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Computational Astrophysics Spring 2027

Logistics and Overview

Course Overview
Using These Notes

Tour of Python

Jupyter
Python Basics
Functions and Classes
- Functions
- Classes
NumPy
- NumPy
- NumPy Copying and Indexing
matplotlib

Fundamentals

Floating Point Format
- Numerical Errors: Roundoff and Truncation
Differentiation
Integration
Root Finding
Linear Algebra

Ordinary Differential Equations

Basic Methods for ODEs
Adaptive Timesteps
✱ Boundary Value Problems
- Two Point Boundary Value Problems
- Application: Stellar Structure
✱ Stiff ODEs
More Applications
- Application: One-zone X-ray burst

Interlude Git and Github

Version Control
A Git Walkthrough
Git Branches
github
- Pull requests

Working with Data Samples

Fourier Transforms
Interpolation
Least Squares Regression

Partial Differential Equations

Partial Differential Equations
Advection
✱ Burgers' Equation
- Burgers’ Riemann Problem
- Solving Burgers’ equation
More on Advection and Burgers’ Equation
Poisson problem
✱ Multigrid
Diffusion

✱ Hydrodynamics

Euler Equations
- Euler equations eigensystem
Euler Riemann Problem
- Euler Riemann Problem
- Sampling the Riemann Solution
Second-order Euler solver

Machine Learning

Types of Machine Learning
Artificial Neural Network Basics
Hidden Layers
Diving Deeper into Machine Learning
Machine Learning in Astronomy
Application: Galaxy Classification

Additional examples (for in-class)

ODE Review: Projectile Motion
Linear Algebra Review: Hilbert Matrix
FFT Review: Cleaning a Signal

Repository
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.rst

Basic Methods for ODEs

Basic Methods for ODEs#

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Going Further

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Euler’s Method

By Michael Zingale

© Copyright 2024-2026, Michael Zingale.