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AST 390: Computational Astrophysics

Logistics and Overview

Course Overview
Using These Notes

Tour of Python

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

Git and Github

Version Control
A Git Walkthrough
Git Branches
Git Remotes
github
Pull requests

Fundamentals

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

Ordinary Differential Equations

Basic Methods for ODEs
- 2nd Order Runge-Kutta / Midpoint Method
- 4th-order Runge-Kutta
Adaptive Timesteps
In-Class Example
ODEs and Conservation
- Time Symmetric Integration
Two Point Boundary Value Problems
- Application: Stellar Structure
Stiff ODEs / Implicit Methods
More Applications

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
Poisson problem
Multigrid
Diffusion

Hydrodynamics

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

Machine Learning

Artificial Neural Network Basics
Hidden Layers
Diving Deeper into Machine Learning
Machine Learning in Astronomy

Course Project

Course Project

Repository
Open issue

Index

By Michael Zingale

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