MATH2221: Higher Theory and Applications of Differential Equations

- 2 x 10% workshops
- 20% midterm test
- 60% final exam

A mark of 70 in MATH1231 or MATH1241 or MATH1251 (or DPST1014)

This is one of the level 2 core courses required as part of a mathematics major. For statistics majors, students have the choice of picking between this, and MATH2521/2621 (complex analysis). Differential equations are something students are very accustomed to from first year; they're essentially just trying to find a function that satisfies an equation, which somehow relates the function to its own derivatives. (Can of course, be higher than the first derivative.) This course does introduce significantly more techniques than in first year.

This course is introduced as a toolbox course (which, I note throws off many pure-math wired students). As with every math course, some element of proof is required. But the main focus of this course is in applying various techniques taught to finding/constructing solutions (or solution representations) to differential equations. For the most part, this course is therefore computational. They try to minimise it in this course, but every once in a while the ability to handle demanding algebraic computations becomes important.

But of course, in terms of computations, what they emphasise on is how well you know the techniques. I saw pretty much every technique get examined (power series, reduction of order, variation of parameters in the assignment, Sturm-Liouville theory, formally self adjoint operators, dynamical systems, Steklov eigenpairs, ...).

The course is absolutely crucial to applied mathematics majors. Anyone considering applied mathematics is strongly advised to take this course in second year, as it is a prerequisite for several level 3 applied courses.

The workshops were basically the assignments as far as I was aware. I think they were renamed just to emphasise the peer review component of it. Which wasn't too bad, in the grand scheme of things.

I was originally going to give this course a 4/5 for the content, but then Jan actually boiled the egg in class this year. That was a 0.5 rating in itself. (Students that will take/have taken the course will know what I mean here.)

- 2 hr live session (usually aimed to keep within 1 hr though, and was also optional)
- 1 hr tutorial
- However much time required to watch recordings from previous years, mixed with some new re-recorded ones. (Roughly 4 hours per week)

2.5/5

Yes (live sessions and tutorials were recorded)

Dr. Jan Zika

Full lecture slides given with document camera scribbles from 2019. Some tutorial exercises had full solutions, whilst others just had answers. Live session docs were all released. Past papers for midterm and final prep were released back to 2015.

4.5/5

None were prescribed. A variety was stated as recommended reading, but I used none of them.

20T2

97 HD

Prerequisites:

For a course I thought I'd hate, it was actually quite interesting. The course was quite computational, but Dr. Zika went into quite a bit of depth behind all the concept we learnt, and was very helpful during tutorials. The more conceptual questions were very nice (just like the theoretical vector calculus questions he wrote in the MATH2111 final), and a lot of "advanced" questions in the tutorial problems showed the applications of what we learnt, while also posing more challenging problems. As a lecturer, I found Dr. Zika to be good, especially if you like explanations through examples. Some of the conditions required in the statements of theorems were annoying to remember, but otherwise it was a pretty easy course, and a lot more fun than I had thought it would be.

3x 1hr Lecture, 1x 1hr Tutorial

2/5

Yes - screen and voice recorded, plus document camera when used.

Dr. Jan Zika

Lecture slides all posted online, and past final exams available with solutions. Tutorial problems with brief solutions for most questions.

3/5

Note: I don't use textbooks and can't comment on their usefulness. None prescribed, but useful references:

2018 S2

97 HD