# Teaching

Here are some pedagogical notes on physics/math/astronomy (click on title to access PDF/Jupyter notebook).

Introduction to Numerical Integrators (and Orbits Around Black Holes)

Numerical integration is a very powerful tool for an astrophysicist. In this Jupyter notebook, we will build a simple numerical integrator from scratch and employ it to solve for the motion of particles around black holes.

Tensors for Physicists and Astronomers in Two Class Periods

Tensors are everywhere in physics, and it is nearly impossible to do physics without meeting them in one form or another. However, they are also one of those things that a physics student is expected to understand, but is never taught properly. This note is written to help alleviate this problem.

A Pictorial Guide to (One of) the Singularity Theorems

The singularity theorems are some of the most fascinating results in general relativity. In this series of pictures, we go through the proof of the original Penrose singularity theorem for globally hyperbolic manifolds. While this theorem is most suited for cosmology, the proof of the other singularity theorems (e.g. the one for black holes) are similar in spirit.

Why the Handwavy Integrals in Stellar Structure Works

When studying stellar structures, astrophysicists tend to replace differential quantities with the quantity themselves: dQ~Q. This method of "handwavily integrating" the stellar structure equations has created consternation for many students. In this note we show that this method is well motivated and justifiable.