# MATHS 761 : Dynamical Systems

## Science

### Course Prescription

Mathematical models of systems that change are frequently written in the form of nonlinear differential equations, but it is usually not possible to write down explicit solutions to these equations. This course covers analytical and numerical techniques that are useful for determining the qualitative properties of solutions to nonlinear differential equations.

### Course Overview

Mathematical models of systems that change are frequently written in the form of nonlinear differential equations, but it is usually not possible to write down explicit solutions to these equations. This course covers analytical and numerical techniques that are useful for determining the qualitative properties of solutions to nonlinear differential equations. This is a core applied mathematics course for the BSc(Hons), BAdvSci and PGDipSci. It is also of interest to students majoring in Physics, Engineering Science, Computer Science or Statistics.

### Course Requirements

Prerequisite: B- 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. Use appropriate analytic, qualitative and numerical methods to construct phase portraits, bifurcation diagrams and bifurcation sets for systems of ODEs. (Capability 1, 2, 3, 4 and 5)
2. Use phase portraits, bifurcation diagrams and bifurcation sets for systems of ODEs to draw conclusions about the qualitative behaviour of solutions, (Capability 1, 2, 3, 4 and 5)
3. Explain and illustrate an understanding of dynamical systems through calculation, computation, description and discussion of dynamical phenomena (Capability 1, 2, 3, 4 and 5)

### Assessments

Assessment Type Percentage Classification
Exam 50% Individual Examination
Assignments 30% Individual Coursework
Team activities 20% Group & Individual Coursework
1 2 3
Exam
Assignments
Team activities

### Special Requirements

None.

It is expected that you spend 10 hours per week working on this course. The normal pattern of student study is expected to be (on average, each week):

2 hours lectures;

2 hour lab, including preparation;

3 hours lecture preparation and review;

3 hours assignments and exam preparation.

Students are expected to attend all class meetings. After each class you should review the material from the class and try any recommended examples. You are expected to preview the material provided for each lecture before you come to class.

### Delivery Mode

#### Campus Experience

Attendance is required at scheduled activities including team activities to receive credit for components of the course.
Attendance on campus is required for the exam.
The activities for the course are scheduled as a standard weekly timetable.

### Learning Resources

The textbook for the course is "Stability, Instability and Chaos" by Paul Glendinning, Cambridge University Press (1994). Students are also expected to use and become proficient with the software package XPPAUT, which is freely downloadable from http://www.math.pitt.edu/~bard/xpp/xpp.html

### 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.

### 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.

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.

For COVID disruptions, the following will apply.

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. 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 .

### 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.

Published on 16/02/2021 10:54 a.m.