MTH3011: Partial Differential Equations

First of all, although this unit can count to both Applied Maths major and Pure Maths major, this is totally an Applied Maths unit. I was expecting this unit to cover more pure/theoretical side of PDEs but nonetheless this is an amazing unit.

Topics covered include:

• Introduction to PDEs
• The advection equation
• Numerical solution of ODEs
• The wave equation
• The heat equation
• Numerical solution of the heat equation
• Elliptic PDEs
• Numerical solution of the advection equation

We have covered different classes of PDEs and various methods to solve them both analytically and numerically. In fact, it might be a good thing or bad thing depending on what you think but almost half of the unit is on numerical methods, including accuracies, stablities etc. (It has a slight overlap with MTH3051 Introduction to Computational Mathematics.) PDEs are extremely important in Science and Engineering (a majority of student is doing Sci/Eng degree), and is a prerequisite for most of the honours subjects as well as honours research projects in Applied/Computational Maths, so you really have to do this unit if you ever want to study Applied Maths at a higher level.

Michael is definitely the best lecturer I have ever had so far. (Completely irrelevant but he is a lot like my Specialist teacher.) As there is no typed lecture notes ready on Moodle, it is quite essential to copy down the notes he writes in lecture. (He writes a lot and he write really fast so you might want to copy the notes after lecture otherwise you'll miss what he says. They will be uploaded on Moodle after each lecture.) All the notes are super clear, and what impresses me is that all the notes he writes in lectures are in full sentences! One down side (probably won't happen again) is that Michael takes his time to go through each topics slowly in the first half of the semester (We spent more than 2 lectures just to work on examples of the advection equation), so towards the end, we are obviously behind the schedule by like a week so he is rushing at a bit, for some topics I feel like not enough discussion or examples are given. All the topics in schedule are covered though.

As for the assessments, out of the 11 tutorials, 7 involves a quiz and 3 involve a computer lab exercise (each worth 0.5%). The weekly quizzes are practically free marks. You only have 10 minutes for each quiz but the questions are very easy. If you read your notes after lecture at all you should be able to get full mark or close to full mark for those. As for the computer labs, 1 is on numerical solution of ODEs and the other 2 are on PDEs. We can choose to use either Excel or Matlab to complete the exercise. For these computer lab exercises, we are given a semi-finished program, and we only need to follow the instruction and fill in relevant details. Sure, these are easy marks to get, but I personally find this quite stupid as we have lost the opportunity of actually coding for the numerical methods we have learned in the lectures.

A mid-semester test is held in week 7 during the lecture. It has the same style of questions as the weekly quizzes. It is worth 10% so it's quite important. But if you revise consistently and do all the exercise sheet questions, you should find the test pretty easy.

The problem is the assignments. There are two of them, each worth 7.5%. They are very long and most people find them really challenging. They are nothing like the exercise sheet questions, so make sure you spend time on them or maybe collaborates with your mates.

The final exam is actually doable. It's long, not surprisingly, but the questions are not hard, I actually find them really straight forward. But to do well, you need to have a good memory. Everything covered in lectures is examinable and everything is actually examined. So make sure you understand everything. Also the exam questions are quite similar to those of past years (more than half of the questions are exactly the same), so make sure you do those or at least look at the provided solutions.
Overall, great unit. You actually learn a lot in this unit if you like Applied Maths. Pure people might be disappointed though. The assessments are pretty fair and apparently the pass rate was 85% and 50% of students received a D or better. (These statistics are included in the 2005 exam solutions so is for 2005, but I don't think it would be that different from year to year) Definitely do this unit because no one doesn't like PDEs and Michael Page is awesome.

Associate Professor Michael Page

Yes, two. One with solutions.

4.5 out of 5

Yes, with screen capture.

There is no formal prescribed or recommended textbooks. A list of textbooks on PDEs suitable for this level is included in the unit guide and it is mentioned that Partial Differential Equations: An Introduction by W.A. Strauss is the closest to the unit content. I never really used it though.

2014, Semester 1

TBA