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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
- NumPy
- NumPy Copying and Indexing
matplotlib

Fundamentals

Floating Point Format
- Numerical Errors: Roundoff and Truncation
Differentiation
- In-class Example: Second Derivative
- Application: Reaction Rate Temperature Sensitivity
Integration
Root finding
Linear Algebra

Ordinary Differential Equations

Basic Methods for ODEs
Adaptive Timesteps
ODEs and Conservation
- Time Symmetric Integration
- Application: Stability of Planetary Systems
✱ 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
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

Additional examples (for in-class)

ODE Review: Projectile Motion
Linear Algebra Review: Hilbert Matrix

Homework

Homework 1
- Homework 1 solutions
Homework 2
- Homework 2 solutions
Homework 3
- Homework 3 solutions
Homework 4
- Homework 4 solutions
Homework 5

Project

Course Project

Repository
Open issue

Index

By Michael Zingale

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