Teaching Courses
Celestial Dynamics
This course is aimed at undergraduate astronomy major.
The main aim of this course is to provide the student with an understanding of collision-less particle dynamics, which include the physics of motions of stellar system, star clusters, and galaxyies.
The tools required in celestial dynamics are for the most part ones developed in other fields: classical, celestial, and Hamiltonian mechanics provide the most relevant backgrounds. The mathematical techniques developed in an introductory mechanics course are in constant use.
After a brief overview of basic mathematics, like vector calculus, integral theorems and coordinate transformations, this course takes on the dynamics of stellar systems, including collisionless ones. We detive the equations for two-body, and three-body motions, and then extend to the N-body system. The density-potential theories are also disccussed in the course. Introductory theories of collision-less Boltzmann equations are generally mentioned. After that various astrophysical applications are reviewed, such as black hole binary system, tidal disruption events, planet motions, dynamical frictions for super-massive BHs, galaxies rotations …
2021 Spring, 2022 Spring, 2023 Spring, 2024 Fall
Computational Astrophysics
This course is aimed at graduate astronomy major.
Computing has become a necessary means of scientific study. This course examine the most commonly used methods in computational science, and tries to show, by means of examples coming from different corners of physics, how physical and mathematical questions can be answered using a computer.
At first, we concentrate on some basic aspects associated with numerical approximation of a function, interpolation, least-squares and spline approximations of a curve, and numerical representations of uniform and other distribution functions. Then we introduce some basic computational methods for dealing with numerical differentiation and integration, and numerical schemes for searching for the roots of an equation and the extremes of a function. We introduce some basic numerical methods for solving ordinary differential equations, and discuss the corresponding schemes for partial differential equations and some more advanced techniques for the many-particle Newton equation. Hydrodynamics and magnetohydrodynamics are also shown in the course.
The remaining parts of course tackle the main techniques and applications of computational physics, one after another, including stochastic processes, Monte Carlo methods, N-body methods. Machine-learning techniques may also be introduced.
2021 Fall, 2022 Fall, 2023 Fall, 2024 Fall
Review Lectures
Lectures given in some other courses.