This assignment is due at the beginning of lecture on Monday, 2 March.

1. Which of the following ode could give rise to chaos? Why?
   1. y'' = y - ay' + b cos t
   2. d²φ/dt² = sin φ
   3. x'' = sin x - ax' + b cos t - cx³
   4. d²y/dt² = cos(y + π/3) - a dy/dt
2. In an electromagnetic simulation, an rk4 ode integrator produces an estimated local error of 0.8 V at a particular time when the time step is set to Δt = 15 minutes. If you require a precision of at least 0.1 V, what time step should you use for this particular time?
3. In the problem above, now assume you find that the errors remain roughly constant in time throughout the simulation. If you require the simulation to run for a time of 17 weeks, and can tolerate a global error or of no more than 5 V at the end of the run, what time step (Δt) should you use?
4. Orbital mechanics problems are governed by a central force law: F_G = GMm / r². Write both the figurative construction of vars = [ ... ], and the literal line of MATLAB code corresponding to dvarsdt = [ ... ] for the Cartesian form of this central force law.