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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.

Options please!

Thanks in Advance

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# Which would be more useful?

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