The content of unit 12 in a nutshell, as explained by http://www.youtube.com/user/bullcleo1 – a good summary of this week’s work.
What a brilliantly explained set of videos.
So, with the decision made to drop M248 and pick it up again next year in tandem with a single 30 point level 3 course, I feel mightily relieved.
I now have space and time to a) enjoy MST209, b) read around any parts giving me problems c) forget having to “speed learn”.
Of course, this is odd since I don’t need MST209 for my likely degree route but do need M248.
Except that MST209, while being a huge course with some quite difficult stuff in it, is actually very interesting.
And M248, to me, isn’t, while its maths is, dare I say it, quite elementary.
As maths to a budding mathematician goes, that is. To the average business student, it probably looks sophisticated (no slight intended).
So, I think my degree route might change in light of this – more likely to be a maths and maths only one now, rather than a stats and maths, or econs and maths one. Anyway, I’ll decide that later.
Right now, the emphasis is on needing to get through MST209.
I am technically one week ahead of the course schedule at this point, after taking a few days off.
But, the bug is back – I need to do some more MST209.
So, I started unit 12 – functions of several variables – last night and, well, just kept reading.
Another 8 hours of study and I should be finished the unit and the associated assignment question.
Unit 12 is just awesome and relies heavily on a preceding and good knowledge of single variable calculus. It goes on to deal with the straightforward methods of finding partial derivatives with respect to x and y in a 3-coordinate system (heavy use of finding partials of functions needing the product rule more than anything else), introduces grad, slides off into Taylor polynomials (these seem to appear in every maths course I ever look at), then on to classification of stationary points using eigenvalues (I am currently here :-))
To come: some more least squares approximation and, sadly, some computer algebra.
And that concludes the unit.
Difficulty so far is somewhere around a 5-out-of-10, I think. I’ll reserve judgment until I’ve done the TMA question which I haven’t looked at yet.
One of the functions examined is f(x,y) = (x^2 + y^3)sin(xy), which Wolfram was only too happy to plot for me.
This week’s essential watching – the first three videos are basically what’s in Unit 12; the fourth video is useful for a bit of reinforcement/consolidation:
MST209 – 18 October, 10am to 1pm (think that’s a Tuesday).
M248 – 19 October, 10am to 1pm.
The requirement is now to carry around all the knowledge from a significantly overloaded 60 point calculus and mechanics course (which is more like 90 points) and a 30 point statistics course, and be tested on the whole lot in the space of 27 hours.
This news means I need to phone the OU tomorrow and look at the implications of suspending study of M248. Whether that results in course fail or course postponement, I have no idea. I’ll also phone both course lecturers tomorrow and have a chat.
Did I say ar5e?
Ok, so assignment number three is about done.
I’m just putting the finishing touches to the last (unit 11-related) question.
The unit 9 and unit 10 stuff seemed very fair and quite straightforward.
The second unit 8 question required a step back to see exactly what they wanted from it. The clue is in the question and mark scheme, as ever.
I learned some neat eigenstuff that I wasn’t aware of before in unit 10 – mainly to do with finding eigenvalues and eigenvectors through repeated iteration. The techniques to achieve this, and keep the resulting values to a manageable size, are laid out crystal clear in the book. Very well written piece, I thought.
Unit 11, on systems of differential equations, took some getting used to. The intro was a bit woolly but then, all of a sudden, boom – everything coming at you at once. As the intro says, you need proficiency with matrices and determinants, eigenvalues and eigenvectors, and several methods of solving differential equations.
Unit 11 has clearly signalled the point where various sections of the course suddenly meet up. It looks like lots of the available twigs and moss of knowledge have gathered into a ball (of mass m, of course) and are now rolling down an incline (at theta to the horizontal in the -j direction) towards the end of the course (which is still 17/28ths away).
There is a LOT of work in this course. Last year’s M208 was like a picnic in terms of time demands compared to this.
Unit ratings by difficulty: (1-easy; 10-brain melt)
Unit 9 – matrices and determinants – gets a 2-out-of-10 from me since I did a load of it last year. I can see students with no prior background in the topic getting into a pickle though – the course notes fly through the material at a fair rate.
Unit 10 – eigenvalues and eigenvectors – gets a 4-out-of-10 from me due to the iterative stuff being a touch tricky in places. Tip – get used to using the det and trace to check answers (or even predict answers before invoking the characteristic equation, etc).
Unit 11 – systems of differential equations – was fun but confused me several times. Also had me looking back to unit 2 and unit 3 to check on my fundamentals of differential equations. This is a good thing as it helps consolidate prior learning. Difficulty rating: 5-out-of-10.
That was quick – arrived back yesterday.
Result is up on my OU personal web page as well.
It usually takes a week or more.
Very high pass one, so I’m very happy with that.
I’m on a week’s holiday from now, so intend to catch up on M248 and plough ahead with MST209.
I’m still uncomfortable with unit 8 and energy but have done units 9 and 10, which seemed easy enough, particularly after completing M208 last year.
The notation is different in MST209 in many respects – eg Gaussian row change operations – so I’m sticking to M208 notation since it’s learned and in my head.