Maths - I've already done this exam, but hey, easiest thing first to warm you up :)
This involved, amongst other mind-bendingly boring things:
Vectors - integration; differentiation; Divergence, Stokes' and Greens' Theorems; Div, Grad and Curl of a line. Parametrisation of a line and plane.
It would all have been alot simpler if the lecturer wasn't such a total jerk and didn't do stupid things like change the questions to fit the (originally) wrong answer he got from it. Here is a typical question - one of the rare ones I can actually comprehend and do right - from one of the middle sections of the course.
(I should point out the vector field f is not used for this part of the question).
This basically wants us to find the curl of the gradient of a field (the field is represented by 'phi' - the little circle with a line through it) given by a set of co-ordinates in 3D space. The space is divided by three axes with labels x, y and z. A vector of magnitude (length) one unit (A unit vector) along these axes is labelled i, j or k respective of axis - i for x, j for y, k for z.
What we now do is use a formula for gradient to get a new set of co-ordinates - this was given to us at an earlier stage. The formula states that (x,y,z) co-ordinates in the 'phi' scalar field become (d(phi)/dx, d(phi)/dy, d(phi)/dz) where d(phi)/dx is the derivative of the function 'phi' with respect to x. That gives us the bottom line of the matrix (the box thing with 3 rows and 3 columns) in the answer below. The top row is made up of the i, j and k unit vectors mentioned above. Dont ask me why, thats just what it is, and it works so go along with it.
The middle row of that matrix is made up of a further derivative (one for each axis) which is put there because thats what the formula for curl tells us to do.We must find the determinant of this matrix, and that will give us the values of the curl of the gradient of the scalar field 'phi' in each axis. As you can clearly see, all that you do is multiply it out.. so for the i vector direction (along the x-axis) we take the derivative (with respect to the y axis) of the derivative of 'phi' with respect to the z-axis ((d^2(phi))/(dydz)) and away from that we take the derivative (with respect to z) of the derivative of 'phi' with respect to the y-axis ((d^2(phi))/(dzdy)). Essentially, they are both exactly the same thing and subtracting one from the other leaves you with 0. (You subtract them because that is what you do when finding the determinant *lol*). This 0 is the value of the curl of the gradient of the field along the x-axis. Repeat the steps for the j and k unit vectors (y- and z-axes) and you find they cancel each other out, due to the wierd way one turns out to be a negative and the other positive.
Hence, the answer is (0,0,0) and will always be that, regardless of the actual values of any of the vectors or co-ordinates.
That question would take me about 5 minutes to do in an exam, and I just spent about 30 writing it out for you there, I hope you appreciate that *lol*
Ok, next (and the last for now) is...
Electromagnetism
We had two lecturers for this... the first guy was a fat oaf and the second one was actually a brilliant guy who teaches well, and I understood his section much more easily. This is taken from the fat oaf's part.
He didn't explain what a dielectric actually is and then gave us this set of formulae. Its not a question, I just wanna show you the kinda range of symbols, variables and equations we work with.
I can see how the maths works, I can work through it and get the correct result... but I actually have no idea what its really talking about. Yay :)Don't do physics at university, kids! There are no lasers, no explosions, no spaceships and definitely no young, sexy lecturers. Just loads and loads and loads of that stuff above. Its not even interesting anymore, I dont really know why I bother *lol*
Esmie xXx
3 comments:
I would have to re-read that a couple times to even start to wrap my head around it. I never studied math at that level though.
If you are bored with your current degree, is it too late to change it? You are an excellent writer, and enjoy publishing blogs, perhaps studying journalism/communications would be more rewarding?
Changing degree is such a bitch, and in third year will be hell to do... and honestly, I am not that great at writing and can't imagine making a living out of it or always enjoying it if my subject range is limited or I am unable to write about whatever I want...
Those maths examples are so foreign to me they may as well be written in Klingon. *scream*
I did an arts degree. :-)
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