review.
Class Representatives
Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.
Inclusive Learning
All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.
Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website http://disability.auckland.ac.nz
Special Circumstances
If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.
If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.
This should be done as soon as possible and no later than seven days after the affected test or exam date.
Learning Continuity
In the event of an unexpected disruption we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.
Student Charter and Responsibilities
The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html.
Disclaimer
Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.
In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.