After a fairly intensive couple of days I've managed to complete the final TMA04 for M337 hooray.

The questions were

1) Questions on conformal mapping alright once one had grasped the basic idea.

2) Questions on Fluid Mechanics

This is actually a continuation of part 1 as a large part of the fluid dynamics of an aereofoil can be seen as a conformal transformation discovered by Joukowski. There were two parts

a) Some relatively straightforward questions on Complex Potentials and Stream Functions

b) A quite tricky question on the flow past an obstacle involving the Joukowski transformation

and the Flow ,mapping theorem.

3) Questions on Complex iteration including the properties of the Mandelbrot set

Potentially this should be one of the most interesting units. However short of time I had to skim through the material and did not do justice to the question. Espescially as the question on fixed points seem to give rise to a particularly awful set of fixed points. Also unlike M208 there is no fixed strategy given for say finding the Keep set of a complex function

I think potentially the second unit of this block is the most interesting and I hope to revisit it during revision

On the whole M337 has been a very stimulating course and I'm looking forward to doing the MSc course on Complex Variables. I'll post a full review after the exam. I have the book for the MSc course already and will try and fit some of it in during down time. Tomorrow I'm taking the day off to finish off the last TMA for M208. Then it's a question of trying to do as many past papers under exam like conditions as possible.

For now I'm just going to relax and have a few beers

Chris,

ReplyDeleteWould you say the complex analysis course is more applied or pure, in its approach to teaching complex numbers? I see you mention fluid mechanics there but also the mandelbrot set etc

Dan

The first three parts are definitely pure, the last part is Applied and that includes the Mandelbrot set. It's like being on a journey without knowing the final destination until you reach the peak of Cauchy's Integral theorem. Then you begin to see the relevance

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