MST326 Fluids TMA03

I've jsut completed the above ready to hand to my tutor tomorrow evening after work. This is probably the most hardcore Applied maths block that the OU offers much more involved mathematically than MST324 wonder if any of my colleagues who initially thought MST324 is harder than MST326 still think so.

Anyway the topic is a familiar one solution of Partial differential equations by the Separation of variables but this goes much further than either MST209 or MST326

The first question was on classifying a partial differential equation with mixed coefficents in terms of its type namely hyperbolic a well known example being the wave equation. Parabolic of which the diffusion equation is an example and elliptic which Laplaces equation is an example.

The second part of the question asked us to transform this complicated equation into a simpler form by the chain rule. Which is OK for first derirvatives but for second order partial derivatives the algebra gets quite messy still 5 pages later I transformed the equation into it's simple form and got the general solution.

The last part asked us to find a particular solution for a given boundary conditions I have to say i fouund this quite tricky and potentially confusing so had to leave most of the question. Rough estimate 18/25

Quesiton 2 was solving the Diffusion equation for a given boundaty condition by separation of variables I got most of this out but had to leave a couple of questions at the end so rough guess 20/25

Question 3 was a similar question to question 2 only for the Laplace equation on a rectangular region with variable boundary conditions again got most of this out but had to leave one or two tricky questions. so again about 20/25

Finally question 4. This was an odd's and sod's type question the first question was a relatively straightforward one which could have almost come out of an A level physics question calculating the frequency, wavelength and speed of a composite wave

The second part for just 1 extra mark from part 1 asked us to solve the wave equation using D'Alembert's solution as I've almost lost the will to live after the heavy algebra associatied with questions 2 and 3 I left this

The final part of question 4 involved expressing a Polynomical in terms of Legendre Polynomials and then using the solution to solve a heat conduction problem in a sphere with a variable boundary condition on the surface. Think I got most of this out so about 18/25 overall.

So just under 3/4 of the assignment done looking at about grade 2 or just under for this one. This will probably be my lowest score so far. However being cynical I should get grade 2 overall for the OCAS part of this course. The exam is looming and I still have another TMA coming up before revision starts. There is only a gap of about two weeks between the deadling for the TMA and revision. As I want to start looking at papers by early may so I can do 1 per week then I need to continue the momentum as far as fluids is concerned. If I can get up to speed then I'm looking for a grade 2 pass, but exams have a habit of slipping away.

Those of my colleagues (Duncan Daniel) reading this blog who have deserted Applied maths for Pure maths might like to consider doing  MST326 to complement their pure maths.

As far as the other courses are going I got 90% for my quantum mechanics TMA but was slightly disappointed that my emphasis on the statistical interpretation of quantum mechanics barely got a mention.

For the music the last TMA involved setting some  lyrics to music and showing that we could modulate effectively I got 76% for this which is reasonable but need to work on a few things. This will be embedded in a fuller setting for the final assessment.

Anyway No rest for the wicked another music assignment and an interactive quantum mechanics assignment looms and also I'll snip away at the last TMA for the fluids course.

Bye for now