Department of Mathematics

MATHS 361: Partial Differential EquationsStudy Guide: Semester 1 2016

MATHS 361 is an introductory course in Partial Differential Equations (PDE’s). We coverFourier series, Fourier integrals, boundary value problems, separation of variables, Laplacetransform solutions, and Green’s functions, with application to the solution of second orderPDE’s in one, two and three dimensions.

This document contains important information about the course MATHS 361. Please readit carefully. You should keep this document for future reference.

Lecturers & Contacts

The lecturers for this course are:

• Oliver MacLaren: TBA, (course coordinator)Email: omac010@aucklanduni.ac.nzOffice hours: Monday, Tuesday, Friday 2-3pm

• Philip Sharp: Room 522, Building 303,Email: sharp@math.aucklanda.c.nzOffice hours: Monday and Thursday 10-11am, Friday 9-10am.

Your lecturers are here to help you. You are welcome to speak to them about any aspectof the course. If you want to talk to your lecturer, you can either speak to them after a lectureor in office hours, or you can make an appointment to meet at another time.

Lectures & tutorials

The lectures are at Monday 12-1, Tusday 12-1 and Friday 10-11. The room allocation isavailable on Student Services Online. Check the room allocation before each lecture in thefirst two weeks for up-to-date information.

You must also enrol in one of the tutorial streams, which are 10-11 and 4-5 on Thursdayand 9-10 on Friday. Check room allocations on Student Services Online. It is usually notpossible to attend a tutorial other than the one you are enrolled for. Tutorials start in thesecond week of semester.

Pre-requisites & Restrictions

Before enrolling in this course, you should already have passed Maths 260 and 253, preferablywith at least B-, or have passed PHYSICS 211 or an equivalent course. The most importantprerequisite material assumed is methods for solving linear ordinary differential equations,integration and differentiation. Speak to your lecturer if you have any concerns about yourmathematics background.

Expectations

It is expected that students in this course will spend 10 hours per week working on this course.Students are expected to attend all lectures and tutorials. After each lecture you should reviewthe material from the lecture and try any examples recommended in the lecture. Tutorials area chance for you to work through problems and get assistance with them, and to experimentusing the computers.

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Topics covered in the course

The list below shows the topics that will be covered in the course and the approximate numberof lectures allocated to each topic.

1. Introduction [3 lectures]. PDE’s and boundary conditions. Modelling the diffusion(heat) equation. Introduction to separation of variables.

2. Fourier Series and separation of variables [4 lectures]. Orthogonality of functions andsets of functions. Real trig series. Convergence and sketching Fourier series. ComplexFourier series.

3. Sturm-Liouiville Problems [4 lectures]. Eigenvalues and eigenfunctions. Sturm-Liouvilleeigenvalue problems, existence and orthogonality of solutions, eigenfunction expansions.

4. Separation of variables [3 lectures]. Separation of variables for the wave equation andLaplace’s equation, in several geometries.

5. Wave Equation [1 lectures]. D’Alembert’s solution.

6. Laplace Transforms [4 lectures]. Introduction to transform methods. Calculation andproperties of the transform. Solution of ODEs and PDEs

7. Fourier Transforms [4 lectures]. Fourier representation of delta function. Convolutiontheorem. Application to PDEs.

8. Weak solutions [2 lectures]. Weak solutions

9. Distributions [2 lectures]. Basics of distributions

10. Green’s functions [6 lectures]. Formal derivation of Green’s representation.

Assessment

The final grade for the course will be calculated as follows:

Final exam (2 hours) 60%Mid-semester test (50 minutes) 20%Three assignments 20% Due 23 March, 13 April, 18 May

The mid-semester test will be held April 15 during the lecture time. The room locationwill be confirmed later. Assignments should be handed in to the assignment hand-in boxes inbuilding 303.

If illness or other problems prevent you from completing any of the assignments you shouldcontact your lecturer as soon as possible. A medical certificate will be required if you wish toapply for exemption from an assignment. If you are ill at the time of the mid-semester testor exam you should contact Student Health and Counselling (telephone 373-7599 extension87681) immediately to obtain information on how to apply for an aegrotat or compassionatepass.

Calculators

Calculators are not allowed in the mid-semester test and final exam.

Textbook

The textbook is Mathematical Methods for Engineers and Scientists, Volume 3, by K. T. Tang.

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Use of 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 MuPad in the Undergraduate ComputerLaboratory. A brief guide to the labs can be found by following the links from the webpagehttp://www.scl.ec.auckland.ac.nz

English Language Assistance

The main assistance offered to students who need help with English language is EnglishLanguage Enrichment (ELE), which has a webpage http://www.cad.auckland.ac.nz/ele

This computer-laboratory based service is free and open five days a week. Tutors areavailable to help. Alternatively, there are credit-bearing English language courses (ESOL100/101/102).

Impairment Related Requirements

Students are asked to discuss privately any impairment related requirements face-to-faceand/or in written form with the course coordinator.

Collaborating & Cheating

You are encouraged to discuss problems with one another and to work together on assignments,but you must not copy another person’s assignment. Assignment marks contribute to the finalmark you receive in this course. We view cheating on assignment work as seriously as cheatingin an examination.

Acceptable forms of collaboration include getting help in understanding from staff andtutors, and discussing assignments and tutorial examples and methods of solution with otherstudents. Unacceptable forms of collaboration (cheating) include copying all or part of anotherstudent’s assignment, allowing someone else to do all or part of your assignment for you,allowing another student to copy all or part of your assignment, and doing all or part of anassignment for somebody else.

If you are in any doubt about the permissible degree of collaboration, then please discussyour situation with your lecturer.

Register of Deliberate Academic Misconduct

If a student deliberately cheats and receives a penalty, the case will be recorded in a University-wide Register. The record of the offence will normally remain until one year after the studentgraduates. The Register will help identify repeat offenders, with the risk that these studentswill receive more severe penalties for repeat offences.

Harassment & Complaints

Complaints about marking should be taken to your lecturers who are in a position to do some-thing immediately. More general complaints can be taken up by your class representative. Youmay also approach the Head of Department or the Departmental Manager for Mathematics.

Harassment on any grounds, such as racial, sexual, religious and academic is totally unac-ceptable. Complaints about harassment are best taken to the University Mediator (extension88905). For more information, see the webpage http://www.auckland.ac.nz/mediation

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