Course guide for Semester One 2007

This paper is concerned with 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.

Preparation for the course

Before enrolling in this course, you should already have passed Maths 150 or Maths 208 (preferably with a grade of B- or better), or have passed an equivalent course. Speak to your lecturer if you have any concerns about your mathematics background.

Course web page

The web page for this course is http://www.math.auckland.ac.nz/class260
The web page will contain copies of lecture notes, assignments and answers, tutorial question sheets, and any important handouts (such as this one). The web page will be updated often - be sure to check it frequently.

Text

The text for this paper is: 

Differential Equations,  by P. Blanchard, R. Devaney and G. Hall (First,second or third edition). 

This textbook is very good, and the course makes extensive use of the book. You have to read the book. The book costs about $145 new, after student discount. There may also be second hand copies of the text available. It is also on short loan in the library.

Lecturer

The lecturer for the paper is: 

Dr Allison Heard   (Room 414, Mathematics Building; heard@math.auckland.ac.nz)

If you want to talk to your lecturer, you can either speak to her after a lecture or go to her office. You can also make an appointment to meet at another time. Good ways to make an appointment are to speak to your lecturer after class or to send your lecturer an email message.  Allison's office hours will be Monday and Friday from 2pm to 3pm, Tuesday and Friday 9am - 10am.

Lectures

The lectures are at 11am, Tuesday, Thursday, and Friday. Tuesday and Friday lectures are in Engineering 3407, and Thursday in PLT2.

Tutorials

Tutorials are held on Mondays at 11am and 1pm in BTL (basement teaching laboratory, B75 in Maths building), starting from Week 2. You will enrol in one of these on nDeva. Tutorials are a chance for you to work through problems and get assistance with them, and experiment using the computers. These tutorials contribute 5\% to your final grade.

Use of the Undergraduate Computer Laboratory

In order to complete assignment and tutorial problems and to understand lecture material, students will be required to use the software package Matlab which is available in the Undergraduate Computer Laboratory.  A map showing you how to find the Teaching Laboratory is on the Science computer labs homepage.

Calculators

Unrestricted calculators may be used in the test and final exam. However, you will need to show your working so do not rely on your computer to solve differential equations!

Coursework

Coursework consists of assignments, a mid-semester test and tutorials.  Coursework consists of assignments, mid-semester test and tutorials. Coursework is compulsory and makes up 40% of your final mark.

Four assignments will be set and marked.  The assignments will be due in on the following dates:  13 March, 3 April, 8 and 22 May. Assignment marks will be counted towards the final grade.

A one-hour  test will be held on 24 April, from 6.30-7.30pm (room to be advised). All students should take this test.

If illness or other problems prevent you from completing any of the assignments please contact your lecturer as soon as possible. A medical certificate will be required if you wish to apply for exemption from an assignment. If you are ill or have other problems at the time of the test or exam you should contact Student Health and Counselling (extn 87681) immediately to obtain information on how to apply for an aegrotat or compassionate pass.

Final Mark

The final mark for the course will consist of:

    60% final exam (2 hours)

    20% mid-semester test

    15% assignments

    5% tutorials.

Doing well in Maths 260

You should plan to spend 10 hours each week working on this course. This includes attending lectures, reading the textbook and doing assignment questions.

Try hard not to miss lectures. If you miss a lecture, get the lecture notes from the web site and go over them before the next lecture. You should review the material from the previous lecture before coming to class. You can also read the recommended sections in the textbook - these are listed on the lecture notes handed out in the previous lecture.

You can only learn mathematics by doing mathematics and it is important to supplement lecture material by trying some of the recommended problems from the textbook. Problems appropriate to each lecture are listed on the lecture notes distributed in class. Answers to these problems are given in the back of the textbook. Try some of the problems every week. Don't wait until it is time to study for the exam.

Attempt all the assignment questions. Once your assignment is marked, go over the assignment to check where you made mistakes. Sample solutions to the assignments will be distributed - read them, as they contain helpful information such as alternative ways to answer questions.

If you are having problems with material in the course, first make sure you have read the appropriate parts of the lecture notes and the textbook. Then speak to your lecturer, either in lectures or tutorials or by making an appointment with your lecturer for another time. Good ways to make an appointment are by speaking to your lecturer after class or by emailing your lecturer.  Don't be scared to approach your lecturers for help - they are happy to help students who are trying to help themselves.

Some help with Maths 260 may also be available in the Mathematics Department assistance room (Room B25 in the Maths Building), starting from the second week of semester.

If you need help with computer use in the computer laboratory, ask a demonstrator in the laboratory. Demonstrators on duty will be wearing a sash and there will always be a demonstrator on duty when the Maths/Stats laboratory is open. If the demonstrators are unable to help you with details of the Matlab package used, then ask your lecturer for help.

To prepare for the test or exam, first make sure you understand your lecture notes and make sure you can do all assignment and tutorial questions. Go over some old exam papers (these can be downloaded from the University Library webpages). The recommended problems listed in the lecture summaries can be used for extra practice. If you have problems, see your lecturer.

Topics covered in Maths 260

The approximate number of lectures spent on each topic is indicated in brackets.  Relevant sections in the text (2nd edition) are given.

1.         First order differential equations [12 lectures] (Text sections 1.1-1.8.) Introduction to differential equations and modelling with differential equations.  Introduction to the software packages Matlab. Separable equations amd linear equations.  Slope fields.  Numerical methods (introduction only). The phase line, equilibria, and bifurcations.

2.         First order systems of differential equations [16 lectures]. (Text sections 2.1-2.5, 3.1-3.5, 3.8, 5.1, 5.2.) Phase plane and qualitative analysis.  Linear systems, including classification of equilibria.  Nonlinear systems, including classification of equilibria.

3.         Higher order differential equations [5 lectures]. (Text sections 3.6, 4.1-4.3.)