- to familiarize the students with the field of computational astrophysics.
- to introduce more advanced concepts of Python (use of specialized libraries) and Data Science (querying databases, machine learning techniques)
-to appreciate the applicability of numerical methods in different fields (physics, astrophysics, data science applications)
- gain a broader perspective on the complex problem of galaxy dynamics. Students will integrate theoretical knowledge and with practical knowledge (developing numerical algorithms and analyzing observational data).

(LO1) The student will understand and be able to implement N-body
dynamics in simulations

(LO2) The student will understand how to apply fluid dynamics in an
astrophysical context

(LO3) The student will have experience in applying data science concepts
to astronomical datasets

(LO4) The student will have demonstrated how to use machine learning
techniques using astrophysics datasets extracted from existing sources

I. Basic numerical methods used in computational astrophysics
• Numerical integration
• Numerical solution of differential equations
• Root-finding and minimization
• Interpolation
• Fourier transforms

II. Computational Galaxy Dynamics
• The Poisson equation. Poisson solutions
• Fourier methods
• Example of problem in a Milky Way gravitational potential
• Python libraries for Galaxy Dynamics: AstroPy, GalPy, SciPy.

Workshops 1 and 2:
• Computing orbits in a simple gravitational potential; Colliding planets; Orbits of black holes.
• Fitting a density profile (e.g. a Navarro-Frenk-White, or an Einasto profile) to a N- body distribution of dark matter particles from a cosmological simulation.
• Computing the goodness of fit of the analytical profile.

III. Data Science methods in Galaxy Dynamics
• Applications of k-clustering techniques and HDBSCAN.
• Data mining methods. Basic concepts of SQL
• Examples of queries of using the ESA Cosmos SQL database for Gaia data.
• Tools/software for visualisation large data sets.
• Practical examples using images from computer simulations and astronomical surveys.
Workshop 3: Finding clusters of stars with a k-clustering method in a simulation of a Milky Way-type galaxy.

IV. N-body particle methods
• Introduction to the N-body problem
• Euler and Runge-Kutta methods
• The description of orbital motion; The 3-body problem
• Lyapunov time estimation
• N-body codes for large N
• The Tree method
V. Smoothed particle hydrodynamics (SPH):
• Basic concepts of fluid dynamics and SPH implementation
• Example of an SPH test: Collidi ng planets
Worhshops 4, 5, 6 will be devoted to groupwork projects.

The planned structure of the course is a mix of lectures and workshops. Material learned during lectures will be applied directly in practical examples, either in the assigned workshops, or included in the problem sets/computational project. For the large computational project in CA2, students will be working in small groups and they will learn how to write code more efficiently by dividing the work in a team.