Dear students,
please find below a few announcements, in view of the forthcoming exam sessions:
1. You can now find a new section on moodle, where I uploaded texts of exams from past years. Please keep in mind that the course was previously held by prof. Mapelli, hence the style of the exercises might change a bit from would I will assign. Nevertheless, the uploaded examples are good for practising.
2. Let me also remind you that, as specified in class, *there won't be any exercise on PDEs in the January and February 2024 sessions (whereas it will possible to find them from June onwards).*
3. Finally, if you want more examples of exam-like exercises, please refer to the following ones, which you can find on moodle either in my Jupyter notebooks or in the slides:
LINEAR ALGEBRA: electric circuit exercise from the slides (the corresponding linear system is solved in the notebook), gauss-seidel exercise in the notebook
INTEGRATION: Growth factor and NFW profile
MONTE-CARLO INTEGRATION: all exercises in the notebook
ROOT FINDING: all exercises in the notebook
FOURIER TRANSFORM: musical instruments, sunspots
ODEs: implementation of rk1,rk2,rk4,Verlet. Lotka-Volterra,comet orbit, earth orbit,shooting method,2-body problem
RANDOM NUMBERS: generation of random numbers following different distributions, like in the assign_positions, assign_velocities, assign_masses functions, which are coded up in the "cluster simulation" exercise (Note that in an exam I would ask *only* to write code to generate r.v.'s according to different distributions but I would not *ask* to embed those in a more complex/longer exercise, like I do in the full cluster simulation exercise.)
4. Other examples in the notebooks, which are not listed in point 3., are more complex than what I would assign for an exam, but they are of course still very useful for exam preparation.
5. To solve exercises during the exam, you will be free to use functions from python libraries, *unless* I specifically ask to code up some *simple* method. For example, if I ask you to solve an ODE, you are free use the solver from scipy (or any other), *unless* I specifically ask you to code up your own solver. In the latter case, that would be some simple RK or leapfrog/Verlet solver, and *not* an adative stepsize RK, or Bulirsch-Stoer.
Best,
ML