Tests done!
Dec. 19th, 2013 10:13 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
davvYay, all my finals are done... for now. So now I can focus on doing very little until mid-January.
(Though I always will be doing something, even if that is writing weird things here, or making fractal renderers for fun.)
Somehow, I feel quite tired, though. Perhaps I should try not to burden my mind too much, since I have been burdening it quite a bit on the preparations for the finals. But that's easier said than done, because I like using my mind. We'll see how that goes - I know I should rest a bit, but the tiredness itself makes it harder to do the right kind of decisions, so there's some element of positive feedback there.
As for the subjects I had tests in, there were three: mathematics (mostly calculus), numerical analysis (including plain old differential equations), and basic scientific programming. I think I did best at programming, then mathematics, then analysis. Amusingly enough, it was not so much the computer parts of numerical analysis that got me down as the mathematical ones (e.g. analytically solving linear and separable ODEs). I know the logic, but knowing the logic isn't enough: I also have to practice it, and I hadn't done that enough.
The only error I think I made on the programming thing was thinking that a Python dict is a primitive and so clones when you do an assignment of the type x = y. Call-by-sharing languages that exempt some types (but not all) from being references go against my aesthetics (for inconsistency purposes - but I've said so before) and I suppose it's only fitting that what snagged me was that particular feature :)
(Though I always will be doing something, even if that is writing weird things here, or making fractal renderers for fun.)
Somehow, I feel quite tired, though. Perhaps I should try not to burden my mind too much, since I have been burdening it quite a bit on the preparations for the finals. But that's easier said than done, because I like using my mind. We'll see how that goes - I know I should rest a bit, but the tiredness itself makes it harder to do the right kind of decisions, so there's some element of positive feedback there.
As for the subjects I had tests in, there were three: mathematics (mostly calculus), numerical analysis (including plain old differential equations), and basic scientific programming. I think I did best at programming, then mathematics, then analysis. Amusingly enough, it was not so much the computer parts of numerical analysis that got me down as the mathematical ones (e.g. analytically solving linear and separable ODEs). I know the logic, but knowing the logic isn't enough: I also have to practice it, and I hadn't done that enough.
The only error I think I made on the programming thing was thinking that a Python dict is a primitive and so clones when you do an assignment of the type x = y. Call-by-sharing languages that exempt some types (but not all) from being references go against my aesthetics (for inconsistency purposes - but I've said so before) and I suppose it's only fitting that what snagged me was that particular feature :)
no subject
Date: 2014-01-08 06:49 pm (UTC)First, being separable, so that, for example, a basis element obeys A(x,y,z) = B(x)C(y)D(z). For linear PDEs, at least, this allows you to to break apart the PDE into several ODEs, but at the cost of adding parameters (so you don't have one ODE to solve, you have a whole class of them). For instance, in spherically symmetric quantum mechanical systems, the parameters are energy, total angular momentum, and the z-component of angular momentum. Requiring convergence or periodicity of the functions will impose conditions on the parameters -- this is the origin of quantization, as it happens.
Second, having a trivial time-evolution equation. Basis elements in quantum mechanics tend to be eigenvectors of the Hamiltonian operator (that is, they are states with a definite energy), so their evolution is just harmonic oscillation. The full solution (with given initial conditions) will be neither separable nor harmonic, since these qualities break down when you start adding basis functions. But you can get around this by: expanding your initial state in terms of basis functions (this is usually some integral expression you have to derive); evolving the basis functions, in their trivial manner; recovering the evolved initial function by adding together the evolved basis functions. In lots of cases certain basis functions will have outsized importance (e.g. the ground state in QM), so you can cut corners.
This explanation is weighed toward what we do in physics, mind you.