MATHS 260 : Differential Equations
2020 Semester One (1203) (15 POINTS)
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.
Capabilities Developed in this Course
|Capability 1:||Disciplinary Knowledge and Practice|
|Capability 2:||Critical Thinking|
|Capability 3:||Solution Seeking|
|Capability 5:||Independence and Integrity|
- Identify analytic, qualitative and numerical methods suitable for the analysis of ODEs. (Capability 1, 2 and 5)
- Use simple analytic, qualitative and numerical methods, as appropriate, for the analysis of ODEs. (Capability 1, 2 and 3)
- Assess, describe and modify simple ODE models of physical phenomena. (Capability 1, 2 and 3)
- Write appropriately detailed and structured mathematical arguments in simple contexts. (Capability 1, 2 and 3)
|Final Exam (2 hours)||50%||Individual Examination|
|Mid-Term Test||20%||Individual Test|
|Three Assignments||20%||Individual Coursework|
|Assessment Type||Learning Outcome Addressed|
|Final Exam (2 hours)|
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.
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- 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 classification of equilibria. Nonlinear systems, including classification of equilibria.
- Higher order differential equations [4 lectures].
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.
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.
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.
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
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.
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).
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.