# MATHS 260 : Differential Equations

## Science

### Course Prescription

The study of differential equations is central to mathematical modelling of systems that change. This course develops methods for understanding the behaviour of solutions to ordinary differential equations. Qualitative and elementary numerical methods for obtaining information about solutions are discussed, as well as some analytical techniques for finding exact solutions in certain cases. Some applications of differential equations to scientific modelling are discussed. A core course for Applied Mathematics.

### Course Overview

This course will be useful for students in mathematics, applied mathematics, computational science, physics or other scientific disciplines that require knowledge about ordinary differential equations.  Students who complete MATHS 260 will have a good understanding of some qualitative, numerical and analytical methods for studying the behaviour of solutions to ordinary differential equations. MATHS 260 is part of the major in mathematics and is a prerequisite for most Stage 3 Applied Mathematics courses.

### Course Requirements

Prerequisite: MATHS 208 or 250 or ENGSCI 211 or a concurrent enrolment in MATHS 250

### Capabilities Developed in this Course

 Capability 3: Knowledge and Practice Capability 4: Critical Thinking Capability 5: Solution Seeking Capability 6: Communication Capability 7: Collaboration
Graduate Profile: Bachelor of Science

### Learning Outcomes

By the end of this course, students will be able to:
1. Identify analytic, qualitative and numerical methods suitable for the analysis of ODEs. (Capability 3, 4, 5, 6 and 7)
2. Use simple analytic, qualitative and numerical methods, as appropriate, for the analysis of ODEs. (Capability 3, 4, 5, 6 and 7)
3. Assess, describe and modify simple ODE models of physical phenomena. (Capability 3, 4, 5, 6 and 7)
4. Write appropriately detailed and structured mathematical arguments in simple contexts. (Capability 3, 4, 5, 6 and 7)

### Assessments

Assessment Type Percentage Classification
Final Exam (2 hours) 50% Individual Examination
Mid-Term Test 20% Individual Test
Assignments (3) 20% Individual Coursework
Tutorials 5% Individual Coursework
Quizzes 5% Individual Coursework
Assessment Type Learning Outcome Addressed
1 2 3 4
Final Exam (2 hours)
Mid-Term Test
Assignments (3)
Tutorials
Quizzes
A minimum of 35% in the exam is required to pass the course.
The use of calculators in the test and exam is not permitted.

### Tuākana

Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at
https://www.auckland.ac.nz/en/science/study-with-us/pacific-in-our-faculty.html
https://www.auckland.ac.nz/en/science/study-with-us/maori-in-our-faculty.html

Whanaungatanga and manaakitanga are fundamental principles of our Tuākana Mathematics programme which provides support for Māori and Pasifika students who are taking mathematics courses. The Tuākana Maths programme consists of workshops and drop-in times, and provides a space where Māori and Pasifika students are able to work alongside our Tuākana tutors and other Māori and Pasifika students who are studying mathematics.

### Key Topics

First order differential equations [12 lectures]
1. Introduction to differential equations and modelling with differential equations.
2. Introduction to the software for the course.
3. Separable equations and linear equations.
4. Slope fields.
5. Numerical methods (introduction only).
6. The phase line, equilibria and bifurcations.
First order systems of differential equations [16 lectures]
1. Phase plane and qualitative analysis.
2. Linear systems, including classification of equilibria.
3. Nonlinear systems, including classification of equilibria.
Higher order differential equations [4 lectures]

### Special Requirements

In order to complete assignment and tutorial problems, and to understand lecture material, students will be required to use the Undergraduate Computer Laboratory. Information about the labs can be found from the webpage:
http://www.scl.ec.auckland.ac.nz

More information about laboratory use will be distributed in lectures. The software used in this course can also be installed on a laptop or home computer. Information about this will be available on the course Canvas page.

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 of this course, you can expect 3 hours of lectures, a 1-hour tutorial, 2 hours of reading and thinking about the content and 4 hours of work on assignments, quizzes, and/or test preparation.

### Delivery Mode

#### Campus Experience

• Attendance is required at scheduled activities, including tutorials, to receive credit for components of the course.
• Lectures will be available as recordings. Other learning activities, including tutorials, will not be available as recordings.
• 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.

Required Text:
• "Differential Equations", by P. Blanchard, R. Devaney and G. Hall. Any edition is acceptable, but the lecturers are currently using the 4th edition.
You must read the textbook, as the course makes extensive use of it. There are several copies of the text on Short Loan in the Kate Edgar Commons and in the General Library. New copies of the 4th edition may be available from Ubiq and second-hand copies may be available (look online). Electronic copies are also available for purchase online. If you purchase an older edition of the text, be sure to check which sections are relevant, as there are some important differences between the 4th edition and earlier editions.

In addition to the textbook, a printed coursebook with all lecture slides will be available for purchase at about \$20.

### 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.

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 for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

### 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.

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 course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.

### 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 students may be asked to submit 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. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 31/10/2023 10:52 a.m.