MATHS 765 : Mathematical Modelling


2021 Semester Two (1215) (15 POINTS)

Course Prescription

Advanced topics in mathematical modelling, including selected topics in a range of application areas, principally taken from the physical and biological sciences.

Course Overview

MATHS 765 is an applied mathematics course for the BSc(Hons), BAdvSci and PGDipSci programmes and will also be of interest to students majoring in Computer Science, Engineering Science, Physics or Statistics. The skills developed in this course are particularly useful for those wishing to have a career involving mathematical modelling techniques in their field of study. After successfully completing MATHS 765 students will be well prepared to decide what makes a model a good model for a given real-world problem, what a model can teach us, and what its limits of validity are. 

Course Requirements

Prerequisite: At least B- or better in both MATHS 340 and 361

Capabilities Developed in this Course

Capability 1: Disciplinary Knowledge and Practice
Capability 2: Critical Thinking
Capability 3: Solution Seeking
Capability 4: Communication and Engagement
Capability 5: Independence and Integrity

Learning Outcomes

By the end of this course, students will be able to:
  1. Formulate and explain mathematical models of example systems with time-dependent behaviour. (Capability 1, 2, 3, 4 and 5)
  2. Critically analyse the validity of a mathematical model in its application context. (Capability 1, 2 and 3)
  3. Constructively review and critique aspects of the system that have not been modelled. (Capability 1, 2, 4 and 5)
  4. Develop and demonstrate the ability to apply mathematical techniques to the investigation of mathematical models. (Capability 1, 2, 3 and 5)
  5. Explain and communicate what conclusions can be drawn from a mathematical model. (Capability 1, 2, 4 and 5)


Assessment Type Percentage Classification
Assignments 100% Individual Coursework
Assessment Type Learning Outcome Addressed
1 2 3 4 5


Māori and Pasifika students are encouraged to participate in the Maths Tuākana Programme and use their free drop-in tutorial sessions. The programme can be accessed through the Tuākana (Science) - Maths canvas page. For more information, please visit

Key Topics

1. Basics of modelling: what is modelled, what is not? 
2. Periodic motion from the harmonic oscillator to the pendulum.
3. Nonlinear oscillations in a driven laser: understanding the model and what it tells us.
4. Basic models of species competition.
5. Feedback loops: models with delay and how to analyse them.
6. The upside-down pendulum with delayed control.
7. Modelling of traffic flows.

Special Requirements

No special requirements.

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 this course, you can expect 3 hours of lectures,  3 hours of reading and thinking about the content and 4 hours of work on assignments and/or test preparation.

Delivery Mode

Campus Experience

Attendance is expected at scheduled activities including lectures and and computer labs classes to receive credit for components of the course. Lectures will be available as recordings. Computer labs classes will not be available as recordings. The activities for the course are scheduled as a standard weekly timetable.

Learning Resources

There are no required learning resources; the following text books can be consulted as reference texts:

Mathematical Modelling: A case studies approach by Illner, Bohun, McCollum & Roode

Nonlinear Dynamics and Chaos: With applications to Physics, Biology, Chemistry, and Engineering by Strogatz

Student Feedback

During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.

At the end of the course 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.

Your feedback helps to improve the course and its delivery for all students.

Other Information

No other information.

Digital 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.

Academic Integrity

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework 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. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms.


The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.

You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

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

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

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.

Level 1: Delivered normally as specified in delivery mode.

Level 2: You will not be required to attend in person. All teaching and assessment will have a remote option. The following activities will also have an on campus / in person option: Lectures and computer lab classes.

Level 3 / 4: All teaching activities and assessments are delivered remotely.

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


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.

Published on 27/04/2021 01:42 p.m.