MATHS 260 : Differential Equations

Science

Course Prescription

The study of differential equations is central to mathematical modelling of systems that change. 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 pre-requisite 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 1: Disciplinary Knowledge and Practice Capability 2: Critical Thinking Capability 3: Solution Seeking Capability 5: Independence and Integrity

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 1, 2 and 5)
2. Use simple analytic, qualitative and numerical methods, as appropriate, for the analysis of ODEs. (Capability 1, 2 and 3)
3. Assess, describe and modify simple ODE models of physical phenomena. (Capability 1, 2 and 3)
4. Write appropriately detailed and structured mathematical arguments in simple contexts. (Capability 1, 2 and 3)

Assessments

Assessment Type Percentage Classification
Final Exam (2 hours) 50% Individual Examination
Mid-Term Test 20% Individual Test
Three Assignments 20% Individual Coursework
Tutorials 5% Individual Coursework
Quizzes 5% Individual Coursework
1 2 3 4
Final Exam (2 hours)
Mid-Term Test
Three Assignments
Tutorials
Quizzes

The student must achieve at least 35% in the final exam in order to pass the course.

Calculators are not allowed in the test and final exam.

Tuākana

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

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

Key Topics

The list below shows the topics that will be covered in the course and the order in which the material will be taught.
• First order differential equations [12 lectures]. Introduction to differential equations and modelling with differential equations. Introduction to the software for the course. Separable equations and linear equations. Slope fields. Numerical methods (introduction only). The phase line, equilibria, and bifurcations.
• First order systems of differential equations [16 lectures]. Phase plane and qualitative analysis. Linear systems, including classi fication of equilibria. Nonlinear systems, including classi fication of equilibria.
• Higher order differential equations [4 lectures].

Learning Resources

The text for this paper is "Differential Equations", by P. Blanchard, R. Devaney and G. Hall. Any edition is acceptable, but the lecturers are currently using the 4th edition.

This textbook is very good, and the course makes extensive use of the book. You must read the textbook. 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 also 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.

Special Requirements

There is no compulsory attendance and no must-pass assessments although 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.  The test is usually held during a lecture in week 5 or 6.

This course is a standard 15 point course and students are expected to spend 10 hours per week working on the course.

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

Other Information

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 by following the links 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.

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 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.

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.

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 at 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.

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.

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.

Published on 11/01/2020 03:12 p.m.