# Which would be more useful?

Hi All,

I have the opportunity to take two different courses this year (alas the limit on 120 credits per year means I can't take both), and I seek advice on which one would be more appropriate considering I wish to move into theoretical physics (like particle physics, field theory, general relativity) after my current natural sciences degree:

First Option:
"Differential Equations

Fourier series. Partial differential equations (PDEs): diffusion equation, wave equation, Laplace's equation. Solution by separation of variables in Cartesian and polar co-ordinates. Ordinary differential equations (ODEs): solution by reduction of order and variation of parameters. Series solution and the method of Forbenius. Legendre's and Bessel's equations: Legendre polynomials, Bessel functions and their recurrence relations."

Second Option:
"Dynamical Systems:

Qualitative behaviour of discrete and continuous systems. General first order systems in two variables. Classification of equilibrium points. Periodic orbits and limit cycles. Bifurcation theory. Saddle- node, transcritical, pitchfork and Hopf bifurcations. Stability of limit cycles. The Logistic map, period-doubling, transition to chaos. Henon map, Lorenz system, Rossler system."

To me, the first seems like it might be more useful, considering the introduction to DEs in the calculus module was very light, but the second seems like it might be more interesting and have more immediate physical applications (that's not to say the first won't be interesting!).

Also, I have covered everything up to separation of variables in cartesian coordinates in other parts of the degree, but I've covered nothing in the dynamical systems module.

CompuChip
Homework Helper
Fourier series [quantum field theory]
Partial differential equations (PDEs): wave equation [qft], Laplace's equation [Maxwell electromagnetism].
Solution by separation of variables in Cartesian and polar co-ordinates [quantum mechanics / Schrodinger equation (!)].
Legendre's and Bessel's equations: Legendre polynomials, Bessel functions and their recurrence relations. [qm problems with spherical symmetry]

I'm not sure about the second one, I learned most of those in my (math department) DE course, but I never really used them in physics. The subjects that I quoted from your post, however, are extremely useful in theoretical physics. For each I listed at least one area of physics for which I have actually used this method during my Master's in theoretical physics.

Therefore, though I am not really familiar with either course, I am strongly inclined to recommend the former to you.

nicksauce
Homework Helper
Definitely the first one. All the things you mentioned will come up over and over again in physics. Dynamical systems is a super interesting course (and I'd encourage you to audit it if your university allows it), but DEs will be much more useful.

Judging by what you wrote, it looks like the differential equations course something of a "first course" in differential equations; meaning that you have not had a previous course on differential equations. If this is true, then I would recommend taking this course first. The reason being that dynamical systems are 95-99% all differential equations. Meaning that you should already have experience with differential equations before tackling dynamical systems.

Thanks guys! I suspected as much but it's nice to get opinions from more experienced people.

@CompuChip: The list of applications is especially interesting. It would appear I've managed to do 20 credits of QM without adequate background!

@nicksauce: UK universities seem to be very inflexible about the number of credits a student can take. However, I can attend the lectures unofficially :)

@cmos Yes, as I said, we covered a small amount of DEs in first year calculus, but very little since. It's interesting you say that, because the Dynamical systems course has a very small amount of DE related pre-requisites. A quirk of the modular system I suppose...

Thanks Again!
Scott

CompuChip